Finite Group Databasebeta

← #14721995

Subgroups — #14721995

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082512C211yesmaximal, characteristic
2#13077630C211yesmaximal, characteristic, complemented
3#13067248C211yesmaximal, characteristic, complemented
4#13067245C211yesmaximal, characteristic, complemented
5#13067239C211yesmaximal, characteristic, complemented
6#13067237C211yesmaximal, characteristic, complemented
7#13067234C211yesmaximal, characteristic, complemented
8#13067232C211yesmaximal, characteristic, complemented
9#13067230C211yesmaximal, characteristic, complemented
10#13067224C211yesmaximal, characteristic, complemented
11#13067221C211yesmaximal, characteristic, complemented
12#13067205C211yesmaximal, characteristic, complemented
13#13067202C211yesmaximal, characteristic, complemented
14C2×#10622102C211yesmaximal, characteristic, complemented
15C11×#2970C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623361C411yescharacteristic
18#10623356C411yescharacteristic
19#10623099—21no—
20#10623099—21no—
21#10623090—21no—
22#10623090—21no—
23#10623087—21no—
24#10623087—21no—
25#10623087—21no—
26#10623087—21no—
27#10623065C411yescharacteristic
28#10623065C411yescharacteristic
29#10623065C411yescharacteristic
30#10623065C411yescharacteristic
31#10623052C411yescharacteristic
32#10623047C411yescharacteristic
33#10623010C2211yescharacteristic
34#10623010C2211yescharacteristic
35#10623010C2211yescharacteristic
36#10623010C2211yescharacteristic
37C2×#66928C2211yescharacteristic
38#10623001C2211yescharacteristic
39C11×#446—21no—
40C11×#435—21no—
41C11×#435—21no—
42C8×D4×C11—21no—
43C11×#432C2211yescharacteristic
44C11×#432C2211yescharacteristic, complemented
45C11×#432C2211yescharacteristic, complemented
46C4×C11×M16C2211yescharacteristic, complemented
47C2×C11×#97C2211yescharacteristic
48C2×C11×#97C2211yescharacteristic, complemented
49#10622637—21no—
50#10622624—21no—
51#10622624—21no—
52D4×C11⋊C8—21no—
53#10622539C2211yescharacteristic
54#10622539C2211yescharacteristic, complemented
55#10622539C2211yescharacteristic, complemented
56C4×#4318C2211yescharacteristic, complemented
57C2×#66867C2211yescharacteristic
58C2×#66867C2211yescharacteristic, complemented
59#10622103C2211yescharacteristic, complemented
60#10622103C2211yescharacteristic, complemented
61#10622103C2211yescharacteristic, complemented
62#10622103C2211yescharacteristic, complemented
63#10622103C2211yescharacteristic, complemented
64#10622103C2211yescharacteristic, complemented
65#10622103C2211yescharacteristic, complemented
66#10622103C2211yescharacteristic, complemented
67#10622102C2211yescharacteristic
68#10622102C2211yescharacteristic
69#10622102C2211yescharacteristic
70#10622102C2211yescharacteristic
71#10622102C2211yescharacteristic
72#10622102C2211yescharacteristic
73#10622102C2211yescharacteristic
74#10622102C2211yescharacteristic
