Finite Group Databasebeta

← C23×#36857 #19184483

Subgroups — C23×#36857 #19184483

Order 5888.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2849C211yesmaximal, characteristic, complemented
2C23×#2847C211yesmaximal, characteristic, complemented
3C23×#2788C211yesmaximal, characteristic, complemented
4C23×#2757C211yesmaximal, characteristic, complemented
5C23×#2756C211yesmaximal, characteristic, complemented
6C23×#2749C211yesmaximal, characteristic, complemented
7C23×#2737C211yesmaximal, characteristic, complemented
8C23×#2712C211yesmaximal, characteristic, complemented
9C23×#2701C211yesmaximal, characteristic, complemented
10C23×#2688C211yesmaximal, characteristic, complemented
11C23×#2688C211yesmaximal, characteristic, complemented
12C23×#2687C211yesmaximal, characteristic, complemented
13C23×#2684C211yesmaximal, characteristic, complemented
14C23×#2678C211yesmaximal, characteristic, complemented
15C23×#2676C211yesmaximal, characteristic, complemented
16C23×#2673C211yesmaximal, characteristic, complemented
17C23×#2670C211yesmaximal, characteristic, complemented
18C23×#2669C211yesmaximal, characteristic, complemented
19C23×#2631C211yesmaximal, characteristic, complemented
20C23×#2630C211yesmaximal, characteristic, complemented
21C23×#2577C211yesmaximal, characteristic, complemented
22C23×#2572C211yesmaximal, characteristic, complemented
23C23×#2557C211yesmaximal, characteristic, complemented
24C23×#2555C211yesmaximal, characteristic, complemented
25C23×#2464C211yesmaximal, characteristic, complemented
26C23×#2457C211yesmaximal, characteristic, complemented
27C23×#2445C211yesmaximal, characteristic, complemented
28C23×#2427C211yesmaximal, characteristic, complemented
29C23×#2337C211yesmaximal, characteristic, complemented
30C23×#2333C211yesmaximal, characteristic, complemented
31C4×C23×#120C211yesmaximal, characteristic, complemented
32C24×C4×C23C2211yescharacteristic
33C2×C23×#127C2211yescharacteristic
34C2×C23×#124C2211yescharacteristic
35C2×C23×#124C2211yescharacteristic
36C2×C23×#124C2211yescharacteristic
37C2×C23×#124C2211yescharacteristic, complemented
38C2×C23×#123C2211yescharacteristic
39C2×C23×#123C2211yescharacteristic
40C2×C23×#123C2211yescharacteristic
41C2×C23×#123C2211yescharacteristic, complemented
42C2×C23×C22⋊Q8C2211yescharacteristic, complemented
43C2×C23×#121C2211yescharacteristic
44C2×C23×#121C2211yescharacteristic
45C2×C23×#121C2211yescharacteristic
46C2×C23×#121C2211yescharacteristic
47C2×C23×#121C2211yescharacteristic
48C2×C23×#121C2211yescharacteristic
49C2×C23×#121C2211yescharacteristic, complemented
50C2×C23×#120C2211yescharacteristic
51C2×C23×#120C2211yescharacteristic
52C2×C23×#120C2211yescharacteristic
53C2×C23×#120C2211yescharacteristic
54C2×C4×D4×C23C2211yescharacteristic
55C2×C4×D4×C23C2211yescharacteristic
56C2×C4×D4×C23C2211yescharacteristic
57C23×#400C2211yescharacteristic, complemented
58C23×#400C2211yescharacteristic, complemented
59C23×#400C2211yescharacteristic, complemented
60C23×#398C2211yescharacteristic, complemented
61C23×#398C2211yescharacteristic, complemented
62C23×#398C2211yescharacteristic, complemented
63C23×#397C2211yescharacteristic
64C23×#397C2211yescharacteristic
65C23×#397C2211yescharacteristic
66C23×#397C2211yescharacteristic, complemented
67C23×#397C2211yescharacteristic, complemented
68C23×#397C2211yescharacteristic, complemented
69C23×#397C2211yescharacteristic, complemented
70C23×#397C2211yescharacteristic, complemented
71C23×#397C2211yescharacteristic, complemented
72C23×#396C2211yescharacteristic
73C23×#396C2211yescharacteristic, complemented
74C23×#396C2211yescharacteristic, complemented
75C23×#395C2211yescharacteristic, complemented
76C23×#394C2211yescharacteristic
77C23×#394C2211yescharacteristic
78C23×#394C2211yescharacteristic
79C23×#394C2211yescharacteristic
80C23×#394C2211yescharacteristic
81C23×#394C2211yescharacteristic
82C23×#394C2211yescharacteristic
83C23×#394C2211yescharacteristic
84C23×#394C2211yescharacteristic, complemented
85C23×#394C2211yescharacteristic, complemented
86C23×#394C2211yescharacteristic, complemented
87C23×#394C2211yescharacteristic, complemented
88C23×#394C2211yescharacteristic, complemented
89C23×#393C2211yescharacteristic
90C23×#393C2211yescharacteristic
91C23×#393C2211yescharacteristic
92C23×#393C2211yescharacteristic, complemented
93C23×#393C2211yescharacteristic, complemented
94C23×#392C2211yescharacteristic
95C23×#392C2211yescharacteristic
96C23×#392C2211yescharacteristic
97C23×#392C2211yescharacteristic
98C23×#392C2211yescharacteristic
99C23×#392C2211yescharacteristic
100C23×#392C2211yescharacteristic
101C23×#392C2211yescharacteristic
102C23×#392C2211yescharacteristic
103C23×#392C2211yescharacteristic, complemented
104C23×#392C2211yescharacteristic, complemented
105C23×#391C2211yescharacteristic, complemented
106C23×#391C2211yescharacteristic, complemented
107C23×#391C2211yescharacteristic, complemented
108C23×#390C2211yescharacteristic
109C23×#390C2211yescharacteristic
110C23×#390C2211yescharacteristic
111C23×#390C2211yescharacteristic
112C23×#390C2211yescharacteristic, complemented
113C23×#390C2211yescharacteristic, complemented
114C23×#389C2211yescharacteristic, complemented
115C23×#389C2211yescharacteristic, complemented
116C23×#388C2211yescharacteristic
117C23×#388C2211yescharacteristic
118C23×#388C2211yescharacteristic
119C23×#388C2211yescharacteristic
120C23×#388C2211yescharacteristic
121C23×#388C2211yescharacteristic
122C23×#388C2211yescharacteristic
123C23×#388C2211yescharacteristic, complemented
124C23×#388C2211yescharacteristic, complemented
125C23×#388C2211yescharacteristic, complemented
126C23×#388C2211yescharacteristic, complemented
127C23×#388C2211yescharacteristic, complemented
128C23×#388C2211yescharacteristic, complemented
129C23×#388C2211yescharacteristic, complemented
130C23×#387C2211yescharacteristic, complemented
131C23×#387C2211yescharacteristic, complemented
132C23×#387C2211yescharacteristic, complemented
133C23×#387C2211yescharacteristic, complemented
