Finite Group Databasebeta

← C23×#14116 #19161742

Subgroups — C23×#14116 #19161742

Order 5888.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#389C211yesmaximal, characteristic, complemented
2C2×C23×#388C211yesmaximal, characteristic
3C2×C23×#388C211yesmaximal, characteristic
4C2×C23×#385C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C23C211yesmaximal, characteristic
6C23×#1442C211yesmaximal, characteristic, complemented
7C23×#1441C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic
9C23×#1439C211yesmaximal, characteristic
10C23×#1436C211yesmaximal, characteristic, complemented
11C23×#1436C211yesmaximal, characteristic, complemented
12C23×#1436C211yesmaximal, characteristic, complemented
13C23×C4⋊#95C211yesmaximal, characteristic, complemented
14C23×C22⋊#95C211yesmaximal, characteristic
15C4×C23×#95C211yesmaximal, characteristic, complemented
16C24×C4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C4⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C42×C23C2211yescharacteristic
30C22×C42×C23C2211yescharacteristic
31C22×C42×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C23×#389—24no—
34C23×#388—24no—
35C23×#388C418yescomplemented
36C23×#385—24no—
37C4×C22⋊C4×C23—24no—
38C2×C23×#95C2211yescharacteristic
39C2×C23×#95C2211yescharacteristic
40C2×C23×#95C2211yescharacteristic
41C2×C23×#95C2211yescharacteristic
42C2×C23×#95C2211yescharacteristic
43C2×C23×#95C2211yescharacteristic
44C2×C23×#95C2211yescharacteristic
45C2×C23×#95C2211yescharacteristic
46C2×C23×#95C2211yescharacteristic
47C2×C23×#95C2211yescharacteristic
48C2×C23×#95C2211yescharacteristic
49C2×C23×#95C2211yescharacteristic
50C2×C23×#95C2211yescharacteristic
51C2×C23×#95C2211yescharacteristic
52C2×C23×#95C2211yescharacteristic
53C2×C23×#95C2211yescharacteristic
54C2×C23×#95C2211yescharacteristic
55C2×C23×#95C2211yescharacteristic
56C25×C23C2311yescharacteristic
57C23×C4×C23—22no—
58C23×C4×C23—22no—
59C23×C4×C23—22no—
60C23×C4×C23—22no—
61C23×C4×C23—22no—
62C23×C4×C23—41no—
63C23×C4×C23—41no—
64C23×C4×C23C2311yescharacteristic
65C23×C4×C23C2311yescharacteristic
66C23×C4×C23C2311yescharacteristic
67C23×C4×C23C2311yescharacteristic
68C23×C4×C23C2311yescharacteristic
69C23×C4×C23C2311yescharacteristic
70C23×C4×C23C2311yescharacteristic
71C23×C4×C23C2311yescharacteristic
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—22no—
81C2×C4⋊C4×C23—22no—
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—22no—
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—22no—
86C2×C4⋊C4×C23—22no—
87C2×C4⋊C4×C23—22no—
88C2×C4⋊C4×C23—22no—
89C2×C4⋊C4×C23—22no—
90C2×C4⋊C4×C23—22no—
91C2×C4⋊C4×C23—41no—
92C2×C4⋊C4×C23—41no—
93C2×C4⋊C4×C23—41no—
94C2×C4⋊C4×C23—41no—
95C2×C4⋊C4×C23C2×C414yescomplemented
96C2×C22⋊C4×C23—22no—
97C2×C22⋊C4×C23—22no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
100C2×C22⋊C4×C23—22no—
101C2×C22⋊C4×C23—22no—
102C2×C22⋊C4×C23—22no—
103C2×C22⋊C4×C23—22no—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—41no—
106C2×C22⋊C4×C23—41no—
107C2×C22⋊C4×C23—41no—
108C2×C22⋊C4×C23—41no—