75C2×C11×#41C2×C411yescharacteristic
76C22×D44C2×C411yescharacteristic
77C22×Dic22C2×C411yescharacteristic
78C2×C11×M16—21no—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C4×Q8×C11D411yescharacteristic
82C4×Q8×C11D411yescharacteristic
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C4×D4×C11D411yescharacteristic
89C11×#117C2×C411yescharacteristic
90C11×#117C2×C411yescharacteristic
91C11×#117C2×C411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95#67000—21no—
96#66997—21no—
97#66993—21no—
98#66990—21no—
99#66990—21no—
100#66989—21no—
101#66988—21no—
102#66988—21no—
103#66983C2×C411yescharacteristic
104#66983C2×C411yescharacteristic
105#66983C2×C411yescharacteristic
106#66983C2×C411yescharacteristic
107#66982—21no—
108#66982—21no—
109#66982—21no—
110#66982—21no—
111C4×C22⋊D11—21no—
112C4×C22⋊D11—21no—
113C4×C22⋊D11—21no—
114C4×C22⋊D11—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117#66979C2×C411yescharacteristic
118#66979C2×C411yescharacteristic
119#66977—21no—
120#66977—21no—
121#66977C2×C411yescharacteristic
122#66977C2×C411yescharacteristic
123#66977C2×C411yescharacteristic
124#66977C2×C411yescharacteristic
125C2×#4318—21no—
126C22×C11⋊C8—21no—
127C22×C11⋊C8—21no—
128#66951—21no—
129#66951—21no—
130#66951—21no—
131#66951—21no—
132#66949—21no—
133#66949—21no—
134#66949—21no—
135#66949—21no—
136#66946—21no—
137#66946—21no—
138#66940—21no—
139#66940—21no—
140#66938—21no—
141#66938—21no—
142#66938—21no—
143#66938—21no—
144#66936—21no—
145#66936—21no—
146#66936—21no—
147#66936—21no—
148C22⋊C4×D11—21no—
149C22⋊C4×D11—21no—
150#66930—21no—
151#66930—21no—
152#66929—21no—
153#66929—21no—
154#66929—21no—
155#66929—21no—
156#66928—21no—
157#66928—21no—
158#66928C2×C411yescharacteristic
159#66928C2×C411yescharacteristic
160#66928C2311yescharacteristic
161#66928C2311yescharacteristic
162C4×D44C2×C411yescharacteristic
163C4×D44C2×C411yescharacteristic
164C4×D44C2×C411yescharacteristic
165C4×D44C2×C411yescharacteristic
166#66925—21no—
167#66925—21no—
168#66925—21no—
169#66925—21no—
170#66923C2311yescharacteristic
171#66923C2311yescharacteristic
172#66922C2×C411yescharacteristic
173#66922C2×C411yescharacteristic
174C4×Dic22—21no—
175C4×Dic22—21no—
176C4×Dic22C2×C411yescharacteristic
177C4×Dic22C2×C411yescharacteristic
178C4×Dic22C2×C411yescharacteristic
179C4×Dic22C2×C411yescharacteristic
180C11×C4⋊C8—21no—
181C11×C4⋊C8—21no—
182C11×C4⋊C8—21no—
183C11×C22⋊C8—21no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×#97—21no—
187C11×#97—21no—
188C11×#97C2311yescharacteristic
189C11×#97C2311yescharacteristic
190C11×#97C2311yescharacteristic
191C11×#97C2311yescharacteristic
192C4×C8×C11—21no—
193C22⋊(C11⋊C8)—21no—
194C22⋊(C11⋊C8)—21no—
195C22⋊(C11⋊C8)—21no—
196C4⋊(C11⋊C8)—21no—
197C4⋊(C11⋊C8)—21no—
198C4⋊(C11⋊C8)—21no—
199#66867—21no—
200#66867—21no—
201#66867C2311yescharacteristic