134C23×#387C2211yescharacteristic, complemented
135C23×#386C2211yescharacteristic
136C23×#386C2211yescharacteristic
137C23×#386C2211yescharacteristic
138C23×#386C2211yescharacteristic
139C23×#386C2211yescharacteristic
140C23×#386C2211yescharacteristic
141C23×#386C2211yescharacteristic
142C23×#386C2211yescharacteristic
143C23×#386C2211yescharacteristic
144C23×#386C2211yescharacteristic
145C23×#386C2211yescharacteristic
146C23×#386C2211yescharacteristic
147C23×#386C2211yescharacteristic
148C23×#386C2211yescharacteristic
149C23×#386C2211yescharacteristic
150C23×#386C2211yescharacteristic
151C23×#386C2211yescharacteristic
152C23×#386C2211yescharacteristic
153C23×#386C2211yescharacteristic, complemented
154C23×#386C2211yescharacteristic, complemented
155C23×#386C2211yescharacteristic, complemented
156C23×#386C2211yescharacteristic, complemented
157C23×#386C2211yescharacteristic, complemented
158C23×#386C2211yescharacteristic, complemented
159C23×#385C2211yescharacteristic
160C23×#385C2211yescharacteristic
161C23×#385C2211yescharacteristic
162C23×#385C2211yescharacteristic
163C23×#385C2211yescharacteristic
164C23×#385C2211yescharacteristic
165C23×#385C2211yescharacteristic
166C23×#385C2211yescharacteristic, complemented
167C23×#383C2211yescharacteristic, complemented
168C23×#383C2211yescharacteristic, complemented
169C23×#383C2211yescharacteristic, complemented
170C23×#381C2211yescharacteristic
171C23×#381C2211yescharacteristic
172C23×#381C2211yescharacteristic, complemented
173C23×#381C2211yescharacteristic, complemented
174C23×#380C2211yescharacteristic
175C23×#380C2211yescharacteristic
176C23×#380C2211yescharacteristic
177C23×#380C2211yescharacteristic, complemented
178C23×#379C2211yescharacteristic
179C23×#379C2211yescharacteristic
180C4×C4⋊C4×C23C2211yescharacteristic, complemented
181C4×C22⋊C4×C23C2211yescharacteristic
182C4×C22⋊C4×C23C2211yescharacteristic
183C4×C22⋊C4×C23C2211yescharacteristic
184C4×C22⋊C4×C23C2211yescharacteristic, complemented
185C4×C22⋊C4×C23C2211yescharacteristic, complemented
186C4×C22⋊C4×C23C2211yescharacteristic, complemented
187C25×C23C2311yescharacteristic
188C22×Q8×C23C2311yescharacteristic
189C22×Q8×C23C2311yescharacteristic
190C22×D4×C23C2311yescharacteristic
191C22×D4×C23C2311yescharacteristic
192C22×D4×C23C2311yescharacteristic
193C22×D4×C23C2311yescharacteristic
194C22×D4×C23C2311yescharacteristic
195C22×D4×C23C2311yescharacteristic
196C22×D4×C23C2311yescharacteristic
197C22×D4×C23C2311yescharacteristic
198C22×D4×C23C2311yescharacteristic
199C22×D4×C23C2311yescharacteristic
200C22×D4×C23C2311yescharacteristic
201C22×D4×C23C2311yescharacteristic
202C22×D4×C23C2311yescharacteristic
203C22×D4×C23C2311yescharacteristic
204C22×D4×C23C2311yescharacteristic
205C22×D4×C23C2311yescharacteristic
206C22×D4×C23C2311yescharacteristic
207C22×D4×C23C2311yescharacteristic
208C23×C4×C23—42no—
209C23×C4×C23—42no—
210C23×C4×C23—42no—
211C23×C4×C23C2311yescharacteristic
212C23×C4×C23C2311yescharacteristic
213C23×C4×C23C2311yescharacteristic
214C23×C4×C23C2311yescharacteristic
215C23×C4×C23C2311yescharacteristic
216C23×C4×C23C2311yescharacteristic
217C23×C4×C23C2311yescharacteristic
218C23×C4×C23C2311yescharacteristic
219C23×C4×C23C2311yescharacteristic
220C23×C4×C23C2311yescharacteristic
221C23×#127—42no—
222C23×#124—24no—
223C23×#124—42no—
224C23×#124—42no—
225C23×#124—42no—
226C23×#123—42no—
227C23×#123—42no—
228C23×#123—42no—
229C23×#123—42no—
230C23×C22⋊Q8—42no—
231C23×#121—24no—
232C23×#121—42no—
233C23×#121—42no—
234C23×#121—42no—
235C23×#121—42no—
236C23×#121—42no—
237C23×#121—42no—
238C23×#120—24no—
239C23×#120—42no—
240C23×#120—42no—
241C23×#120—42no—
242C4×D4×C23—42no—
243C4×D4×C23—42no—
244C4×D4×C23—42no—
245C2×C4⋊C4×C23C2311yescharacteristic
246C2×C4⋊C4×C23C2311yescharacteristic
247C2×C4⋊C4×C23C2311yescharacteristic
248C2×C4⋊C4×C23C2311yescharacteristic
249C2×C4⋊C4×C23C2311yescharacteristic
250C2×C4⋊C4×C23C2311yescharacteristic
251C2×C4⋊C4×C23C2311yescharacteristic
252C2×C4⋊C4×C23C2311yescharacteristic
253C2×C4⋊C4×C23C2311yescharacteristic
254C2×C4⋊C4×C23C2311yescharacteristic
255C2×C4⋊C4×C23C2311yescharacteristic
256C2×C4⋊C4×C23C2311yescharacteristic
257C2×C4⋊C4×C23C2311yescharacteristic
258C2×C4⋊C4×C23C2311yescharacteristic
259C2×C4⋊C4×C23C2311yescharacteristic
260C2×C4⋊C4×C23C2311yescharacteristic
261C2×C4⋊C4×C23C2311yescharacteristic
262C2×C4⋊C4×C23C2311yescharacteristic
263C2×C4⋊C4×C23C2311yescharacteristic
264C2×C4⋊C4×C23C2311yescharacteristic
265C2×C22⋊C4×C23C2311yescharacteristic
266C2×C22⋊C4×C23C2311yescharacteristic
267C2×C22⋊C4×C23C2311yescharacteristic
268C2×C22⋊C4×C23C2311yescharacteristic
269C2×C22⋊C4×C23C2311yescharacteristic
270C2×C22⋊C4×C23C2311yescharacteristic
271C2×C22⋊C4×C23C2311yescharacteristic
272C2×C22⋊C4×C23C2311yescharacteristic
273C2×C22⋊C4×C23C2311yescharacteristic
274C2×C22⋊C4×C23C2311yescharacteristic
275C2×C22⋊C4×C23C2311yescharacteristic
276C2×C22⋊C4×C23C2311yescharacteristic
277C2×C22⋊C4×C23C2311yescharacteristic
278C2×C22⋊C4×C23C2311yescharacteristic
279C2×C22⋊C4×C23C2311yescharacteristic
280C2×C22⋊C4×C23C2311yescharacteristic
281C2×C22⋊C4×C23C2311yescharacteristic
282C2×C22⋊C4×C23C2311yescharacteristic
283C2×C22⋊C4×C23C2311yescharacteristic
284C2×C22⋊C4×C23C2311yescharacteristic
285C2×C22⋊C4×C23C2311yescharacteristic
286C2×C22⋊C4×C23C2311yescharacteristic
287C2×C22⋊C4×C23C2311yescharacteristic
288C2×C22⋊C4×C23C2311yescharacteristic
289C2×C22⋊C4×C23C2311yescharacteristic
290C2×C22⋊C4×C23C2311yescharacteristic
291C2×C22⋊C4×C23C2311yescharacteristic
292C2×C22⋊C4×C23C2311yescharacteristic
293C2×C22⋊C4×C23C2311yescharacteristic
294C2×C22⋊C4×C23C2311yescharacteristic
295C2×C22⋊C4×C23C2311yescharacteristic
296C2×C22⋊C4×C23C2311yescharacteristic
297C2×C22⋊C4×C23C2311yescharacteristic
298C2×C22⋊C4×C23C2311yescharacteristic
299C2×C22⋊C4×C23C2311yescharacteristic
300C2×C22⋊C4×C23C2311yescharacteristic
301C2×C22⋊C4×C23C2311yescharacteristic
302C2×C22⋊C4×C23C2311yescharacteristic
303C2×C22⋊C4×C23C2311yescharacteristic