109C2×C22⋊C4×C23C2×C414yes—
110C2×C22⋊C4×C23C2×C414yes—
111C2×C22⋊C4×C23C2×C414yes—
112C2×C22⋊C4×C23D414yes—
113C2×C22⋊C4×C23Q814yes—
114C2×C42×C23—22no—
115C2×C42×C23—22no—
116C2×C42×C23—22no—
117C2×C42×C23—22no—
118C2×C42×C23—22no—
119C2×C42×C23—22no—
120C2×C42×C23—41no—
121C2×C42×C23—41no—
122C2×C42×C23—41no—
123C2×C42×C23—41no—
124C2×C42×C23—41no—
125C2×C42×C23C2×C414yescomplemented
126C23×#95—22no—
127C23×#95—22no—
128C23×#95—22no—
129C23×#95—22no—
130C23×#95—22no—
131C23×#95—22no—
132C23×#95—22no—
133C23×#95—22no—
134C23×#95—22no—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—41no—
139C23×#95—41no—
140C23×#95—41no—
141C23×#95C2×C414yescomplemented
142C23×#95C2×C414yescomplemented
143C23×#95D414yes—
144C24×C23—21no—
145C24×C23—21no—
146C24×C23—21no—
147C24×C23—21no—
148C24×C23—21no—
149C24×C23—21no—
150C24×C23—21no—
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23C22×C412yes—
157C24×C23C2×D412yes—
158C24×C23C2×Q812yes—
159C24×C23C2411yescharacteristic
160C22×C4×C23—21no—
161C22×C4×C23—21no—
162C22×C4×C23—21no—
163C22×C4×C23—21no—
164C22×C4×C23—21no—
165C22×C4×C23—21no—
166C22×C4×C23—21no—
167C22×C4×C23—21no—
168C22×C4×C23—21no—
169C22×C4×C23—21no—
170C22×C4×C23—21no—
171C22×C4×C23—21no—
172C22×C4×C23—21no—
173C22×C4×C23—21no—
174C22×C4×C23—21no—
175C22×C4×C23—21no—
176C22×C4×C23—28no—
177C22×C4×C23—21no—
178C22×C4×C23—21no—
179C22×C4×C23—21no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—44no—
240C22×C4×C23—44no—
241C22×C4×C23—44no—
242C22×C4×C23—44no—
243C22×C4×C23—44no—
244C22×C4×C23—44no—
245C22×C4×C23C22×C412yes—
246C22×C4×C23C22×C412yes—
247C22×C4×C23C22×C412yes—
248C22×C4×C23C22×C412yes—
249C22×C4×C23C22×C412yes—
250C22×C4×C23C22×C412yes—
251C22×C4×C23C2×D412yes—
252C22×C4×C23C2×D412yes—
253C22×C4×C23C2×D412yes—
254C22×C4×C23C2×D412yes—
255C22×C4×C23C2×D412yes—
256C22×C4×C23C2×Q812yes—
257C22×C4×C23C2×Q812yes—
258C22×C4×C23#4112yes—
259C22×C4×C23#4112yes—
260C22×C4×C23#4112yes—
261C22×C4×C23#4112yes—
262C22×C4×C23#4112yes—
263C22×C4×C23#4112yes—
264C22×C4×C23#4112yes—
265C4⋊C4×C23—28no—
266C4⋊C4×C23—44no—
267C4⋊C4×C23—44no—
268C4⋊C4×C23—44no—
269C4⋊C4×C23—44no—
270C4⋊C4×C23—44no—
271C22⋊C4×C23—28no—
272C22⋊C4×C23—28no—
273C22⋊C4×C23—44no—
274C22⋊C4×C23—44no—
275C22⋊C4×C23—44no—
276C22⋊C4×C23C4⋊C4116yescomplemented
277C42×C23—44no—
278C42×C23—44no—
279C42×C23—44no—
280C42×C23—44no—
281#14116C2311yesmaximal, characteristic, direct product factor, Sylow
282C23×C23—22no—
283C23×C23—22no—
284C23×C23—22no—
285C23×C23—22no—
286C23×C23—22no—
287C23×C23—22no—
288C23×C23—22no—
289C23×C23—22no—
290C23×C23—22no—
291C23×C23—22no—
292C23×C23—22no—
293C23×C23—22no—
294C23×C23—22no—
295C23×C23—22no—
296C23×C23—22no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—22no—
300C23×C23—41no—
301C23×C23—41no—
302C23×C23—41no—
303C23×C23—41no—
304C23×C23—41no—
305C23×C23—41no—
306C23×C23—41no—
307C23×C23—41no—
308C23×C23—41no—
309C23×C23—41no—
310C23×C23—41no—
311C23×C23—41no—
312C23×C23—41no—
313C23×C23—41no—
314C23×C23—41no—
315C23×C23—41no—