202#66867C2311yescharacteristic
203#66867C2311yescharacteristic
204#66867C2311yescharacteristic
205C4×C11⋊C8—21no—
206#17686—111nomaximal, Sylow
207C23×D11—21no—
208C11×#41—42no—
209C2×Q8×C11C22⋊C411yescharacteristic
210C2×D4×C11C22⋊C411yescharacteristic
211C2×D4×C11C22⋊C411yescharacteristic
212C2×D4×C11C22⋊C411yescharacteristic
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C2×C22⋊D11—21no—
226C22×Dic11—21no—
227C2×D44—21no—
228C2×D44—42no—
229C2×D44C22×C411yescharacteristic
230C2×D44C22×C411yescharacteristic
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—42no—
239C2×Dic22C22×C411yescharacteristic
240C2×Dic22C22×C411yescharacteristic
241C11×M16—42no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—42no—
247C2×C8×C11—42no—
248C11×C4⋊C4C22⋊C411yescharacteristic
249C11×C4⋊C4C22⋊C411yescharacteristic
250C11×C4⋊C4C22⋊C411yescharacteristic
251C11×C4⋊C4C22⋊C411yescharacteristic
252C11×C4⋊C4C22⋊C411yescharacteristic
253C11×C4⋊C4C22⋊C411yescharacteristic
254C11×C22⋊C4C22⋊C411yescharacteristic
255C11×C22⋊C4C22⋊C411yescharacteristic
256C11×C22⋊C4C22⋊C411yescharacteristic
257C11×C22⋊C4C22⋊C411yescharacteristic
258C11×C22⋊C4C22⋊C411yescharacteristic
259C11×C22⋊C4C22⋊C411yescharacteristic
260C42×C11C22×C411yescharacteristic
261C42×C11C22×C411yescharacteristic
262C42×C11C22×C411yescharacteristic
263C42×C11C2×D411yescharacteristic
264C42×C11C2×D411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2×D411yescharacteristic
267C42×C11C2×D411yescharacteristic
268C42×C11C2×D411yescharacteristic
269C42×C11C2411yescharacteristic
270C22⋊Dic11—21no—
271C22⋊Dic11—21no—
272C22⋊Dic11—21no—
273C22⋊Dic11—21no—
274C22⋊Dic11—21no—
275C22⋊Dic11—21no—
276(C2×D11)⋊C4—21no—
277(C2×D11)⋊C4—21no—
278(C2×D11)⋊C4—21no—
279(C2×D11)⋊C4—21no—
280(C2×D11)⋊C4—21no—
281(C2×D11)⋊C4—21no—
282(C2×D11)⋊C4—21no—
283(C2×D11)⋊C4—21no—
284(C2×D11)⋊C4—21no—
285(C2×D11)⋊C4—21no—
286(C2×D11)⋊C4—21no—
287(C2×D11)⋊C4—21no—
288(C2×D11)⋊C4—21no—
289(C2×D11)⋊C4—21no—
290(C2×D11)⋊C4—21no—
291(C2×D11)⋊C4—21no—
292C4⋊Dic11—21no—
293C4⋊Dic11—21no—
294C4⋊Dic11C22×C411yescharacteristic
295C4⋊Dic11C22×C411yescharacteristic
296C4⋊Dic11C22×C411yescharacteristic
297C4⋊Dic11C22×C411yescharacteristic
298Dic11⋊C4—21no—
299Dic11⋊C4—21no—
300Dic11⋊C4—21no—
301Dic11⋊C4—21no—
302Dic11⋊C4—21no—
303Dic11⋊C4—21no—
304Dic11⋊C4—21no—
305Dic11⋊C4—21no—
306Dic11⋊C4—21no—
307Dic11⋊C4—21no—
308Dic11⋊C4—21no—
309Dic11⋊C4—21no—
310C4×Dic11—21no—
311C4×Dic11—21no—
312C4×Dic11—21no—
313C4×Dic11—21no—
314C4×Dic11—21no—
315C4×Dic11—21no—
316#4318—42no—
317C2×C11⋊C8—21no—
318C2×C11⋊C8—21no—
319C2×C11⋊C8—21no—
320C2×C11⋊C8—21no—
321C2×C11⋊C8—42no—
322C2×C11⋊C8—42no—
323#3510—111no—
324#2970—111no—
325#2970D1111yescharacteristic, complemented
326#1535—111no—
327#1535—111no—
328#1533—111no—
329#1532—111no—
330#1532—111no—
331#1531—111no—
332#1531—111no—
333#1529—111no—
334#1529—111no—
335#1524—111no—
