Finite Group Databasebeta

← C23×#14112 #19161738

Subgroups — C23×#14112 #19161738

Order 5888.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 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×C23×#385C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C23C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C23C211yesmaximal, characteristic
8C23×#1444C211yesmaximal, characteristic, complemented
9C23×#1441C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic
11C23×#1439C211yesmaximal, characteristic
12C23×#1436C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×#1436C211yesmaximal, characteristic, complemented
15C23×C4⋊#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×C4⋊C4×C23C2211yescharacteristic
24C22×C4⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C42×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C22×C42×C23C2211yescharacteristic
34C22×C42×C23C2211yescharacteristic
35C23×#389—24no—
36C23×#388—24no—
37C23×#388C418yescomplemented
38C23×#385—24no—
39C23×#385—24no—
40C4×C4⋊C4×C23—24no—
41C4×C22⋊C4×C23—24no—
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
56C2×C23×#95C2211yescharacteristic
57C2×C23×#95C2211yescharacteristic
58C25×C23C2311yescharacteristic
59C23×C4×C23—22no—
60C23×C4×C23—22no—
61C23×C4×C23—22no—
62C23×C4×C23—22no—
63C23×C4×C23—22no—
64C23×C4×C23—41no—
65C23×C4×C23—41no—
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
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
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—22no—
92C2×C4⋊C4×C23—22no—
93C2×C4⋊C4×C23—22no—
94C2×C4⋊C4×C23—22no—
95C2×C4⋊C4×C23—22no—
96C2×C4⋊C4×C23—22no—
97C2×C4⋊C4×C23—22no—
98C2×C4⋊C4×C23—41no—
99C2×C4⋊C4×C23—41no—
100C2×C4⋊C4×C23—41no—
101C2×C4⋊C4×C23—41no—
102C2×C4⋊C4×C23C2×C414yescomplemented
103C2×C4⋊C4×C23D414yes—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—22no—
110C2×C22⋊C4×C23—22no—
111C2×C22⋊C4×C23—22no—
112C2×C22⋊C4×C23—22no—
113C2×C22⋊C4×C23—22no—
114C2×C22⋊C4×C23—22no—
115C2×C22⋊C4×C23—41no—
116C2×C22⋊C4×C23—41no—
117C2×C22⋊C4×C23C2×C414yes—
118C2×C22⋊C4×C23C2×C414yes—
119C2×C22⋊C4×C23C2×C414yes—
120C2×C22⋊C4×C23D414yes—
121C2×C22⋊C4×C23Q814yes—
122C2×C42×C23—22no—
123C2×C42×C23—22no—
124C2×C42×C23—22no—
125C2×C42×C23—22no—
126C2×C42×C23—22no—
127C2×C42×C23—22no—
128C2×C42×C23—22no—
129C2×C42×C23—22no—
130C2×C42×C23—41no—
131C2×C42×C23—41no—
132C2×C42×C23—41no—
133C2×C42×C23C2×C414yescomplemented
134C23×#95—22no—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—22no—
142C23×#95—22no—
143C23×#95—22no—
144C23×#95—22no—
145C23×#95—22no—
146C23×#95—41no—
147C23×#95C2×C414yescomplemented
148C23×#95C2×C414yescomplemented
149C23×#95D414yes—
150C24×C23—21no—
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—21no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—21no—
161C24×C23—21no—
162C24×C23C22×C412yes—
163C24×C23C2×D412yes—
164C24×C23C2×Q812yes—
165C24×C23C2411yescharacteristic
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—21no—
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—28no—
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—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—44no—
244C22×C4×C23—44no—
245C22×C4×C23—44no—