316C23×C23C2×C4⋊C414yes—
317C23×C23C23×C411yescharacteristic
318C23×C23C22×D411yescharacteristic
319C23×C23C22×D411yescharacteristic
320C23×C23C22×Q811yescharacteristic
321C23×C23C2×#4111yescharacteristic
322C23×C23C2×#4111yescharacteristic
323C23×C23C2×#4111yescharacteristic
324C23×C23C2×#4111yescharacteristic
325C23×C23C2×#4111yescharacteristic
326C23×C23C2×#4111yescharacteristic
327C23×C23C2×#4111yescharacteristic
328C23×C23H(5,𝔽2)11yescharacteristic
329C23×C23H(5,𝔽2)11yescharacteristic
330C23×C23H(5,𝔽2)11yescharacteristic
331C23×C232−1+411yescharacteristic
332C2×C4×C23—22no—
333C2×C4×C23—22no—
334C2×C4×C23—22no—
335C2×C4×C23—22no—
336C2×C4×C23—22no—
337C2×C4×C23—22no—
338C2×C4×C23—22no—
339C2×C4×C23—22no—
340C2×C4×C23—22no—
341C2×C4×C23—22no—
342C2×C4×C23—22no—
343C2×C4×C23—22no—
344C2×C4×C23—22no—
345C2×C4×C23—22no—
346C2×C4×C23—22no—
347C2×C4×C23—22no—
348C2×C4×C23—22no—
349C2×C4×C23—22no—
350C2×C4×C23—22no—
351C2×C4×C23—22no—
352C2×C4×C23—22no—
353C2×C4×C23—22no—
354C2×C4×C23—22no—
355C2×C4×C23—22no—
356C2×C4×C23—22no—
357C2×C4×C23—22no—
358C2×C4×C23—22no—
359C2×C4×C23—22no—
360C2×C4×C23—22no—
361C2×C4×C23—22no—
362C2×C4×C23—22no—
363C2×C4×C23—22no—
364C2×C4×C23—22no—
365C2×C4×C23—22no—
366C2×C4×C23—22no—
367C2×C4×C23—22no—
368C2×C4×C23—22no—
369C2×C4×C23—22no—
370C2×C4×C23—22no—
371C2×C4×C23—22no—
372C2×C4×C23—22no—
373C2×C4×C23—22no—
374C2×C4×C23—22no—
375C2×C4×C23—22no—
376C2×C4×C23—22no—
377C2×C4×C23—22no—
378C2×C4×C23—22no—
379C2×C4×C23—22no—
380C2×C4×C23—416no—
381C2×C4×C23—41no—
382C2×C4×C23—41no—
383C2×C4×C23—41no—
384C2×C4×C23—41no—
385C2×C4×C23—41no—
386C2×C4×C23—41no—
387C2×C4×C23—41no—
388C2×C4×C23—41no—
389C2×C4×C23—41no—
390C2×C4×C23—41no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—41no—
394C2×C4×C23—41no—
395C2×C4×C23—41no—
396C2×C4×C23—41no—
397C2×C4×C23—41no—
398C2×C4×C23—41no—
399C2×C4×C23—41no—
400C2×C4×C23—41no—
401C2×C4×C23—41no—
402C2×C4×C23—41no—
403C2×C4×C23—41no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—41no—
411C2×C4×C23—41no—
412C2×C4×C23—41no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23—41no—
421C2×C4×C23—41no—
422C2×C4×C23—41no—
423C2×C4×C23—41no—
424C2×C4×C23—41no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23C2×C4⋊C414yes—
428C2×C4×C23C2×C4⋊C414yes—
429C2×C4×C23C4×D414yes—
430C2×C4×C23#12414yes—
431C2×#389C2×C2311yescharacteristic, complemented
432C2×#388C2×C2311yescharacteristic
433C2×#388C2×C2311yescharacteristic
434C2×#385C2×C2311yescharacteristic
435C2×C4×C22⋊C4C2×C2311yescharacteristic
436#1442C2×C2311yescharacteristic, complemented
437#1441C2×C2311yescharacteristic, complemented
438#1439C2×C2311yescharacteristic
439#1439C2×C2311yescharacteristic
440#1436C2×C2311yescharacteristic, complemented
441#1436C2×C2311yescharacteristic, complemented
442#1436C2×C2311yescharacteristic, complemented
443C4⋊#95C2×C2311yescharacteristic, complemented
444C22⋊#95C2×C2311yescharacteristic
445C4×#95C2×C2311yescharacteristic, complemented
446C22×C23—24no—
447C22×C23—24no—
448C22×C23—24no—
449C22×C23—42no—
450C22×C23—42no—
