Finite Group Databasebeta

← #14917041

Subgroups — #14917041

Order 2816.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic
2#13071762C212yesmaximal, complemented
3#13071762C212yesmaximal, complemented
4#13071742C212yesmaximal, complemented
5#13071730C212yesmaximal, complemented
6#13071586C212yesmaximal, complemented
7#13071551C212yesmaximal, complemented
8#13071497C212yesmaximal, complemented
9#13071471C212yesmaximal, complemented
10#13071428C212yesmaximal, complemented
11#13071419C212yesmaximal, complemented
12#13071381C211yesmaximal, characteristic
13#13071378C211yesmaximal, characteristic
14#13071374C211yesmaximal, characteristic, complemented
15#13071261C212yesmaximal, complemented
16#13071248C212yesmaximal, complemented
17#13071010C211yesmaximal, characteristic, complemented
18#13071007C211yesmaximal, characteristic, complemented
19C11×#2332C211yesmaximal, characteristic, complemented
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25#10623155C4116yescomplemented
26C2×#66951C2212yes—
27C2×#66946C2211yescharacteristic
28C2×#66945C2212yes—
29C2×#66943C2211yescharacteristic
30C2×#66939C2212yes—
31C2×(C22⋊D11)⋊C4C2212yes—
32C11×#391C2212yes—
33C11×#388C2212yes—
34C11×#388C2212yes—
35C11×#387C2212yes—
36C11×#387C2212yes—
37C11×#381C2211yescharacteristic
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C22⋊C4C2211yescharacteristic
40#10622843C2212yes—
41#10622824C2211yescharacteristic
42C4×C22⋊Dic11C2211yescharacteristic
43#10622603C2212yes—
44#10622602C2212yes—
45#10622602C2212yes—
46#10622600C2212yes—
47#10622594C2212yes—
48#10622594C2212yes—
49#10622591C2212yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2212yes—
52#10622586C2212yes—
53#10622586C2212yes—
54#10622570C2212yes—
55#10622570C2212yes—
56#10622569C2212yes—
57#10622569C2212yes—
58#10622564C2212yes—
59#10622564C2212yes—
60#10622556C2212yes—
61#10622555C2211yescharacteristic
62#10622555C2211yescharacteristic
63#10622555C2212yes—
64C22⋊C4×Dic11C2211yescharacteristic
65C22⋊C4×Dic11C2211yescharacteristic
66#10622553C2212yes—
67#10622553C2212yes—
68#10622553C2212yes—
69C4×(C2×D11)⋊C4C2212yes—
70C4×(C2×D11)⋊C4C2212yes—
71C4×(C2×D11)⋊C4C2212yes—
72#10622545C2211yescharacteristic
73#10622545C2211yescharacteristic
74#10622545C2212yes—
75C4×Dic11⋊C4C2212yes—
76C4×Dic11⋊C4C2211yescharacteristic
77C4×Dic11⋊C4C2211yescharacteristic
78#10622541C2212yes—
79#10622541C2212yes—
80#10622283C2212yes—
81#10622282C2212yes—
82#10622282C2212yes—
83#10622282C2212yes—
84#10622281C2212yes—
85#10622281C2212yes—
86#10622279C2212yes—
87#10622279C2212yes—
88#10622278C2212yes—
89#10622278C2212yes—
90#10622277C2212yes—
91D11×#95C2212yes—
92#10622268C2212yes—
93#10622267C2212yes—
94#10622267C2212yes—
95#10622267C2212yes—
96#10622266C2212yes—
97#10622266C2212yes—
98#10622266C2212yes—
99#10622264C2212yes—
100#10622264C2212yes—
101#10622264C2212yes—
102#10622263C2212yes—
103#10622263C2212yes—
104#10622263C2212yes—
105#10622262C2212yes—
106#10622262C2212yes—
107#10622261C2212yes—
108C22×Q8×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11C2312yes—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C22×D44C2311yescharacteristic
114C22×C4×D11C2312yes—
115C22×C4×D11C2312yes—
116C22×C4×D11C2312yes—
117C11×C22⋊Q8C2×C418yescomplemented
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C22⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C42×C11C2312yes—
127C2×C42×C11C2312yes—
128C2×C42×C11C2311yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C2×C22⋊Dic11C2311yescharacteristic
131C2×C22⋊Dic11C2311yescharacteristic
132C2×C22⋊Dic11C2312yes—
133#67000C2×C418yes—
134Q8×Dic11C2×C418yescomplemented
135#66983C2×C418yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2312yes—
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×C4×Dic11C2×C418yescomplemented
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2311yescharacteristic
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2311yescharacteristic
169C2×C4×Dic11C2311yescharacteristic
170C2×C4×Dic11C2311yescharacteristic
171C2×C4×Dic11C2311yescharacteristic
172#66951C2×C4116yescomplemented
173#66946C2×C418yes—
174#66945C2×C4116yescomplemented
175#66943C2×C418yescomplemented
176#66939C2×C4116yescomplemented
177(C22⋊D11)⋊C4C2×C4116yescomplemented
178C11×#95C2312yes—
179C11×#95C2312yes—
180C11×#95C2312yes—
181C11×#95C2312yes—
182C11×#95C2312yes—
183C11×#95C2312yes—
184C11×#95C2312yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206#34400—111nomaximal, Sylow
207C24×C11C2411yescharacteristic
208C23×D11C2412yes—
209C2×Q8×C11—41no—
210C2×Q8×C11—41no—
211C2×Q8×C11C22×C414yes—
212C22×C4×C11—41no—
213C22×C4×C11—41no—