336#1524—111no—
337C2×#329—111no—
338C23×C11C2×C22⋊C411yescharacteristic
339C23×C11C2×C22⋊C411yescharacteristic
340C23×C11C2×C22⋊C411yescharacteristic
341C22×D11—21no—
342C22×D11—21no—
343C22×D11—42no—
344C22×D11—81no—
345C22×D11—81no—
346Q8×C11—41no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—41no—
350C2×C4×C11—22no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11C2×C22⋊C411yescharacteristic
360C2×C4×C11C2×C22⋊C411yescharacteristic
361C2×C4×C11C2×C22⋊C411yescharacteristic
362C2×C4×C11C2×C22⋊C411yescharacteristic
363C2×C4×C11C2×C22⋊C411yescharacteristic
364C2×C4×C11C2×C22⋊C411yescharacteristic
365C2×C4×C11C2×C22⋊C411yescharacteristic
366C2×C4×C11C2×C22⋊C411yescharacteristic
367C2×C4×C11C2×C22⋊C411yescharacteristic
368C2×C4×C11C23×C411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C22⋊D11—81no—
372C22⋊D11—81no—
373C22⋊D11—81no—
374C22⋊D11—81no—
375C2×Dic11—21no—
376C2×Dic11—21no—
377C2×Dic11—21no—
378C2×Dic11—21no—
379C2×Dic11—21no—
380C2×Dic11—21no—
381C2×Dic11—42no—
382D44—41no—
383D44—41no—
384D44—42no—
385C4×D11—81no—
386C4×D11—81no—
387C4×D11—81no—
388C4×D11—81no—
389Dic22—42no—
390Dic22—41no—
391Dic22—41no—
392Dic22—81no—
393Dic22—81no—
394C8×C11—22no—
395C8×C11—41no—
396C8×C11—41no—
397C8×C11—41no—
398C11⋊C8—22no—
399C11⋊C8—41no—
400C11⋊C8—41no—
401C11⋊C8—41no—
402#559—221no—
403#559—221no—
404#556—221no—
405#556—221no—
406#551—221no—
407#551—221no—
408#551—221no—
409#551—221no—
410#542—111no—
411#542—111no—
412#542—111no—
413#542—111no—
414#536—111no—
415#535—111no—
416#533—111no—
417#529—111no—
418#529—111no—
419#529—111no—
420#529—111no—
421C2×#124—111no—
422#519—111no—
423#518—111no—
424C4×#41C2×D1111yescharacteristic
425#446—21no—
426#446—221no—
427#435—21no—
428#435—21no—
429#435—221no—
430#435—221no—
431C8×D4—21no—
432C8×D4—221no—
433#432—111no—
434#432—111no—
435#432—111no—
436#432C2×D1111yescharacteristic
437#432C2×D1111yescharacteristic, complemented
438#432C2×D1111yescharacteristic, complemented
439C4×M16—111no—
440C4×M16C2×D1111yescharacteristic, complemented
441C2×#97—111no—
442C2×#97—111no—
443C2×#97C2×D1111yescharacteristic
444C2×#97C2×D1111yescharacteristic, complemented
445#330—111no—
446#330—111no—
447#330—111no—
448#330—111no—
449#330—111no—
450#330—111no—
451#330—111no—
452#330—111no—
453#329—111no—
454#329—111no—
455#329—111no—
456#329—111no—
457#329—111no—
458#329—111no—
459#329—111no—
460#329—111no—
461C22×C11—21no—
462C22×C11—21no—
463C22×C11—21no—
464C22×C11—21no—
465C22×C11—21no—
466C22×C11—21no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11#41312yes—
470C22×C11C22×C22⋊C411yescharacteristic
471C2×D11—41no—
472C2×D11—41no—
473C2×D11—41no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—41no—
477C2×D11—162no—
478C4×C11—21no—
479C4×C11—21no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—21no—
486C4×C11—21no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—21no—