451C22×C23—42no—
452C22×C23—42no—
453C22×C23—42no—
454C22×C23—42no—
455C22×C23—42no—
456C22×C23—42no—
457C22×C23—42no—
458C22×C23—42no—
459C22×C23—42no—
460C22×C23—42no—
461C22×C23C22×C4⋊C411yescharacteristic
462C22×C23C2×C4×D411yescharacteristic
463C22×C23C4×#4111yescharacteristic
464C22×C23C4×#4111yescharacteristic
465C22×C23C4×#4111yescharacteristic
466C22×C23#51811yescharacteristic
467C22×C23#52011yescharacteristic
468C22×C23#52511yescharacteristic
469C22×C23#52511yescharacteristic
470C22×C23C2×#12411yescharacteristic
471C22×C23#52911yescharacteristic
472C22×C23#52911yescharacteristic
473C22×C23#53211yescharacteristic
474C22×C23#53311yescharacteristic
475C22×C23#53311yescharacteristic
476C22×C23#53811yescharacteristic
477C22×C23#53911yescharacteristic
478C22×C23#54011yescharacteristic
479C22×C23#54211yescharacteristic
480C22×C23D4211yescharacteristic
481C22×C23#54611yescharacteristic
482C22×C23#54611yescharacteristic
483C22×C23#54611yescharacteristic
484C22×C23#54611yescharacteristic
485C22×C23#54711yescharacteristic
486C22×C23D4×Q811yescharacteristic
487C22×C23#55111yescharacteristic
488C22×C23#55211yescharacteristic
489C22×C23#55311yescharacteristic
490C22×C23#55311yescharacteristic
491C22×C23#55311yescharacteristic
492C22×C23#55411yescharacteristic
493C22×C23#55411yescharacteristic
494C22×C23#55411yescharacteristic
495C22×C23#55611yescharacteristic
496C4×C23—24no—
497C4×C23—24no—
498C4×C23—24no—
499C4×C23—24no—
500C4×C23—42no—
501C4×C23—42no—
502C4×C23—42no—
503C4×C23—42no—
504C4×C23—42no—
505C4×C23—42no—
506C4×C23—42no—
507C4×C23—42no—
508C4×C23—81no—
509C4×C23—81no—
510C24×C4C22×C2311yescharacteristic
511C22×C4⋊C4C22×C2311yescharacteristic
512C22×C4⋊C4C22×C2311yescharacteristic
513C22×C4⋊C4C22×C2311yescharacteristic
514C22×C4⋊C4C22×C2311yescharacteristic
515C22×C4⋊C4C22×C2311yescharacteristic
516C22×C4⋊C4C22×C2311yescharacteristic
517C22×C22⋊C4C22×C2311yescharacteristic
518C22×C22⋊C4C22×C2311yescharacteristic
519C22×C22⋊C4C22×C2311yescharacteristic
520C22×C22⋊C4C22×C2311yescharacteristic
521C22×C22⋊C4C22×C2311yescharacteristic
522C22×C22⋊C4C22×C2311yescharacteristic
523C22×C42C22×C2311yescharacteristic
524C22×C42C22×C2311yescharacteristic
525C22×C42C22×C2311yescharacteristic
526C22×C42C22×C2311yescharacteristic
527#389—24no—
528#388—24no—
529#388C4×C2318yescomplemented
530#385—24no—
531C4×C22⋊C4—24no—
532C2×#95C22×C2311yescharacteristic
533C2×#95C22×C2311yescharacteristic
534C2×#95C22×C2311yescharacteristic
535C2×#95C22×C2311yescharacteristic
536C2×#95C22×C2311yescharacteristic
537C2×#95C22×C2311yescharacteristic
538C2×#95C22×C2311yescharacteristic
539C2×#95C22×C2311yescharacteristic
540C2×#95C22×C2311yescharacteristic
541C2×#95C22×C2311yescharacteristic
542C2×#95C22×C2311yescharacteristic
543C2×#95C22×C2311yescharacteristic
544C2×#95C22×C2311yescharacteristic
545C2×#95C22×C2311yescharacteristic
546C2×#95C22×C2311yescharacteristic
547C2×#95C22×C2311yescharacteristic
548C2×#95C22×C2311yescharacteristic
549C2×#95C22×C2311yescharacteristic
550C2×C23—44no—