214C22×C4×C11C22×C414yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C2×C22⋊D11—42no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11C22×C418yes—
226C22×Dic11—42no—
227C22×Dic11—42no—
228C22×Dic11C22×C414yes—
229C22×Dic11C22×C414yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2411yescharacteristic
235C22×Dic11C2411yescharacteristic
236C22×Dic11C2412yes—
237C22×Dic11C2411yescharacteristic
238C22×Dic11C2411yescharacteristic
239C2×D44—41no—
240C2×D44—41no—
241C2×D44C22×C414yes—
242C2×C4×D11—42no—
243C2×C4×D11—42no—
244C2×C4×D11—42no—
245C2×C4×D11—42no—
246C2×C4×D11—42no—
247C2×C4×D11—42no—
248C2×C4×D11—42no—
249C2×C4×D11—42no—
250C2×C4×D11C22×C418yes—
251C11×C4⋊C4—42no—
252C11×C4⋊C4—42no—
253C11×C4⋊C4C22×C414yes—
254C11×C4⋊C4C22×C418yes—
255C11×C22⋊C4—41no—
256C11×C22⋊C4—42no—
257C11×C22⋊C4—41no—
258C11×C22⋊C4C22×C418yes—
259C42×C11—41no—
260C42×C11—41no—
261C42×C11—42no—
262C42×C11—42no—
263C22⋊Dic11—42no—
264C22⋊Dic11—41no—
265C22⋊Dic11—41no—
266(C2×D11)⋊C4—42no—
267(C2×D11)⋊C4—42no—
268(C2×D11)⋊C4—42no—
269(C2×D11)⋊C4—42no—
270(C2×D11)⋊C4—42no—
271(C2×D11)⋊C4—42no—
272(C2×D11)⋊C4C22×C418yes—
273(C2×D11)⋊C4C22×C418yes—
274(C2×D11)⋊C4C22×C418yes—
275(C2×D11)⋊C4C22×C418yes—
276C4⋊Dic11—42no—
277C4⋊Dic11—42no—
278C4⋊Dic11C22×C418yes—
279C4⋊Dic11C22×C418yes—
280C4⋊Dic11C22×C414yes—
281Dic11⋊C4—42no—
282Dic11⋊C4—42no—
283Dic11⋊C4—42no—
284Dic11⋊C4—42no—
285Dic11⋊C4—42no—
286Dic11⋊C4—42no—
287Dic11⋊C4C22×C418yes—
288C4×Dic11—41no—
289C4×Dic11—41no—
290C4×Dic11—42no—
291C4×Dic11—42no—
292C4×Dic11—42no—
293C4×Dic11—42no—
294C4×Dic11—42no—
295C4×Dic11—42no—
296C4×Dic11C22×C418yes—
297C4×Dic11C22×C414yes—
298C4×Dic11C22×C414yes—
299C4×Dic11C22×C414yes—
300C4×Dic11C22×C414yes—
301C2×#529—111no—
302#2376—112no—
303#2376—112no—
304#2373—112no—
305#2373—112no—
306#2357—112no—
307#2353—112no—
308#2346—112no—
309#2343—112no—
310#2337—112no—
311#2336—112no—
312#2333—111no—
313#2333—111no—
314#2332—111no—
315#2332D1111yescharacteristic, complemented
316#2320—112no—
317#2318—112no—
318#2283—111no—
319#2283—111no—
320C23×C11—22no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—22no—
324C23×C11C23×C412yes—
325C23×C11C2511yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11C23×C414yes—
333Q8×C11—44no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—44no—
355C2×C4×C11C23×C412yes—
356C2×C4×C11C23×C412yes—
357C2×C4×C11C23×C414yes—
358C2×C4×C11C23×C414yes—
359C22⋊D11—48no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—44no—
379C2×Dic11—44no—
380C2×Dic11C23×C412yes—
381C2×Dic11C23×C412yes—
382C2×Dic11C23×C412yes—
383C2×Dic11C23×C412yes—
384C2×Dic11C23×C414yes—
385D44—44no—
386C4×D11—48no—
387C4×D11—84no—
388C4×D11—84no—
389#529—1116no—
390C2×#126—112no—
391C2×#125—111no—
392C2×#124—111no—
393C2×#123—112no—
394C2×C22⋊Q8C2×D1111yescharacteristic
395C2×#121—111no—
396C2×C4×Q8—111no—
397C2×C4×D4—111no—
398C2×C4×D4—112no—
399C2×#117—112no—
400C22×C42—111no—
401#391—112no—
402#391C2×D1112yes—
403#390—112no—
404#390—112no—
405#389—112no—
406#389—112no—
407#389—112no—
408#389—112no—
409#388—112no—
410#388—112no—
411#388—112no—
412#388—112no—
413#388—112no—
414#388—112no—
415#388—112no—
416#388—112no—
417#388—112no—
418#388—112no—
419#388C2×D1112yes—
420#388C2×D1112yes—
421#387—112no—
422#387—112no—
423#387—112no—
424#387—112no—
425#387—112no—
426#387—112no—
427#387—112no—
428#387—112no—
429#387—112no—
430#387—112no—
431#387C2×D1112yes—
432#387C2×D1112yes—
433#386—112no—
434#386—112no—
435#386—112no—
436#386—112no—
437#385—112no—
438#385—112no—
439#385—112no—
440#385—112no—
441#383—112no—
442#383—112no—
443#383—112no—
444#382—112no—
445#382—112no—
446#382—112no—
447#381—111no—
448#381—112no—
449#381—112no—
450#381C2×D1111yescharacteristic
451#380—112no—
452#380—112no—
453#380—111no—
454#380—111no—
455C4×C4⋊C4—112no—
456C4×C4⋊C4—112no—
457C4×C4⋊C4—112no—
458C4×C4⋊C4—111no—
459C4×C4⋊C4—111no—
460C4×C4⋊C4—112no—
461C4×C4⋊C4—112no—
462C4×C4⋊C4C2×D1112yes—
463C4×C22⋊C4—111no—
464C4×C22⋊C4—111no—
465C4×C22⋊C4—111no—
466C4×C22⋊C4—112no—
467C4×C22⋊C4—112no—
468C4×C22⋊C4—112no—
469C4×C22⋊C4—112no—
470C4×C22⋊C4—112no—
471C4×C22⋊C4C2×D1111yescharacteristic
472#376—112no—
473#376—111no—
474#376—111no—
475#376—112no—
476C2×#95—112no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11C24×C411yescharacteristic
483C22×C11#58512yes—
484C22×C11#58511yescharacteristic
485C22×C11#58511yescharacteristic
486C22×C11#58512yes—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C4×C11—22no—
495C4×C11—22no—
496C4×C11—24no—
497C4×C11—24no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—42no—
502Dic11—22no—
503Dic11—22no—
504Dic11—22no—
505Dic11—22no—
506Dic11—24no—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511C22×Q8C22×D1111yescharacteristic