490Dic11—41no—
491Dic11—41no—
492Dic11—41no—
493Dic11—41no—
494Dic11—41no—
495Dic11—41no—
496C2×#41C4×D1111yescharacteristic
497C22×Q8—111no—
498C22×D4—111no—
499C2×M16—21no—
500C2×M16—221no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—221no—
504C22×C8—221no—
505C4⋊Q8—111no—
506C4⋊Q8—111no—
507C4⋊Q8—221no—
508#127—221no—
509#126—221no—
510#126—221no—
511#126—221no—
512#126—221no—
513#126—221no—
514#126—221no—
515#126—221no—
516#126—221no—
517#125—111no—
518#125—111no—
519#124—111no—
520#124—111no—
521#124—111no—
522#124—111no—
523#124—221no—
524#124—221no—
525#124—221no—
526#124—221no—
527#124—221no—
528#124—221no—
529#124—221no—
530#124—221no—
531#123—221no—
532#123—221no—
533#123—221no—
534#123—221no—
535#123—221no—
536#123—221no—
537#123—221no—
538#123—221no—
539#123—221no—
540#123—221no—
541C22⋊Q8—111no—
542C22⋊Q8—111no—
543C22⋊Q8—111no—
544C22⋊Q8—111no—
545C22⋊Q8—221no—
546C22⋊Q8—221no—
547C22⋊Q8—221no—
548C22⋊Q8—221no—
549C22⋊Q8—221no—
550C22⋊Q8—221no—
551#121—111no—
552#121—111no—
553#121—111no—
554#121—111no—
555#120—221no—
556#120—221no—
557C4×Q8—111no—
558C4×Q8—111no—
559C4×Q8—111no—
560C4×Q8—111no—
561C4×Q8—221no—
562C4×Q8—221no—
563C4×Q8—221no—
564C4×Q8—221no—
565C4×Q8D4411yescharacteristic
566C4×Q8C22⋊D1111yescharacteristic
567C4×D4—111no—
568C4×D4—111no—
569C4×D4—111no—
570C4×D4—111no—
571C4×D4—221no—
572C4×D4—221no—
573C4×D4—221no—
574C4×D4—221no—
575C4×D4—221no—
576C4×D4—221no—
577C4×D4D4411yescharacteristic
578C4×D4D4411yescharacteristic
579C4×D4D4411yescharacteristic
580C4×D4C22⋊D1111yescharacteristic
581C4×D4C22⋊D1111yescharacteristic
582C4×D4C22⋊D1111yescharacteristic
583#117—111no—
584#117—111no—
585#117—221no—
586#117—221no—
587#117—221no—
588#117—221no—
589#117—221no—
590#117—221no—
591#117C4×D1111yescharacteristic
592#117C4×D1111yescharacteristic
593#117C4×D1111yescharacteristic
594C2×C22⋊C4—221no—
595C2×C22⋊C4—221no—
596C2×C22⋊C4—221no—
597C2×C22⋊C4—221no—
598C2×C42C22×D1111yescharacteristic
599C2×C42C22×D1111yescharacteristic
600C2×C42C22×D1111yescharacteristic
601C4⋊C8—21no—
602C4⋊C8—21no—
603C4⋊C8—21no—
604C4⋊C8—221no—
605C4⋊C8—221no—
606C4⋊C8—221no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609C22⋊C8—21no—
610C22⋊C8—221no—
611C22⋊C8—221no—
612C22⋊C8—221no—
613#97—21no—
614#97—21no—
615#97—111no—
616#97—111no—
617#97—111no—
618#97—111no—
619#97—221no—
620#97—221no—
621#97C22×D1111yescharacteristic
622#97C22×D1111yescharacteristic
623#97C22×D1111yescharacteristic
624#97C22×D1111yescharacteristic
625C4×C8—21no—
626C4×C8—221no—
627C2×C11—22no—
628C2×C11—41no—
629C2×C11—41no—
630C2×C11C2×#41311yescharacteristic
631C2×C11#290111yescharacteristic
632C2×C11#290111yescharacteristic
633D11—81no—
634D11—81no—
635C24—221no—
636#41—42no—
637C2×Q8—111no—
638C2×Q8—111no—
639C2×Q8—221no—
640C2×Q8—221no—
641C2×Q8—221no—
642C2×Q8—442no—