246C22×C4×C23—44no—
247C22×C4×C23—44no—
248C22×C4×C23—44no—
249C22×C4×C23C22×C412yes—
250C22×C4×C23C22×C412yes—
251C22×C4×C23C22×C412yes—
252C22×C4×C23C22×C412yes—
253C22×C4×C23C22×C412yes—
254C22×C4×C23C22×C412yes—
255C22×C4×C23C2×D412yes—
256C22×C4×C23C2×D412yes—
257C22×C4×C23C2×D412yes—
258C22×C4×C23C2×D412yes—
259C22×C4×C23C2×D412yes—
260C22×C4×C23C2×D412yes—
261C22×C4×C23C2×D412yes—
262C22×C4×C23C2×D412yes—
263C22×C4×C23C2×Q812yes—
264C22×C4×C23C2×Q812yes—
265C22×C4×C23#4112yes—
266C22×C4×C23#4112yes—
267C22×C4×C23#4112yes—
268C22×C4×C23#4112yes—
269C22×C4×C23#4112yes—
270C22×C4×C23#4112yes—
271C4⋊C4×C23—28no—
272C4⋊C4×C23—28no—
273C4⋊C4×C23—28no—
274C4⋊C4×C23—44no—
275C4⋊C4×C23—44no—
276C4⋊C4×C23—44no—
277C4⋊C4×C23—44no—
278C4⋊C4×C23—44no—
279C22⋊C4×C23—28no—
280C22⋊C4×C23—28no—
281C22⋊C4×C23—28no—
282C22⋊C4×C23—44no—
283C22⋊C4×C23—44no—
284C22⋊C4×C23C4⋊C4116yescomplemented
285C42×C23—28no—
286C42×C23—44no—
287C42×C23—44no—
288C42×C23—44no—
289#14112C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
301C23×C23—22no—
302C23×C23—22no—
303C23×C23—22no—
304C23×C23—22no—
305C23×C23—22no—
306C23×C23—22no—
307C23×C23—22no—
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×C23—41no—
317C23×C23—41no—
318C23×C23—41no—
319C23×C23—41no—
320C23×C23—41no—
321C23×C23—41no—
322C23×C23—41no—
323C23×C23—41no—
324C23×C23C2×C4⋊C414yes—
325C23×C23C23×C411yescharacteristic
326C23×C23C22×D411yescharacteristic
327C23×C23C22×D411yescharacteristic
328C23×C23C22×D411yescharacteristic
329C23×C23C22×Q811yescharacteristic
330C23×C23C2×#4111yescharacteristic
331C23×C23C2×#4111yescharacteristic
332C23×C23C2×#4111yescharacteristic
333C23×C23C2×#4111yescharacteristic
334C23×C23C2×#4111yescharacteristic
335C23×C23C2×#4111yescharacteristic
336C23×C23H(5,𝔽2)11yescharacteristic
337C23×C23H(5,𝔽2)11yescharacteristic
338C23×C232−1+411yescharacteristic
339C23×C232−1+411yescharacteristic
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—22no—
381C2×C4×C23—22no—
382C2×C4×C23—22no—
383C2×C4×C23—22no—
384C2×C4×C23—22no—
385C2×C4×C23—22no—
386C2×C4×C23—22no—
387C2×C4×C23—22no—
388C2×C4×C23—22no—
389C2×C4×C23—22no—
390C2×C4×C23—22no—
391C2×C4×C23—416no—
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×C23—41no—
428C2×C4×C23—41no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—41no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23C2×C4⋊C414yes—
435C2×C4×C23C2×C4⋊C414yes—
436C2×C4×C23C4×D414yes—
437C2×C4×C23C4×D414yes—
438C2×C4×C23#12114yes—
439C2×#389C2×C2311yescharacteristic, complemented
440C2×#388C2×C2311yescharacteristic
441C2×#388C2×C2311yescharacteristic
442C2×#385C2×C2311yescharacteristic
443C2×#385C2×C2311yescharacteristic
444C2×C4×C4⋊C4C2×C2311yescharacteristic, complemented
445C2×C4×C22⋊C4C2×C2311yescharacteristic
446#1444C2×C2311yescharacteristic, complemented
447#1441C2×C2311yescharacteristic, complemented
448#1439C2×C2311yescharacteristic
449#1439C2×C2311yescharacteristic
450#1436C2×C2311yescharacteristic, complemented
451#1436C2×C2311yescharacteristic, complemented
452#1436C2×C2311yescharacteristic, complemented
453C4⋊#95C2×C2311yescharacteristic, complemented
454C22×C23—24no—
455C22×C23—24no—
456C22×C23—24no—
457C22×C23—42no—