551C2×C23#229611yescharacteristic
552C2×C23C4×#12411yescharacteristic
553C2×C23#233511yescharacteristic
554C2×C23D4×C4⋊C411yescharacteristic
555C2×C23#234911yescharacteristic
556C2×C23#236411yescharacteristic
557C2×C23#237311yescharacteristic
558C2×C23#246411yescharacteristic
559C2×C23#246611yescharacteristic
560C2×C23#247011yescharacteristic
561C2×C23#247211yescharacteristic
562C2×C23#249211yescharacteristic
563C2×C23#252211yescharacteristic
564C2×C23#255611yescharacteristic
565C2×C23#258711yescharacteristic
566C25C23×C2311yescharacteristic
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C23×C2311yescharacteristic
575C23×C4C23×C2311yescharacteristic
576C23×C4C23×C2311yescharacteristic
577C23×C4C23×C2311yescharacteristic
578C23×C4C23×C2311yescharacteristic
579C23×C4C23×C2311yescharacteristic
580C23×C4C23×C2311yescharacteristic
581C23×C4C23×C2311yescharacteristic
582C23×C4C23×C2311yescharacteristic
583C23×C4C23×C2311yescharacteristic
584C23×C4C23×C2311yescharacteristic
585C23×C4C23×C2311yescharacteristic
586C23×C4C23×C2311yescharacteristic
587C23×C4C23×C2311yescharacteristic
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4C2×C4×C2314yescomplemented
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4C2×C4×C2314yes—
620C2×C22⋊C4C2×C4×C2314yes—
621C2×C22⋊C4C2×C4×C2314yes—
622C2×C22⋊C4D4×C2314yes—
623C2×C22⋊C4Q8×C2314yes—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42C2×C4×C2314yescomplemented
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95C2×C4×C2314yescomplemented
652#95C2×C4×C2314yescomplemented
653#95D4×C2314yes—
654C23#1411611yescharacteristic, direct product factor, Sylow
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C2312yes—
668C24C2×D4×C2312yes—
669C24C2×Q8×C2312yes—
670C24C24×C2311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4C22×C4×C2312yes—
757C22×C4C22×C4×C2312yes—
758C22×C4C22×C4×C2312yes—
759C22×C4C22×C4×C2312yes—
760C22×C4C22×C4×C2312yes—
761C22×C4C22×C4×C2312yes—
762C22×C4C2×D4×C2312yes—
763C22×C4C2×D4×C2312yes—
764C22×C4C2×D4×C2312yes—
765C22×C4C2×D4×C2312yes—
766C22×C4C2×D4×C2312yes—
767C22×C4C2×Q8×C2312yes—
768C22×C4C2×Q8×C2312yes—
769C22×C4#41×C2312yes—
770C22×C4#41×C2312yes—
771C22×C4#41×C2312yes—
772C22×C4#41×C2312yes—
773C22×C4#41×C2312yes—
774C22×C4#41×C2312yes—
775C22×C4#41×C2312yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4C4⋊C4×C23116yescomplemented
788C42—44no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C2314yes—
827C23C23×C4×C2311yescharacteristic
828C23C22×D4×C2311yescharacteristic
829C23C22×D4×C2311yescharacteristic
830C23C22×Q8×C2311yescharacteristic
831C23C2×#41×C2311yescharacteristic
832C23C2×#41×C2311yescharacteristic
833C23C2×#41×C2311yescharacteristic
834C23C2×#41×C2311yescharacteristic
835C23C2×#41×C2311yescharacteristic
836C23C2×#41×C2311yescharacteristic
837C23C2×#41×C2311yescharacteristic
838C23C23×H(5,𝔽2)11yescharacteristic
839C23C23×H(5,𝔽2)11yescharacteristic
840C23C23×H(5,𝔽2)11yescharacteristic
841C23C23×2−1+411yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4C2×C4⋊C4×C2314yes—