304C2×C22⋊C4×C23C2311yescharacteristic
305C2×C22⋊C4×C23C2311yescharacteristic
306C2×C22⋊C4×C23C2311yescharacteristic
307C2×C22⋊C4×C23C2311yescharacteristic
308C2×C22⋊C4×C23C2311yescharacteristic
309C2×C22⋊C4×C23C2311yescharacteristic
310C2×C22⋊C4×C23C2311yescharacteristic
311C2×C22⋊C4×C23C2311yescharacteristic
312C2×C22⋊C4×C23C2311yescharacteristic
313C2×C22⋊C4×C23C2311yescharacteristic
314C2×C22⋊C4×C23C2311yescharacteristic
315C2×C22⋊C4×C23C2311yescharacteristic
316C2×C22⋊C4×C23C2311yescharacteristic
317C2×C22⋊C4×C23C2311yescharacteristic
318C2×C22⋊C4×C23C2311yescharacteristic
319C2×C22⋊C4×C23C2311yescharacteristic
320C2×C22⋊C4×C23C2311yescharacteristic
321C2×C42×C23C2311yescharacteristic
322C2×C42×C23C2311yescharacteristic
323C2×C42×C23C2311yescharacteristic
324C2×C42×C23C2311yescharacteristic
325C2×C42×C23C2311yescharacteristic
326C2×C42×C23C2311yescharacteristic
327C2×C42×C23C2311yescharacteristic
328C2×C42×C23C2311yescharacteristic
329C23×#95C2311yescharacteristic
330C23×#95C2311yescharacteristic
331C23×#95C2311yescharacteristic
332C23×#95C2311yescharacteristic
333C23×#95C2311yescharacteristic
334C23×#95C2311yescharacteristic
335C23×#95C2311yescharacteristic
336C23×#95C2311yescharacteristic
337C23×#95C2311yescharacteristic
338C23×#95C2311yescharacteristic
339C23×#95C2311yescharacteristic
340C23×#95C2311yescharacteristic
341C23×#95C2311yescharacteristic
342C23×#95C2311yescharacteristic
343C23×#95C2311yescharacteristic
344C23×#95C2311yescharacteristic
345C23×#95C2311yescharacteristic
346C23×#95C2311yescharacteristic
347C23×#95C2311yescharacteristic
348C23×#95C2311yescharacteristic
349C23×#95C2311yescharacteristic
350C23×#95C2311yescharacteristic
351C23×#95C2311yescharacteristic
352C23×#95C2311yescharacteristic
353C23×#95C2311yescharacteristic
354C23×#95C2311yescharacteristic
355C23×#95C2311yescharacteristic
356C23×#95C2311yescharacteristic
357C23×#95C2311yescharacteristic
358C23×#95C2311yescharacteristic
359C23×#95C2311yescharacteristic
360C23×#95C2311yescharacteristic
361C23×#95C2311yescharacteristic
362C23×#95C2311yescharacteristic
363C23×#95C2311yescharacteristic
364C23×#95C2311yescharacteristic
365C23×#95C2311yescharacteristic
366C23×#95C2311yescharacteristic
367C23×#95C2311yescharacteristic
368C23×#95C2311yescharacteristic
369C24×C23—22no—
370C24×C23—22no—
371C24×C23—22no—
372C24×C23—41no—
373C24×C23—41no—
374C24×C23—41no—
375C24×C23—41no—
376C24×C23C2411yescharacteristic
377C24×C23C2411yescharacteristic
378C24×C23C2411yescharacteristic
379C24×C23C2411yescharacteristic
380C24×C23C2411yescharacteristic
381C24×C23C2411yescharacteristic
382C24×C23C2411yescharacteristic
383C2×Q8×C23—22no—
384C2×Q8×C23—41no—
385C2×Q8×C23—41no—
386C2×Q8×C23—41no—
387C2×Q8×C23—41no—
388C2×Q8×C23—41no—
389C2×D4×C23—22no—
390C2×D4×C23—22no—
391C2×D4×C23—22no—
392C2×D4×C23—22no—
393C2×D4×C23—22no—
394C2×D4×C23—22no—
395C2×D4×C23—22no—
396C2×D4×C23—22no—
397C2×D4×C23—22no—
398C2×D4×C23—22no—
399C2×D4×C23—22no—
400C2×D4×C23—22no—
401C2×D4×C23—22no—
402C2×D4×C23—22no—
403C2×D4×C23—22no—
404C2×D4×C23—22no—
405C2×D4×C23—41no—
406C2×D4×C23—41no—
407C2×D4×C23—41no—
408C2×D4×C23—41no—
409C2×D4×C23—41no—
410C2×D4×C23—41no—
411C2×D4×C23—41no—
412C2×D4×C23—41no—
413C2×D4×C23—41no—
414C2×D4×C23—41no—
415C2×D4×C23—41no—
416C2×D4×C23—41no—
417C2×D4×C23—41no—
418C2×D4×C23—41no—
419C2×D4×C23—41no—
420C2×D4×C23—41no—
421C2×D4×C23—41no—
422C2×D4×C23—41no—
423C2×D4×C23—41no—
424C2×D4×C23—41no—
425C2×D4×C23—41no—
426C2×D4×C23—41no—
427C2×D4×C23—41no—
428C2×D4×C23—41no—
429C2×D4×C23—41no—
430C2×D4×C23—41no—
431C2×D4×C23—41no—
432C2×D4×C23—41no—
433C2×D4×C23—41no—
434C2×D4×C23—41no—
435C2×D4×C23—41no—
436C2×D4×C23—41no—
437C2×D4×C23—41no—
438C2×D4×C23—41no—
439C2×D4×C23—41no—
440C2×D4×C23—41no—
441C2×D4×C23—41no—
442C2×D4×C23—41no—
443C22×C4×C23—22no—
444C22×C4×C23—22no—
445C22×C4×C23—22no—
446C22×C4×C23—22no—
447C22×C4×C23—22no—
448C22×C4×C23—22no—
449C22×C4×C23—22no—
450C22×C4×C23—22no—
451C22×C4×C23—22no—
452C22×C4×C23—22no—
453C22×C4×C23—41no—
454C22×C4×C23—41no—
455C22×C4×C23—41no—
456C22×C4×C23—41no—
457C22×C4×C23—41no—
458C22×C4×C23—41no—
459C22×C4×C23—41no—
460C22×C4×C23—41no—
461C22×C4×C23—41no—
462C22×C4×C23—41no—
463C22×C4×C23—41no—
464C22×C4×C23—41no—
465C22×C4×C23—41no—
466C22×C4×C23—41no—
467C22×C4×C23—41no—
468C22×C4×C23—41no—
469C22×C4×C23—41no—
470C22×C4×C23—41no—
471C22×C4×C23—41no—
472C22×C4×C23—41no—
473C22×C4×C23—416no—
474C22×C4×C23C2411yescharacteristic
475C22×C4×C23C2411yescharacteristic
476C22×C4×C23C2411yescharacteristic
477C22×C4×C23C2411yescharacteristic
478C22×C4×C23C2411yescharacteristic
479C22×C4×C23C2411yescharacteristic
480C22×C4×C23C2411yescharacteristic
481C22×C4×C23C2411yescharacteristic
482C22×C4×C23C2411yescharacteristic
483C22×C4×C23C2411yescharacteristic
484C22×C4×C23C2411yescharacteristic
485C22×C4×C23C2411yescharacteristic
486C22×C4×C23C2411yescharacteristic
487C22×C4×C23C2411yescharacteristic
488C22×C4×C23C2411yescharacteristic
489C22×C4×C23C2411yescharacteristic
490C22×C4×C23C2411yescharacteristic
491C22×C4×C23C2411yescharacteristic
492C22×C4×C23C2411yescharacteristic
493C22×C4×C23C2411yescharacteristic
494C22×C4×C23C2411yescharacteristic
495C22×C4×C23C2411yescharacteristic
496C22×C4×C23C2411yescharacteristic
497C22×C4×C23C2411yescharacteristic
498C4⋊C4×C23—22no—
499C4⋊C4×C23—22no—
500C4⋊C4×C23—22no—
501C4⋊C4×C23—22no—
502C4⋊C4×C23—22no—
503C4⋊C4×C23—41no—
504C4⋊C4×C23—41no—
505C4⋊C4×C23—41no—
506C4⋊C4×C23—41no—
507C4⋊C4×C23—41no—
508C4⋊C4×C23—41no—
509C4⋊C4×C23—41no—
510C4⋊C4×C23—41no—
511C4⋊C4×C23—41no—
512C4⋊C4×C23—41no—
513C4⋊C4×C23—41no—
514C4⋊C4×C23—41no—
515C4⋊C4×C23—41no—
516C4⋊C4×C23—41no—
517C4⋊C4×C23—41no—
518C22⋊C4×C23—22no—
519C22⋊C4×C23—22no—
520C22⋊C4×C23—22no—
521C22⋊C4×C23—22no—
522C22⋊C4×C23—22no—
523C22⋊C4×C23—22no—
524C22⋊C4×C23—22no—
525C22⋊C4×C23—22no—
526C22⋊C4×C23—22no—
527C22⋊C4×C23—22no—
528C22⋊C4×C23—22no—
529C22⋊C4×C23—22no—
530C22⋊C4×C23—22no—
531C22⋊C4×C23—22no—
532C22⋊C4×C23—22no—
533C22⋊C4×C23—22no—
534C22⋊C4×C23—22no—