458C22×C23—42no—
459C22×C23—42no—
460C22×C23—42no—
461C22×C23—42no—
462C22×C23—42no—
463C22×C23—42no—
464C22×C23—42no—
465C22×C23—42no—
466C22×C23—42no—
467C22×C23—42no—
468C22×C23—42no—
469C22×C23C22×C4⋊C411yescharacteristic
470C22×C23C2×C4×D411yescharacteristic
471C22×C23C2×C4×D411yescharacteristic
472C22×C23C4×#4111yescharacteristic
473C22×C23C4×#4111yescharacteristic
474C22×C23#52011yescharacteristic
475C22×C23#52011yescharacteristic
476C22×C23C2×#12111yescharacteristic
477C22×C23#52511yescharacteristic
478C22×C23#52511yescharacteristic
479C22×C23#52511yescharacteristic
480C22×C23#52911yescharacteristic
481C22×C23#53211yescharacteristic
482C22×C23#53311yescharacteristic
483C22×C23#53311yescharacteristic
484C22×C23#53811yescharacteristic
485C22×C23#53911yescharacteristic
486C22×C23#54111yescharacteristic
487C22×C23#54211yescharacteristic
488C22×C23D4211yescharacteristic
489C22×C23D4211yescharacteristic
490C22×C23#54611yescharacteristic
491C22×C23#54611yescharacteristic
492C22×C23#54711yescharacteristic
493C22×C23#54711yescharacteristic
494C22×C23#54711yescharacteristic
495C22×C23#54811yescharacteristic
496C22×C23D4×Q811yescharacteristic
497C22×C23D4×Q811yescharacteristic
498C22×C23#55111yescharacteristic
499C22×C23#55211yescharacteristic
500C22×C23#55411yescharacteristic
501C22×C23#55411yescharacteristic
502C22×C23#55611yescharacteristic
503C22×C23#55911yescharacteristic
504C4×C23—24no—
505C4×C23—24no—
506C4×C23—24no—
507C4×C23—24no—
508C4×C23—24no—
509C4×C23—42no—
510C4×C23—42no—
511C4×C23—42no—
512C4×C23—42no—
513C4×C23—42no—
514C4×C23—42no—
515C4×C23—42no—
516C4×C23—81no—
517C4×C23—81no—
518C24×C4C22×C2311yescharacteristic
519C22×C4⋊C4C22×C2311yescharacteristic
520C22×C4⋊C4C22×C2311yescharacteristic
521C22×C4⋊C4C22×C2311yescharacteristic
522C22×C4⋊C4C22×C2311yescharacteristic
523C22×C4⋊C4C22×C2311yescharacteristic
524C22×C4⋊C4C22×C2311yescharacteristic
525C22×C4⋊C4C22×C2311yescharacteristic
526C22×C4⋊C4C22×C2311yescharacteristic
527C22×C22⋊C4C22×C2311yescharacteristic
528C22×C22⋊C4C22×C2311yescharacteristic
529C22×C22⋊C4C22×C2311yescharacteristic
530C22×C22⋊C4C22×C2311yescharacteristic
531C22×C22⋊C4C22×C2311yescharacteristic
532C22×C22⋊C4C22×C2311yescharacteristic
533C22×C42C22×C2311yescharacteristic
534C22×C42C22×C2311yescharacteristic
535C22×C42C22×C2311yescharacteristic
536C22×C42C22×C2311yescharacteristic
537#389—24no—
538#388—24no—
539#388C4×C2318yescomplemented
540#385—24no—
541#385—24no—
542C4×C4⋊C4—24no—
543C4×C22⋊C4—24no—
544C2×#95C22×C2311yescharacteristic
545C2×#95C22×C2311yescharacteristic
546C2×#95C22×C2311yescharacteristic
547C2×#95C22×C2311yescharacteristic
548C2×#95C22×C2311yescharacteristic
549C2×#95C22×C2311yescharacteristic
550C2×#95C22×C2311yescharacteristic
551C2×#95C22×C2311yescharacteristic
552C2×#95C22×C2311yescharacteristic
553C2×#95C22×C2311yescharacteristic
554C2×#95C22×C2311yescharacteristic
555C2×#95C22×C2311yescharacteristic
556C2×#95C22×C2311yescharacteristic
557C2×#95C22×C2311yescharacteristic
558C2×#95C22×C2311yescharacteristic
559C2×#95C22×C2311yescharacteristic
560C2×C23—44no—
561C2×C23#229611yescharacteristic
562C2×C23C4×#12111yescharacteristic
563C2×C23#233411yescharacteristic