512C22×D4—112no—
513C22×D4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—112no—
517C23×C4—112no—
518C23×C4—112no—
519C23×C4C22×D1111yescharacteristic
520#126—1116no—
521#125—118no—
522#124—118no—
523#123—1116no—
524C22⋊Q8C4×D1118yescomplemented
525#121—118no—
526C4×Q8—118no—
527C4×D4—118no—
528C4×D4—1116no—
529#117—1116no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4C22×D1112yes—
543C2×C4⋊C4C22×D1112yes—
544C2×C4⋊C4C22×D1112yes—
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C22⋊C4—112no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—111no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4C22×D1111yescharacteristic
560C2×C22⋊C4C22×D1111yescharacteristic
561C2×C22⋊C4C22×D1112yes—
562C2×C22⋊C4C22×D1112yes—
563C2×C42—118no—
564C2×C42—111no—
565C2×C42—112no—
566C2×C42—111no—
567C2×C42—111no—
568C2×C42—111no—
569C2×C42—112no—
570C2×C42—111no—
571C2×C42—112no—
572C2×C42—111no—
573C2×C42—112no—
574C2×C42—112no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42C22×D1111yescharacteristic
578C2×C42C22×D1112yes—
579C2×C42C22×D1111yescharacteristic
580C2×C42C22×D1112yes—
581#95—112no—
582#95—112no—
583#95—112no—
584#95—112no—
585#95—112no—
586#95—112no—
587#95—112no—
588#95—112no—
589#95—112no—
590#95—112no—
591#95—112no—
592#95—112no—
593#95—112no—
594#95—112no—
595#95—112no—
596#95—112no—
597#95—112no—
598#95—112no—
599#95—112no—
600#95—112no—
601#95—112no—
602#95C22×D1112yes—
603#95C22×D1112yes—
604#95C22×D1112yes—
605#95C22×D1112yes—
606#95C22×D1112yes—
607#95C22×D1112yes—
608#95C22×D1112yes—
609C2×C11—42no—
610C2×C11#342811yescharacteristic
611C2×C11#342811yescharacteristic
612C2×C11#342811yescharacteristic
613C2×C11#356612yes—
614C2×C11#356612yes—
615D11—44no—
616C24—112no—
617C24C23×D1111yescharacteristic
618C2×Q8—41no—
619C2×Q8—41no—
620C2×Q8C2×C4×D1114yes—
621C2×D4—118no—
622C2×D4—114no—
623C2×D4—441no—
624C2×D4—441no—
625C2×D4—442no—
626C2×D4—442no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—112no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—114no—
635C22×C4—114no—
636C22×C4—118no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—442no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4—442no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4C2×C4×D1114yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1111yescharacteristic
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—118no—
663C4⋊C4—118no—
664C4⋊C4—114no—
665C4⋊C4—118no—
666C4⋊C4—442no—
667C4⋊C4—442no—
668C4⋊C4—442no—
669C4⋊C4—442no—
670C4⋊C4—442no—
671C4⋊C4—442no—
672C4⋊C4—442no—
673C4⋊C4—442no—
674C4⋊C4C2×C4×D1118yes—
675C4⋊C4C2×C4×D1114yes—
676C22⋊C4—42no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—118no—
680C22⋊C4—118no—
681C22⋊C4—118no—
682C22⋊C4—118no—
683C22⋊C4—442no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C22⋊C4—442no—
689C22⋊C4—442no—
690C22⋊C4—441no—
691C22⋊C4—441no—
692C22⋊C4C2×C4×D1118yes—
693C42—42no—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—114no—
698C42—114no—
699C42—114no—
700C42—114no—
701C42—118no—
702C42—442no—
703C42—441no—
704C42—441no—
705C42—442no—
706C42—442no—
707C42—442no—
708C42—442no—
709C42—442no—
710C11#3440011yescharacteristic, complemented, Sylow
711C23—22no—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—114no—
716C23—222no—
717C23—222no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23C22×C4×D1112yes—
723C23C24×D1111yescharacteristic
724Q8—44no—
725D4—444no—
726D4—448no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—44no—
748C2×C4—112no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—112no—
752C2×C4—114no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—448no—
772C2×C4—444no—
773C2×C4—444no—
774C2×C4—884no—
775C2×C4—884no—
776C2×C4C22×C4×D1112yes—
777C2×C4C22×C4×D1112yes—
778C2×C4C22×C4×D1114yes—
779C2×C4C22×C4×D1114yes—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—42no—
784C22—42no—
785C22—224no—
786C22—224no—
787C22—224no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22C23×C4×D1111yescharacteristic
793C22#1062345312yes—
794C22#1062345511yescharacteristic
795C22#1062345511yescharacteristic
796C22#1062345712yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—222no—
806C4—222no—
807C4—222no—
808C4—222no—
809C4—224no—
810C4—442no—
811C4—442no—
812C4—442no—
813C4—442no—
814C2—42no—
815C2—444no—
816C2#1308181411yescharacteristic
817C2#1308181511yescharacteristic
818C2#1308181811yescharacteristic
819C2#1308327212yes—
820C2#1308329612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2332C2
socle, cosocleC23×C11C25
prime radicalC2×#66983C22
hypercenter#2332D11
hypocenterC11#34400
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2332