535C22⋊C4×C23—41no—
536C22⋊C4×C23—41no—
537C22⋊C4×C23—41no—
538C22⋊C4×C23—41no—
539C22⋊C4×C23—41no—
540C22⋊C4×C23—41no—
541C22⋊C4×C23—41no—
542C22⋊C4×C23—41no—
543C22⋊C4×C23—41no—
544C22⋊C4×C23—41no—
545C22⋊C4×C23—41no—
546C22⋊C4×C23—41no—
547C22⋊C4×C23—41no—
548C22⋊C4×C23—41no—
549C22⋊C4×C23—41no—
550C22⋊C4×C23—41no—
551C22⋊C4×C23—41no—
552C22⋊C4×C23—41no—
553C22⋊C4×C23—41no—
554C22⋊C4×C23—41no—
555C22⋊C4×C23—41no—
556C22⋊C4×C23—41no—
557C22⋊C4×C23—41no—
558C22⋊C4×C23—41no—
559C22⋊C4×C23—41no—
560C22⋊C4×C23—41no—
561C22⋊C4×C23—41no—
562C22⋊C4×C23—41no—
563C22⋊C4×C23—41no—
564C22⋊C4×C23—41no—
565C22⋊C4×C23—41no—
566C22⋊C4×C23—41no—
567C22⋊C4×C23—41no—
568C22⋊C4×C23—41no—
569C22⋊C4×C23—41no—
570C22⋊C4×C23—41no—
571C22⋊C4×C23—41no—
572C22⋊C4×C23—41no—
573C22⋊C4×C23#4114yes—
574C42×C23—22no—
575C42×C23—22no—
576C42×C23—41no—
577C42×C23—41no—
578C42×C23—41no—
579C42×C23—41no—
580C42×C23—41no—
581C42×C23—41no—
582#36857C2311yesmaximal, characteristic, direct product factor, Sylow
583C23×C23—21no—
584C23×C23—21no—
585C23×C23—21no—
586C23×C23—21no—
587C23×C23—21no—
588C23×C23—21no—
589C23×C23—21no—
590C23×C23—21no—
591C23×C23—21no—
592C23×C23—21no—
593C23×C23—21no—
594C23×C23—21no—
595C23×C23—21no—
596C23×C23—21no—
597C23×C23—21no—
598C23×C23—21no—
599C23×C23—21no—
600C23×C23—21no—
601C23×C23—21no—
602C23×C23—21no—
603C23×C23—21no—
604C23×C23—21no—
605C23×C23—21no—
606C23×C23—21no—
607C23×C23—21no—
608C23×C23—21no—
609C23×C23—21no—
610C23×C23—21no—
611C23×C23—21no—
612C23×C23—21no—
613C23×C23—21no—
614C23×C23—21no—
615C23×C23—21no—
616C23×C23—21no—
617C23×C23—21no—
618C23×C23—21no—
619C23×C23—21no—
620C23×C23—21no—
621C23×C23—21no—
622C23×C23—21no—
623C23×C23—21no—
624C23×C23—21no—
625C23×C23—21no—
626C23×C23—21no—
627C23×C23—21no—
628C23×C23—21no—
629C23×C23—44no—
630C23×C23—44no—
631C23×C23—44no—
632C23×C23—44no—
633C23×C23—44no—
634C23×C23—44no—
635C23×C23—44no—
636C23×C23C2×#4112yes—
637C23×C23H(5,𝔽2)12yes—
638C23×C23H(5,𝔽2)12yes—
639C23×C23C2511yescharacteristic
640Q8×C23—82no—
641Q8×C23—82no—
642D4×C23—44no—
643D4×C23—44no—
644D4×C23—44no—
645D4×C23—82no—
646D4×C23—82no—
647D4×C23—82no—
648D4×C23—82no—
649D4×C23—82no—
650D4×C23—82no—
651D4×C23—82no—
652D4×C23—82no—
653D4×C23—82no—
654D4×C23—82no—
655D4×C23—82no—
656D4×C23—82no—
657D4×C23—82no—
658D4×C23—82no—
659D4×C23—82no—
660C2×C4×C23—21no—
661C2×C4×C23—21no—
662C2×C4×C23—21no—
663C2×C4×C23—21no—
664C2×C4×C23—21no—
665C2×C4×C23—21no—
666C2×C4×C23—21no—
667C2×C4×C23—21no—
668C2×C4×C23—21no—
669C2×C4×C23—21no—
670C2×C4×C23—21no—
671C2×C4×C23—21no—
672C2×C4×C23—21no—
673C2×C4×C23—21no—
674C2×C4×C23—21no—
675C2×C4×C23—21no—
676C2×C4×C23—21no—
677C2×C4×C23—21no—
678C2×C4×C23—21no—
679C2×C4×C23—21no—
680C2×C4×C23—21no—
681C2×C4×C23—21no—
682C2×C4×C23—21no—
683C2×C4×C23—21no—
684C2×C4×C23—21no—
685C2×C4×C23—21no—
686C2×C4×C23—21no—
687C2×C4×C23—21no—
688C2×C4×C23—21no—
689C2×C4×C23—21no—
690C2×C4×C23—21no—
691C2×C4×C23—21no—
692C2×C4×C23—21no—
693C2×C4×C23—21no—
694C2×C4×C23—21no—
695C2×C4×C23—21no—
696C2×C4×C23—21no—
697C2×C4×C23—21no—
698C2×C4×C23—21no—
699C2×C4×C23—21no—
700C2×C4×C23—21no—
701C2×C4×C23—21no—
702C2×C4×C23—21no—
703C2×C4×C23—21no—
704C2×C4×C23—21no—
705C2×C4×C23—21no—
706C2×C4×C23—21no—
707C2×C4×C23—21no—
708C2×C4×C23—21no—
709C2×C4×C23—21no—
710C2×C4×C23—21no—
711C2×C4×C23—21no—
712C2×C4×C23—21no—
713C2×C4×C23—21no—
714C2×C4×C23—21no—
715C2×C4×C23—21no—
716C2×C4×C23—21no—
717C2×C4×C23—21no—
718C2×C4×C23—21no—
719C2×C4×C23—21no—
720C2×C4×C23—21no—
721C2×C4×C23—21no—
722C2×C4×C23—21no—
723C2×C4×C23—21no—
724C2×C4×C23—21no—
725C2×C4×C23—21no—
726C2×C4×C23—21no—
727C2×C4×C23—21no—
728C2×C4×C23—44no—
729C2×C4×C23—44no—
730C2×C4×C23—44no—
731C2×C4×C23—44no—
732C2×C4×C23—44no—
733C2×C4×C23—44no—
734C2×C4×C23—82no—
735C2×C4×C23—82no—
736C2×C4×C23—82no—
737C2×C4×C23—82no—
738C2×C4×C23C2×#4112yes—
739C2×C4×C23C2×#4112yes—
740C2×C4×C23H(5,𝔽2)12yes—
741C2×C4×C23H(5,𝔽2)12yes—
742#2849C2×C2311yescharacteristic, complemented
743#2847C2×C2311yescharacteristic, complemented
744#2788C2×C2311yescharacteristic, complemented
745#2757C2×C2311yescharacteristic, complemented
746#2756C2×C2311yescharacteristic, complemented
747#2749C2×C2311yescharacteristic, complemented
748#2737C2×C2311yescharacteristic, complemented
749#2712C2×C2311yescharacteristic, complemented
750#2701C2×C2311yescharacteristic, complemented
751#2688C2×C2311yescharacteristic, complemented
752#2688C2×C2311yescharacteristic, complemented
753#2687C2×C2311yescharacteristic, complemented
754#2684C2×C2311yescharacteristic, complemented
755#2678C2×C2311yescharacteristic, complemented
756#2676C2×C2311yescharacteristic, complemented
757#2673C2×C2311yescharacteristic, complemented
758#2670C2×C2311yescharacteristic, complemented
759#2669C2×C2311yescharacteristic, complemented
760#2631C2×C2311yescharacteristic, complemented
761#2630C2×C2311yescharacteristic, complemented
762#2577C2×C2311yescharacteristic, complemented
763#2572C2×C2311yescharacteristic, complemented
764#2557C2×C2311yescharacteristic, complemented
765#2555C2×C2311yescharacteristic, complemented
766#2464C2×C2311yescharacteristic, complemented
767#2457C2×C2311yescharacteristic, complemented
768#2445C2×C2311yescharacteristic, complemented
769#2427C2×C2311yescharacteristic, complemented
770#2337C2×C2311yescharacteristic, complemented
771#2333C2×C2311yescharacteristic, complemented
772C4×#120C2×C2311yescharacteristic, complemented
773C22×C23—22no—
774C22×C23—22no—
775C22×C23—22no—
776C22×C23—22no—
777C22×C23—22no—
778C22×C23—22no—
779C22×C23—22no—
780C22×C23—22no—
781C22×C23—22no—
782C22×C23—416no—
783C22×C23—41no—
784C22×C23—41no—
785C22×C23—41no—
786C22×C23—41no—
787C22×C23—41no—
788C22×C23—41no—
789C22×C23—41no—
790C22×C23—41no—
791C22×C23—41no—
792C22×C23—41no—
793C22×C23—41no—
794C22×C23—41no—
795C22×C23—41no—
796C22×C23—41no—
797C22×C23—41no—
798C22×C23—41no—
799C22×C23—41no—
800C22×C23—41no—
801C22×C23—41no—
802C22×C23—41no—
803C22×C23—41no—
804C22×C23—41no—
805C22×C23—41no—
806C22×C23—41no—