564C2×C23D4×C4⋊C411yescharacteristic
565C2×C23D4×C4⋊C411yescharacteristic
566C2×C23#235911yescharacteristic
567C2×C23#236711yescharacteristic
568C2×C23#242411yescharacteristic
569C2×C23#242911yescharacteristic
570C2×C23#245511yescharacteristic
571C2×C23#246111yescharacteristic
572C2×C23#246511yescharacteristic
573C2×C23#247811yescharacteristic
574C2×C23#255611yescharacteristic
575C2×C23#258911yescharacteristic
576C25C23×C2311yescharacteristic
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4C23×C2311yescharacteristic
585C23×C4C23×C2311yescharacteristic
586C23×C4C23×C2311yescharacteristic
587C23×C4C23×C2311yescharacteristic
588C23×C4C23×C2311yescharacteristic
589C23×C4C23×C2311yescharacteristic
590C23×C4C23×C2311yescharacteristic
591C23×C4C23×C2311yescharacteristic
592C23×C4C23×C2311yescharacteristic
593C23×C4C23×C2311yescharacteristic
594C23×C4C23×C2311yescharacteristic
595C23×C4C23×C2311yescharacteristic
596C23×C4C23×C2311yescharacteristic
597C23×C4C23×C2311yescharacteristic
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4C2×C4×C2314yescomplemented
621C2×C4⋊C4D4×C2314yes—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4C2×C4×C2314yes—
636C2×C22⋊C4C2×C4×C2314yes—
637C2×C22⋊C4C2×C4×C2314yes—
638C2×C22⋊C4D4×C2314yes—
639C2×C22⋊C4Q8×C2314yes—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—41no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42C2×C4×C2314yescomplemented
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—41no—
665#95C2×C4×C2314yescomplemented
666#95C2×C4×C2314yescomplemented
667#95D4×C2314yes—
668C23#1411211yescharacteristic, direct product factor, Sylow
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C2312yes—
682C24C2×D4×C2312yes—
683C24C2×Q8×C2312yes—
684C24C24×C2311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
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—28no—
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—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C2312yes—
769C22×C4C22×C4×C2312yes—
770C22×C4C22×C4×C2312yes—
771C22×C4C22×C4×C2312yes—
772C22×C4C22×C4×C2312yes—
773C22×C4C22×C4×C2312yes—
774C22×C4C2×D4×C2312yes—
775C22×C4C2×D4×C2312yes—
776C22×C4C2×D4×C2312yes—
777C22×C4C2×D4×C2312yes—
778C22×C4C2×D4×C2312yes—
779C22×C4C2×D4×C2312yes—
780C22×C4C2×D4×C2312yes—
781C22×C4C2×D4×C2312yes—
782C22×C4C2×Q8×C2312yes—
783C22×C4C2×Q8×C2312yes—
784C22×C4#41×C2312yes—
785C22×C4#41×C2312yes—
786C22×C4#41×C2312yes—
787C22×C4#41×C2312yes—
788C22×C4#41×C2312yes—
789C22×C4#41×C2312yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C4⋊C4×C23116yescomplemented
804C42—28no—
805C42—44no—
806C42—44no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C2314yes—
843C23C23×C4×C2311yescharacteristic
844C23C22×D4×C2311yescharacteristic
845C23C22×D4×C2311yescharacteristic
846C23C22×D4×C2311yescharacteristic
847C23C22×Q8×C2311yescharacteristic
848C23C2×#41×C2311yescharacteristic
849C23C2×#41×C2311yescharacteristic
850C23C2×#41×C2311yescharacteristic
851C23C2×#41×C2311yescharacteristic
852C23C2×#41×C2311yescharacteristic
853C23C2×#41×C2311yescharacteristic
854C23C23×H(5,𝔽2)11yescharacteristic
855C23C23×H(5,𝔽2)11yescharacteristic
856C23C23×2−1+411yescharacteristic