938C2×C4C2×C4⋊C4×C2314yes—
939C2×C4C4×D4×C2314yes—
940C2×C4C23×#12414yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C2311yescharacteristic
957C22C2×C4×D4×C2311yescharacteristic
958C22C4×#41×C2311yescharacteristic
959C22C4×#41×C2311yescharacteristic
960C22C4×#41×C2311yescharacteristic
961C22C23×#51811yescharacteristic
962C22C23×#52011yescharacteristic
963C22C23×#52511yescharacteristic
964C22C23×#52511yescharacteristic
965C22C2×C23×#12411yescharacteristic
966C22C23×#52911yescharacteristic
967C22C23×#52911yescharacteristic
968C22C23×#53211yescharacteristic
969C22C23×#53311yescharacteristic
970C22C23×#53311yescharacteristic
971C22C23×#53811yescharacteristic
972C22C23×#53911yescharacteristic
973C22C23×#54011yescharacteristic
974C22C23×#54211yescharacteristic
975C22D42×C2311yescharacteristic
976C22C23×#54611yescharacteristic
977C22C23×#54611yescharacteristic
978C22C23×#54611yescharacteristic
979C22C23×#54611yescharacteristic
980C22C23×#54711yescharacteristic
981C22D4×Q8×C2311yescharacteristic
982C22C23×#55111yescharacteristic
983C22C23×#55211yescharacteristic
984C22C23×#55311yescharacteristic
985C22C23×#55311yescharacteristic
986C22C23×#55311yescharacteristic
987C22C23×#55411yescharacteristic
988C22C23×#55411yescharacteristic
989C22C23×#55411yescharacteristic
990C22C23×#55611yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C23×#229611yescharacteristic
1007C2C4×C23×#12411yescharacteristic
1008C2C23×#233511yescharacteristic
1009C2D4×C4⋊C4×C2311yescharacteristic
1010C2C23×#234911yescharacteristic
1011C2C23×#236411yescharacteristic
1012C2C23×#237311yescharacteristic
1013C2C23×#246411yescharacteristic
1014C2C23×#246611yescharacteristic
1015C2C23×#247011yescharacteristic
1016C2C23×#247211yescharacteristic
1017C2C23×#249211yescharacteristic
1018C2C23×#252211yescharacteristic
1019C2C23×#255611yescharacteristic
1020C2C23×#258711yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC25×C23C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#389C2semidirect
6. C23×#1442C2semidirect
7. C23×#1441C2semidirect
10. C23×#1436C2semidirect
11. C23×#1436C2semidirect
12. C23×#1436C2semidirect
13. C23×C4⋊#95C2semidirect
15. C4×C23×#95C2semidirect
35. C23×#388C4semidirect
95. C2×C4⋊C4×C23C2×C4semidirect
125. C2×C42×C23C2×C4semidirect
141. C23×#95C2×C4semidirect
142. C23×#95C2×C4semidirect
276. C22⋊C4×C23C4⋊C4semidirect
281. #14116C23direct (N × H)
431. C2×#389C2×C23semidirect
436. #1442C2×C23semidirect
437. #1441C2×C23semidirect
440. #1436C2×C23semidirect
441. #1436C2×C23semidirect
442. #1436C2×C23semidirect
443. C4⋊#95C2×C23semidirect
445. C4×#95C2×C23semidirect
529. #388C4×C23semidirect
605. C2×C4⋊C4C2×C4×C23semidirect
635. C2×C42C2×C4×C23semidirect
651. #95C2×C4×C23semidirect
652. #95C2×C4×C23semidirect
654. C23#14116direct (N × H)
787. C22⋊C4C4⋊C4×C23semidirect

Maximal subgroups

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

subgroupindex
C2×C23×#3892
C2×C23×#3882
C2×C23×#3852
C2×C4×C22⋊C4×C232
C23×#14422
C23×#14412
C23×#14392
C23×#14362
C23×C4⋊#952
C23×C22⋊#952
C4×C23×#952
#1411623