807C22×C23—41no—
808C22×C23—41no—
809C22×C23—41no—
810C22×C23—41no—
811C22×C23—41no—
812C22×C23—41no—
813C22×C23—41no—
814C22×C23—41no—
815C22×C23—41no—
816C22×C23—41no—
817C22×C23—41no—
818C22×C23—41no—
819C22×C23—41no—
820C22×C23—41no—
821C22×C23—41no—
822C22×C23—41no—
823C22×C23C22×#4111yescharacteristic
824C22×C23C2×H(5,𝔽2)11yescharacteristic
825C22×C23C2×H(5,𝔽2)11yescharacteristic
826C22×C23C2×H(5,𝔽2)11yescharacteristic
827C22×C23C2×H(5,𝔽2)11yescharacteristic
828C22×C23#58511yescharacteristic
829C22×C23#58511yescharacteristic
830C4×C23—22no—
831C4×C23—22no—
832C4×C23—22no—
833C4×C23—22no—
834C4×C23—41no—
835C4×C23—41no—
836C4×C23—41no—
837C4×C23—41no—
838C4×C23—41no—
839C4×C23—41no—
840C4×C23—41no—
841C4×C23—41no—
842C4×C23—41no—
843C4×C23—41no—
844C4×C23—41no—
845C4×C23—41no—
846C4×C23—41no—
847C4×C23—41no—
848C4×C23—41no—
849C4×C23—41no—
850C4×C23—41no—
851C4×C23—41no—
852C4×C23—41no—
853C4×C23—41no—
854C24×C4C22×C2311yescharacteristic
855C2×#127C22×C2311yescharacteristic
856C2×#124C22×C2311yescharacteristic
857C2×#124C22×C2311yescharacteristic
858C2×#124C22×C2311yescharacteristic
859C2×#124C22×C2311yescharacteristic, complemented
860C2×#123C22×C2311yescharacteristic
861C2×#123C22×C2311yescharacteristic
862C2×#123C22×C2311yescharacteristic
863C2×#123C22×C2311yescharacteristic, complemented
864C2×C22⋊Q8C22×C2311yescharacteristic, complemented
865C2×#121C22×C2311yescharacteristic
866C2×#121C22×C2311yescharacteristic
867C2×#121C22×C2311yescharacteristic
868C2×#121C22×C2311yescharacteristic
869C2×#121C22×C2311yescharacteristic
870C2×#121C22×C2311yescharacteristic
871C2×#121C22×C2311yescharacteristic, complemented
872C2×#120C22×C2311yescharacteristic
873C2×#120C22×C2311yescharacteristic
874C2×#120C22×C2311yescharacteristic
875C2×#120C22×C2311yescharacteristic
876C2×C4×D4C22×C2311yescharacteristic
877C2×C4×D4C22×C2311yescharacteristic
878C2×C4×D4C22×C2311yescharacteristic
879#400C22×C2311yescharacteristic, complemented
880#400C22×C2311yescharacteristic, complemented
881#400C22×C2311yescharacteristic, complemented
882#398C22×C2311yescharacteristic, complemented
883#398C22×C2311yescharacteristic, complemented
884#398C22×C2311yescharacteristic, complemented
885#397C22×C2311yescharacteristic
886#397C22×C2311yescharacteristic
887#397C22×C2311yescharacteristic
888#397C22×C2311yescharacteristic, complemented
889#397C22×C2311yescharacteristic, complemented
890#397C22×C2311yescharacteristic, complemented
891#397C22×C2311yescharacteristic, complemented
892#397C22×C2311yescharacteristic, complemented
893#397C22×C2311yescharacteristic, complemented
894#396C22×C2311yescharacteristic
895#396C22×C2311yescharacteristic, complemented
896#396C22×C2311yescharacteristic, complemented
897#395C22×C2311yescharacteristic, complemented
898#394C22×C2311yescharacteristic
899#394C22×C2311yescharacteristic
900#394C22×C2311yescharacteristic
901#394C22×C2311yescharacteristic
902#394C22×C2311yescharacteristic
903#394C22×C2311yescharacteristic
904#394C22×C2311yescharacteristic
905#394C22×C2311yescharacteristic
906#394C22×C2311yescharacteristic, complemented
907#394C22×C2311yescharacteristic, complemented
908#394C22×C2311yescharacteristic, complemented
909#394C22×C2311yescharacteristic, complemented
910#394C22×C2311yescharacteristic, complemented
911#393C22×C2311yescharacteristic
912#393C22×C2311yescharacteristic
913#393C22×C2311yescharacteristic
914#393C22×C2311yescharacteristic, complemented
915#393C22×C2311yescharacteristic, complemented
916#392C22×C2311yescharacteristic
917#392C22×C2311yescharacteristic
918#392C22×C2311yescharacteristic
919#392C22×C2311yescharacteristic
920#392C22×C2311yescharacteristic
921#392C22×C2311yescharacteristic
922#392C22×C2311yescharacteristic
923#392C22×C2311yescharacteristic
924#392C22×C2311yescharacteristic
925#392C22×C2311yescharacteristic, complemented
926#392C22×C2311yescharacteristic, complemented
927#391C22×C2311yescharacteristic, complemented
928#391C22×C2311yescharacteristic, complemented
929#391C22×C2311yescharacteristic, complemented
930#390C22×C2311yescharacteristic
931#390C22×C2311yescharacteristic
932#390C22×C2311yescharacteristic
933#390C22×C2311yescharacteristic
934#390C22×C2311yescharacteristic, complemented
935#390C22×C2311yescharacteristic, complemented
936#389C22×C2311yescharacteristic, complemented
937#389C22×C2311yescharacteristic, complemented
938#388C22×C2311yescharacteristic
939#388C22×C2311yescharacteristic
940#388C22×C2311yescharacteristic
941#388C22×C2311yescharacteristic
942#388C22×C2311yescharacteristic
943#388C22×C2311yescharacteristic
944#388C22×C2311yescharacteristic
945#388C22×C2311yescharacteristic, complemented
946#388C22×C2311yescharacteristic, complemented
947#388C22×C2311yescharacteristic, complemented
948#388C22×C2311yescharacteristic, complemented
949#388C22×C2311yescharacteristic, complemented
950#388C22×C2311yescharacteristic, complemented
951#388C22×C2311yescharacteristic, complemented
952#387C22×C2311yescharacteristic, complemented
953#387C22×C2311yescharacteristic, complemented
954#387C22×C2311yescharacteristic, complemented
955#387C22×C2311yescharacteristic, complemented
956#387C22×C2311yescharacteristic, complemented
957#386C22×C2311yescharacteristic
958#386C22×C2311yescharacteristic
959#386C22×C2311yescharacteristic
960#386C22×C2311yescharacteristic
961#386C22×C2311yescharacteristic
962#386C22×C2311yescharacteristic
963#386C22×C2311yescharacteristic
964#386C22×C2311yescharacteristic
965#386C22×C2311yescharacteristic
966#386C22×C2311yescharacteristic
967#386C22×C2311yescharacteristic
968#386C22×C2311yescharacteristic
969#386C22×C2311yescharacteristic
970#386C22×C2311yescharacteristic
971#386C22×C2311yescharacteristic
972#386C22×C2311yescharacteristic
973#386C22×C2311yescharacteristic
974#386C22×C2311yescharacteristic
975#386C22×C2311yescharacteristic, complemented
976#386C22×C2311yescharacteristic, complemented
977#386C22×C2311yescharacteristic, complemented
978#386C22×C2311yescharacteristic, complemented