857C23C23×2−1+411yescharacteristic
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—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—416no—
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×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4C2×C4⋊C4×C2314yes—
953C2×C4C2×C4⋊C4×C2314yes—
954C2×C4C4×D4×C2314yes—
955C2×C4C4×D4×C2314yes—
956C2×C4C23×#12114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C2311yescharacteristic
973C22C2×C4×D4×C2311yescharacteristic
974C22C2×C4×D4×C2311yescharacteristic
975C22C4×#41×C2311yescharacteristic
976C22C4×#41×C2311yescharacteristic
977C22C23×#52011yescharacteristic
978C22C23×#52011yescharacteristic
979C22C2×C23×#12111yescharacteristic
980C22C23×#52511yescharacteristic
981C22C23×#52511yescharacteristic
982C22C23×#52511yescharacteristic
983C22C23×#52911yescharacteristic
984C22C23×#53211yescharacteristic
985C22C23×#53311yescharacteristic
986C22C23×#53311yescharacteristic
987C22C23×#53811yescharacteristic
988C22C23×#53911yescharacteristic
989C22C23×#54111yescharacteristic
990C22C23×#54211yescharacteristic
991C22D42×C2311yescharacteristic
992C22D42×C2311yescharacteristic
993C22C23×#54611yescharacteristic
994C22C23×#54611yescharacteristic
995C22C23×#54711yescharacteristic
996C22C23×#54711yescharacteristic
997C22C23×#54711yescharacteristic
998C22C23×#54811yescharacteristic
999C22D4×Q8×C2311yescharacteristic
1000C22D4×Q8×C2311yescharacteristic
1001C22C23×#55111yescharacteristic
1002C22C23×#55211yescharacteristic
1003C22C23×#55411yescharacteristic
1004C22C23×#55411yescharacteristic
1005C22C23×#55611yescharacteristic
1006C22C23×#55911yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C23×#229611yescharacteristic
1023C2C4×C23×#12111yescharacteristic
1024C2C23×#233411yescharacteristic
1025C2D4×C4⋊C4×C2311yescharacteristic
1026C2D4×C4⋊C4×C2311yescharacteristic
1027C2C23×#235911yescharacteristic
1028C2C23×#236711yescharacteristic
1029C2C23×#242411yescharacteristic
1030C2C23×#242911yescharacteristic
1031C2C23×#245511yescharacteristic
1032C2C23×#246111yescharacteristic
1033C2C23×#246511yescharacteristic
1034C2C23×#247811yescharacteristic
1035C2C23×#255611yescharacteristic
1036C2C23×#258911yescharacteristic
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. C2×C4×C4⋊C4×C23C2semidirect
8. C23×#1444C2semidirect
9. C23×#1441C2semidirect
12. C23×#1436C2semidirect
13. C23×#1436C2semidirect
14. C23×#1436C2semidirect
15. C23×C4⋊#95C2semidirect
37. C23×#388C4semidirect
102. C2×C4⋊C4×C23C2×C4semidirect
133. C2×C42×C23C2×C4semidirect
147. C23×#95C2×C4semidirect
148. C23×#95C2×C4semidirect
284. C22⋊C4×C23C4⋊C4semidirect
289. #14112C23direct (N × H)
439. C2×#389C2×C23semidirect
444. C2×C4×C4⋊C4C2×C23semidirect
446. #1444C2×C23semidirect
447. #1441C2×C23semidirect
450. #1436C2×C23semidirect
451. #1436C2×C23semidirect
452. #1436C2×C23semidirect
453. C4⋊#95C2×C23semidirect
539. #388C4×C23semidirect
620. C2×C4⋊C4C2×C4×C23semidirect
651. C2×C42C2×C4×C23semidirect
665. #95C2×C4×C23semidirect
666. #95C2×C4×C23semidirect
668. C23#14112direct (N × H)
803. 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×C4⋊C4×C232
C2×C4×C22⋊C4×C232
C23×#14442
C23×#14412
C23×#14392
C23×#14362
C23×C4⋊#952
#1411223