Complements

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

NH ≅ G/Ntype
2. #13071762C2semidirect
3. #13071762C2semidirect
4. #13071742C2semidirect
5. #13071730C2semidirect
6. #13071586C2semidirect
7. #13071551C2semidirect
8. #13071497C2semidirect
9. #13071471C2semidirect
10. #13071428C2semidirect
11. #13071419C2semidirect
14. #13071374C2semidirect
15. #13071261C2semidirect
16. #13071248C2semidirect
17. #13071010C2semidirect
18. #13071007C2semidirect
19. C11×#2332C2semidirect
25. #10623155C4semidirect
117. C11×C22⋊Q8C2×C4semidirect
134. Q8×Dic11C2×C4semidirect
158. C2×C4×Dic11C2×C4semidirect
172. #66951C2×C4semidirect
174. #66945C2×C4semidirect
175. #66943C2×C4semidirect
176. #66939C2×C4semidirect
177. (C22⋊D11)⋊C4C2×C4semidirect
315. #2332D11semidirect
524. C22⋊Q8C4×D11semidirect
710. C11#34400semidirect

Maximal subgroups

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

subgroupindex
C2×#106231552
#130717622
#130717422
#130717302
#130715862
#130715512
#130714972
#130714712
#130714282
#130714192
#130713812
#130713782
#130713742
#130712612
#130712482
#130710102
#130710072
C11×#23322
#3440011