979#386C22×C2311yescharacteristic, complemented
980#386C22×C2311yescharacteristic, complemented
981#385C22×C2311yescharacteristic
982#385C22×C2311yescharacteristic
983#385C22×C2311yescharacteristic
984#385C22×C2311yescharacteristic
985#385C22×C2311yescharacteristic
986#385C22×C2311yescharacteristic
987#385C22×C2311yescharacteristic
988#385C22×C2311yescharacteristic, complemented
989#383C22×C2311yescharacteristic, complemented
990#383C22×C2311yescharacteristic, complemented
991#383C22×C2311yescharacteristic, complemented
992#381C22×C2311yescharacteristic
993#381C22×C2311yescharacteristic
994#381C22×C2311yescharacteristic, complemented
995#381C22×C2311yescharacteristic, complemented
996#380C22×C2311yescharacteristic
997#380C22×C2311yescharacteristic
998#380C22×C2311yescharacteristic
999#380C22×C2311yescharacteristic, complemented
1000#379C22×C2311yescharacteristic
1001#379C22×C2311yescharacteristic
1002C4×C4⋊C4C22×C2311yescharacteristic, complemented
1003C4×C22⋊C4C22×C2311yescharacteristic
1004C4×C22⋊C4C22×C2311yescharacteristic
1005C4×C22⋊C4C22×C2311yescharacteristic
1006C4×C22⋊C4C22×C2311yescharacteristic, complemented
1007C4×C22⋊C4C22×C2311yescharacteristic, complemented
1008C4×C22⋊C4C22×C2311yescharacteristic, complemented
1009C2×C23—42no—
1010C2×C23—42no—
1011C2×C23—42no—
1012C2×C23—81no—
1013C2×C23—81no—
1014C2×C23—81no—
1015C2×C23—81no—
1016C2×C23#346011yescharacteristic
1017C2×C23#351311yescharacteristic
1018C2×C23#351911yescharacteristic
1019C2×C23#353211yescharacteristic
1020C2×C23#353411yescharacteristic
1021C2×C23#354011yescharacteristic
1022C2×C23#354211yescharacteristic
1023C25C23×C2311yescharacteristic
1024C22×Q8C23×C2311yescharacteristic
1025C22×Q8C23×C2311yescharacteristic
1026C22×D4C23×C2311yescharacteristic
1027C22×D4C23×C2311yescharacteristic
1028C22×D4C23×C2311yescharacteristic
1029C22×D4C23×C2311yescharacteristic
1030C22×D4C23×C2311yescharacteristic
1031C22×D4C23×C2311yescharacteristic
1032C22×D4C23×C2311yescharacteristic
1033C22×D4C23×C2311yescharacteristic
1034C22×D4C23×C2311yescharacteristic
1035C22×D4C23×C2311yescharacteristic
1036C22×D4C23×C2311yescharacteristic
1037C22×D4C23×C2311yescharacteristic
1038C22×D4C23×C2311yescharacteristic
1039C22×D4C23×C2311yescharacteristic
1040C22×D4C23×C2311yescharacteristic
1041C22×D4C23×C2311yescharacteristic
1042C22×D4C23×C2311yescharacteristic
1043C22×D4C23×C2311yescharacteristic
1044C23×C4—42no—
1045C23×C4—42no—
1046C23×C4—42no—
1047C23×C4C23×C2311yescharacteristic
1048C23×C4C23×C2311yescharacteristic
1049C23×C4C23×C2311yescharacteristic
1050C23×C4C23×C2311yescharacteristic
1051C23×C4C23×C2311yescharacteristic
1052C23×C4C23×C2311yescharacteristic
1053C23×C4C23×C2311yescharacteristic
1054C23×C4C23×C2311yescharacteristic
1055C23×C4C23×C2311yescharacteristic
1056C23×C4C23×C2311yescharacteristic
1057#127—42no—
1058#124—24no—
1059#124—42no—
1060#124—42no—
1061#124—42no—
1062#123—42no—
1063#123—42no—
1064#123—42no—
1065#123—42no—
1066C22⋊Q8—42no—
1067#121—24no—
1068#121—42no—
1069#121—42no—
1070#121—42no—
1071#121—42no—
1072#121—42no—
1073#121—42no—
1074#120—24no—
1075#120—42no—
1076#120—42no—
1077#120—42no—
1078C4×D4—42no—
1079C4×D4—42no—
1080C4×D4—42no—
1081C2×C4⋊C4C23×C2311yescharacteristic
1082C2×C4⋊C4C23×C2311yescharacteristic
1083C2×C4⋊C4C23×C2311yescharacteristic
1084C2×C4⋊C4C23×C2311yescharacteristic
1085C2×C4⋊C4C23×C2311yescharacteristic
1086C2×C4⋊C4C23×C2311yescharacteristic
1087C2×C4⋊C4C23×C2311yescharacteristic
1088C2×C4⋊C4C23×C2311yescharacteristic
1089C2×C4⋊C4C23×C2311yescharacteristic
1090C2×C4⋊C4C23×C2311yescharacteristic
1091C2×C4⋊C4C23×C2311yescharacteristic
1092C2×C4⋊C4C23×C2311yescharacteristic
1093C2×C4⋊C4C23×C2311yescharacteristic
1094C2×C4⋊C4C23×C2311yescharacteristic
1095C2×C4⋊C4C23×C2311yescharacteristic
1096C2×C4⋊C4C23×C2311yescharacteristic
1097C2×C4⋊C4C23×C2311yescharacteristic
1098C2×C4⋊C4C23×C2311yescharacteristic
1099C2×C4⋊C4C23×C2311yescharacteristic
1100C2×C4⋊C4C23×C2311yescharacteristic
1101C2×C22⋊C4C23×C2311yescharacteristic
1102C2×C22⋊C4C23×C2311yescharacteristic
1103C2×C22⋊C4C23×C2311yescharacteristic
1104C2×C22⋊C4C23×C2311yescharacteristic
1105C2×C22⋊C4C23×C2311yescharacteristic
1106C2×C22⋊C4C23×C2311yescharacteristic
1107C2×C22⋊C4C23×C2311yescharacteristic
1108C2×C22⋊C4C23×C2311yescharacteristic
1109C2×C22⋊C4C23×C2311yescharacteristic
1110C2×C22⋊C4C23×C2311yescharacteristic
1111C2×C22⋊C4C23×C2311yescharacteristic
1112C2×C22⋊C4C23×C2311yescharacteristic
1113C2×C22⋊C4C23×C2311yescharacteristic
1114C2×C22⋊C4C23×C2311yescharacteristic
1115C2×C22⋊C4C23×C2311yescharacteristic
1116C2×C22⋊C4C23×C2311yescharacteristic
1117C2×C22⋊C4C23×C2311yescharacteristic
1118C2×C22⋊C4C23×C2311yescharacteristic
1119C2×C22⋊C4C23×C2311yescharacteristic
1120C2×C22⋊C4C23×C2311yescharacteristic
1121C2×C22⋊C4C23×C2311yescharacteristic
1122C2×C22⋊C4C23×C2311yescharacteristic
1123C2×C22⋊C4C23×C2311yescharacteristic
1124C2×C22⋊C4C23×C2311yescharacteristic
1125C2×C22⋊C4C23×C2311yescharacteristic
1126C2×C22⋊C4C23×C2311yescharacteristic
1127C2×C22⋊C4C23×C2311yescharacteristic
1128C2×C22⋊C4C23×C2311yescharacteristic
1129C2×C22⋊C4C23×C2311yescharacteristic
1130C2×C22⋊C4C23×C2311yescharacteristic
1131C2×C22⋊C4C23×C2311yescharacteristic
1132C2×C22⋊C4C23×C2311yescharacteristic
1133C2×C22⋊C4C23×C2311yescharacteristic
1134C2×C22⋊C4C23×C2311yescharacteristic
1135C2×C22⋊C4C23×C2311yescharacteristic
1136C2×C22⋊C4C23×C2311yescharacteristic
1137C2×C22⋊C4C23×C2311yescharacteristic
1138C2×C22⋊C4C23×C2311yescharacteristic
1139C2×C22⋊C4C23×C2311yescharacteristic
1140C2×C22⋊C4C23×C2311yescharacteristic
1141C2×C22⋊C4C23×C2311yescharacteristic
1142C2×C22⋊C4C23×C2311yescharacteristic
1143C2×C22⋊C4C23×C2311yescharacteristic
1144C2×C22⋊C4C23×C2311yescharacteristic
1145C2×C22⋊C4C23×C2311yescharacteristic
1146C2×C22⋊C4C23×C2311yescharacteristic
1147C2×C22⋊C4C23×C2311yescharacteristic
1148C2×C22⋊C4C23×C2311yescharacteristic
1149C2×C22⋊C4C23×C2311yescharacteristic
1150C2×C22⋊C4C23×C2311yescharacteristic
1151C2×C22⋊C4C23×C2311yescharacteristic
1152C2×C22⋊C4C23×C2311yescharacteristic
1153C2×C22⋊C4C23×C2311yescharacteristic
1154C2×C22⋊C4C23×C2311yescharacteristic
1155C2×C22⋊C4C23×C2311yescharacteristic
1156C2×C22⋊C4C23×C2311yescharacteristic
1157C2×C42C23×C2311yescharacteristic
1158C2×C42C23×C2311yescharacteristic
1159C2×C42C23×C2311yescharacteristic
1160C2×C42C23×C2311yescharacteristic
1161C2×C42C23×C2311yescharacteristic
1162C2×C42C23×C2311yescharacteristic
1163C2×C42C23×C2311yescharacteristic
1164C2×C42C23×C2311yescharacteristic
1165#95C23×C2311yescharacteristic
1166#95C23×C2311yescharacteristic
1167#95C23×C2311yescharacteristic
1168#95C23×C2311yescharacteristic
1169#95C23×C2311yescharacteristic
1170#95C23×C2311yescharacteristic
1171#95C23×C2311yescharacteristic
1172#95C23×C2311yescharacteristic
1173#95C23×C2311yescharacteristic
1174#95C23×C2311yescharacteristic
1175#95C23×C2311yescharacteristic
1176#95C23×C2311yescharacteristic
1177#95C23×C2311yescharacteristic
1178#95C23×C2311yescharacteristic
1179#95C23×C2311yescharacteristic
1180#95C23×C2311yescharacteristic
1181#95C23×C2311yescharacteristic
1182#95C23×C2311yescharacteristic
1183#95C23×C2311yescharacteristic
1184#95C23×C2311yescharacteristic
1185#95C23×C2311yescharacteristic
1186#95C23×C2311yescharacteristic
1187#95C23×C2311yescharacteristic
1188#95C23×C2311yescharacteristic
1189#95C23×C2311yescharacteristic
1190#95C23×C2311yescharacteristic
1191#95C23×C2311yescharacteristic
1192#95C23×C2311yescharacteristic
1193#95C23×C2311yescharacteristic
1194#95C23×C2311yescharacteristic
1195#95C23×C2311yescharacteristic
1196#95C23×C2311yescharacteristic
1197#95C23×C2311yescharacteristic
1198#95C23×C2311yescharacteristic
1199#95C23×C2311yescharacteristic
1200#95C23×C2311yescharacteristic
1201#95C23×C2311yescharacteristic
1202#95C23×C2311yescharacteristic
1203#95C23×C2311yescharacteristic
1204#95C23×C2311yescharacteristic
1205C23#3685711yescharacteristic, direct product factor, Sylow
1206C24—22no—
1207C24—22no—
1208C24—22no—
1209C24—41no—
1210C24—41no—
1211C24—41no—
1212C24—41no—
1213C24C24×C2311yescharacteristic
1214C24C24×C2311yescharacteristic
1215C24C24×C2311yescharacteristic
1216C24C24×C2311yescharacteristic
1217C24C24×C2311yescharacteristic
1218C24C24×C2311yescharacteristic
1219C24C24×C2311yescharacteristic
1220C2×Q8—22no—
1221C2×Q8—41no—
1222C2×Q8—41no—
1223C2×Q8—41no—
1224C2×Q8—41no—
1225C2×Q8—41no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—41no—
1262C2×D4—41no—
1263C2×D4—41no—
1264C2×D4—41no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—41no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4—41no—
1274C2×D4—41no—
1275C2×D4—41no—
1276C2×D4—41no—
1277C2×D4—41no—
1278C2×D4—41no—
1279C2×D4—41no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—41no—
1304C22×C4—41no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4—41no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—416no—
1311C22×C4C24×C2311yescharacteristic
1312C22×C4C24×C2311yescharacteristic
1313C22×C4C24×C2311yescharacteristic
1314C22×C4C24×C2311yescharacteristic
1315C22×C4C24×C2311yescharacteristic
1316C22×C4C24×C2311yescharacteristic
1317C22×C4C24×C2311yescharacteristic
1318C22×C4C24×C2311yescharacteristic
1319C22×C4C24×C2311yescharacteristic
1320C22×C4C24×C2311yescharacteristic
1321C22×C4C24×C2311yescharacteristic
1322C22×C4C24×C2311yescharacteristic
1323C22×C4C24×C2311yescharacteristic
1324C22×C4C24×C2311yescharacteristic
1325C22×C4C24×C2311yescharacteristic
1326C22×C4C24×C2311yescharacteristic
1327C22×C4C24×C2311yescharacteristic
1328C22×C4C24×C2311yescharacteristic
1329C22×C4C24×C2311yescharacteristic
1330C22×C4C24×C2311yescharacteristic
1331C22×C4C24×C2311yescharacteristic
1332C22×C4C24×C2311yescharacteristic
1333C22×C4C24×C2311yescharacteristic
1334C22×C4C24×C2311yescharacteristic
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—41no—
1348C4⋊C4—41no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C4⋊C4—41no—
1354C4⋊C4—41no—
1355C22⋊C4—22no—
1356C22⋊C4—22no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—22no—
1361C22⋊C4—22no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—22no—
1369C22⋊C4—22no—
1370C22⋊C4—22no—
1371C22⋊C4—22no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—41no—
1393C22⋊C4—41no—
1394C22⋊C4—41no—
1395C22⋊C4—41no—
1396C22⋊C4—41no—
1397C22⋊C4—41no—
1398C22⋊C4—41no—
1399C22⋊C4—41no—
1400C22⋊C4—41no—
1401C22⋊C4—41no—
1402C22⋊C4—41no—
1403C22⋊C4—41no—
1404C22⋊C4—41no—
1405C22⋊C4—41no—
1406C22⋊C4—41no—
1407C22⋊C4—41no—
1408C22⋊C4—41no—
1409C22⋊C4—41no—
1410C22⋊C4#41×C2314yes—
1411C42—22no—
1412C42—22no—
1413C42—41no—
1414C42—41no—
1415C42—41no—
1416C42—41no—
1417C42—41no—
1418C42—41no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—44no—
1466C23—44no—
1467C23—44no—
1468C23—44no—
1469C23—44no—
1470C23—44no—
1471C23—44no—
1472C23C2×#41×C2312yes—
1473C23C23×H(5,𝔽2)12yes—
1474C23C23×H(5,𝔽2)12yes—
1475C23C25×C2311yescharacteristic
1476Q8—82no—
1477Q8—82no—
1478D4—44no—
1479D4—44no—
1480D4—44no—
1481D4—82no—
1482D4—82no—
1483D4—82no—
1484D4—82no—
1485D4—82no—
1486D4—82no—
1487D4—82no—
1488D4—82no—
1489D4—82no—
1490D4—82no—
1491D4—82no—
1492D4—82no—
1493D4—82no—
1494D4—82no—
1495D4—82no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—44no—
1565C2×C4—44no—
1566C2×C4—44no—
1567C2×C4—44no—
1568C2×C4—44no—
1569C2×C4—44no—
1570C2×C4—82no—
1571C2×C4—82no—
1572C2×C4—82no—
1573C2×C4—82no—
1574C2×C4C2×#41×C2312yes—
1575C2×C4C2×#41×C2312yes—
1576C2×C4C23×H(5,𝔽2)12yes—
1577C2×C4C23×H(5,𝔽2)12yes—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—416no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—41no—
1627C22—41no—
1628C22C22×#41×C2311yescharacteristic
1629C22C2×C23×H(5,𝔽2)11yescharacteristic
1630C22C2×C23×H(5,𝔽2)11yescharacteristic
1631C22C2×C23×H(5,𝔽2)11yescharacteristic
1632C22C2×C23×H(5,𝔽2)11yescharacteristic
1633C22C23×#58511yescharacteristic
1634C22C23×#58511yescharacteristic
1635C4—22no—
1636C4—22no—
1637C4—22no—
1638C4—22no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C2—42no—
1660C2—42no—
1661C2—42no—
1662C2—81no—
1663C2—81no—
1664C2—81no—
1665C2—81no—
1666C2C23×#346011yescharacteristic
1667C2C23×#351311yescharacteristic
1668C2C23×#351911yescharacteristic
1669C2C23×#353211yescharacteristic
1670C2C23×#353411yescharacteristic
1671C2C23×#354011yescharacteristic
1672C2C23×#354211yescharacteristic
subgroupG/H
center, socleC23×C23C25
commutator, Frattini, cosocleC23C25×C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×#2849C2semidirect
2. C23×#2847C2semidirect
3. C23×#2788C2semidirect
4. C23×#2757C2semidirect
5. C23×#2756C2semidirect
6. C23×#2749C2semidirect
7. C23×#2737C2semidirect
8. C23×#2712C2semidirect
9. C23×#2701C2semidirect
10. C23×#2688C2semidirect
11. C23×#2688C2semidirect
12. C23×#2687C2semidirect
13. C23×#2684C2semidirect
14. C23×#2678C2semidirect
15. C23×#2676C2semidirect
16. C23×#2673C2semidirect
17. C23×#2670C2semidirect
18. C23×#2669C2semidirect
19. C23×#2631C2semidirect
20. C23×#2630C2semidirect
21. C23×#2577C2semidirect
22. C23×#2572C2semidirect
23. C23×#2557C2semidirect
24. C23×#2555C2semidirect
25. C23×#2464C2semidirect
26. C23×#2457C2semidirect
27. C23×#2445C2semidirect
28. C23×#2427C2semidirect
29. C23×#2337C2semidirect
30. C23×#2333C2semidirect
31. C4×C23×#120C2semidirect
37. C2×C23×#124C22semidirect
41. C2×C23×#123C22semidirect
42. C2×C23×C22⋊Q8C22semidirect
49. C2×C23×#121C22semidirect
57. C23×#400C22semidirect
58. C23×#400C22semidirect
59. C23×#400C22semidirect
60. C23×#398C22semidirect
61. C23×#398C22semidirect
62. C23×#398C22semidirect
66. C23×#397C22semidirect
67. C23×#397C22semidirect
68. C23×#397C22semidirect
69. C23×#397C22semidirect
70. C23×#397C22semidirect
71. C23×#397C22semidirect
73. C23×#396C22semidirect
74. C23×#396C22semidirect
75. C23×#395C22semidirect
84. C23×#394C22semidirect
85. C23×#394C22semidirect
86. C23×#394C22semidirect
87. C23×#394C22semidirect
88. C23×#394C22semidirect
92. C23×#393C22semidirect
93. C23×#393C22semidirect
103. C23×#392C22semidirect
104. C23×#392C22semidirect
105. C23×#391C22semidirect
106. C23×#391C22semidirect
107. C23×#391C22semidirect
112. C23×#390C22semidirect
113. C23×#390C22semidirect
114. C23×#389C22semidirect
115. C23×#389C22semidirect
123. C23×#388C22semidirect
124. C23×#388C22semidirect
125. C23×#388C22semidirect
126. C23×#388C22semidirect
127. C23×#388C22semidirect
128. C23×#388C22semidirect
129. C23×#388C22semidirect
130. C23×#387C22semidirect
131. C23×#387C22semidirect
132. C23×#387C22semidirect
133. C23×#387C22semidirect
134. C23×#387C22semidirect
153. C23×#386C22semidirect
154. C23×#386C22semidirect
155. C23×#386C22semidirect
156. C23×#386C22semidirect
157. C23×#386C22semidirect
158. C23×#386C22semidirect
166. C23×#385C22semidirect
167. C23×#383C22semidirect
168. C23×#383C22semidirect
169. C23×#383C22semidirect
172. C23×#381C22semidirect
173. C23×#381C22semidirect
177. C23×#380C22semidirect
180. C4×C4⋊C4×C23C22semidirect
184. C4×C22⋊C4×C23C22semidirect
185. C4×C22⋊C4×C23C22semidirect
186. C4×C22⋊C4×C23C22semidirect
582. #36857C23direct (N × H)
742. #2849C2×C23semidirect
743. #2847C2×C23semidirect
744. #2788C2×C23semidirect
745. #2757C2×C23semidirect
746. #2756C2×C23semidirect
747. #2749C2×C23semidirect
748. #2737C2×C23semidirect
749. #2712C2×C23semidirect
750. #2701C2×C23semidirect
751. #2688C2×C23semidirect
752. #2688C2×C23semidirect
753. #2687C2×C23semidirect
754. #2684C2×C23semidirect
755. #2678C2×C23semidirect
756. #2676C2×C23semidirect
757. #2673C2×C23semidirect
758. #2670C2×C23semidirect
759. #2669C2×C23semidirect
760. #2631C2×C23semidirect
761. #2630C2×C23semidirect
762. #2577C2×C23semidirect
763. #2572C2×C23semidirect
764. #2557C2×C23semidirect
765. #2555C2×C23semidirect
766. #2464C2×C23semidirect
767. #2457C2×C23semidirect
768. #2445C2×C23semidirect
769. #2427C2×C23semidirect
770. #2337C2×C23semidirect
771. #2333C2×C23semidirect
772. C4×#120C2×C23semidirect
859. C2×#124C22×C23semidirect
863. C2×#123C22×C23semidirect
864. C2×C22⋊Q8C22×C23semidirect
871. C2×#121C22×C23semidirect
879. #400C22×C23semidirect
880. #400C22×C23semidirect
881. #400C22×C23semidirect
882. #398C22×C23semidirect
883. #398C22×C23semidirect
884. #398C22×C23semidirect
888. #397C22×C23semidirect
889. #397C22×C23semidirect
890. #397C22×C23semidirect
891. #397C22×C23semidirect
892. #397C22×C23semidirect
893. #397C22×C23semidirect
895. #396C22×C23semidirect
896. #396C22×C23semidirect
897. #395C22×C23semidirect
906. #394C22×C23semidirect
907. #394C22×C23semidirect
908. #394C22×C23semidirect
909. #394C22×C23semidirect
910. #394C22×C23semidirect
914. #393C22×C23semidirect
915. #393C22×C23semidirect
925. #392C22×C23semidirect
926. #392C22×C23semidirect
927. #391C22×C23semidirect
928. #391C22×C23semidirect
929. #391C22×C23semidirect
934. #390C22×C23semidirect
935. #390C22×C23semidirect
936. #389C22×C23semidirect
937. #389C22×C23semidirect
945. #388C22×C23semidirect
946. #388C22×C23semidirect
947. #388C22×C23semidirect
948. #388C22×C23semidirect
949. #388C22×C23semidirect
950. #388C22×C23semidirect
951. #388C22×C23semidirect
952. #387C22×C23semidirect
953. #387C22×C23semidirect
954. #387C22×C23semidirect
955. #387C22×C23semidirect
956. #387C22×C23semidirect
975. #386C22×C23semidirect
976. #386C22×C23semidirect
977. #386C22×C23semidirect
978. #386C22×C23semidirect
979. #386C22×C23semidirect
980. #386C22×C23semidirect
988. #385C22×C23semidirect
989. #383C22×C23semidirect
990. #383C22×C23semidirect
991. #383C22×C23semidirect
994. #381C22×C23semidirect
995. #381C22×C23semidirect
999. #380C22×C23semidirect
1002. C4×C4⋊C4C22×C23semidirect
1006. C4×C22⋊C4C22×C23semidirect
1007. C4×C22⋊C4C22×C23semidirect
1008. C4×C22⋊C4C22×C23semidirect
1205. C23#36857direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#28492
C23×#28472
C23×#27882
C23×#27572
C23×#27562
C23×#27492
C23×#27372
C23×#27122
C23×#27012
C23×#26882
C23×#26872
C23×#26842
C23×#26782
C23×#26762
C23×#26732
C23×#26702
C23×#26692
C23×#26312
C23×#26302
C23×#25772
C23×#25722
C23×#25572
C23×#25552
C23×#24642
C23×#24572
C23×#24452
C23×#24272
C23×#23372
C23×#23332
C4×C23×#1202
#3685723