643C2×Q8(C2×D11)⋊C411yescharacteristic
644C2×D4—111no—
645C2×D4—111no—
646C2×D4—221no—
647C2×D4—221no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4—221no—
651C2×D4—442no—
652C2×D4(C2×D11)⋊C411yescharacteristic
653C2×D4(C2×D11)⋊C411yescharacteristic
654C2×D4(C2×D11)⋊C411yescharacteristic
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4C2×C4×D1111yescharacteristic
661C22×C4C2×C4×D1111yescharacteristic
662C22×C4C2×C4×D1111yescharacteristic
663C22×C4C2×D4411yescharacteristic
664C22×C4C2×D4411yescharacteristic
665C22×C4C2×D4411yescharacteristic
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669M16—42no—
670M16—442no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—221no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—442no—
682C2×C8—442no—
683C4⋊C4—111no—
684C4⋊C4—111no—
685C4⋊C4—111no—
686C4⋊C4—111no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—221no—
690C4⋊C4—221no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4(C2×D11)⋊C411yescharacteristic
702C4⋊C4(C2×D11)⋊C411yescharacteristic
703C4⋊C4(C2×D11)⋊C411yescharacteristic
704C4⋊C4(C2×D11)⋊C411yescharacteristic
705C4⋊C4(C2×D11)⋊C411yescharacteristic
706C4⋊C4(C2×D11)⋊C411yescharacteristic
707C22⋊C4—221no—
708C22⋊C4—221no—
709C22⋊C4—221no—
710C22⋊C4—221no—
711C22⋊C4—221no—
712C22⋊C4—221no—
713C22⋊C4—221no—
714C22⋊C4—221no—
715C22⋊C4—221no—
716C22⋊C4—221no—
717C22⋊C4—221no—
718C22⋊C4—221no—
719C22⋊C4—221no—
720C22⋊C4—221no—
721C22⋊C4—221no—
722C22⋊C4—221no—
723C22⋊C4—221no—
724C22⋊C4—221no—
725C22⋊C4—221no—
726C22⋊C4—221no—
727C22⋊C4—221no—
728C22⋊C4—221no—
729C22⋊C4(C2×D11)⋊C411yescharacteristic
730C22⋊C4(C2×D11)⋊C411yescharacteristic
731C22⋊C4(C2×D11)⋊C411yescharacteristic
732C22⋊C4(C2×D11)⋊C411yescharacteristic
733C22⋊C4(C2×D11)⋊C411yescharacteristic
734C22⋊C4(C2×D11)⋊C411yescharacteristic
735C42—221no—
736C42—221no—
737C42—221no—
738C42—221no—
739C42—221no—
740C42—221no—
741C42C2×C4×D1111yescharacteristic
742C42C2×C4×D1111yescharacteristic
743C42C2×C4×D1111yescharacteristic
744C42C2×D4411yescharacteristic
745C42C2×D4411yescharacteristic
746C42C2×D4411yescharacteristic
747C42C2×C22⋊D1111yescharacteristic
748C42C2×C22⋊D1111yescharacteristic
749C42C2×C22⋊D1111yescharacteristic
750C42C23×D1111yescharacteristic
751C11#1768611yescharacteristic, complemented, Sylow
752C23—221no—
753C23—221no—
754C23—442no—
755C23—881no—
756C23—881no—
757C23C2×(C2×D11)⋊C411yescharacteristic
758C23C2×(C2×D11)⋊C411yescharacteristic
759C23C2×(C2×D11)⋊C411yescharacteristic
760Q8—41no—
761Q8—441no—
762Q8—441no—
763Q8—442no—
764Q8—881no—
765Q8—881no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—441no—
770D4—441no—
771D4—442no—
772D4—881no—
773D4—881no—
774D4—881no—
775D4—881no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—221no—
786C2×C4—221no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—221no—
791C2×C4—442no—
792C2×C4—881no—
793C2×C4—881no—
794C2×C4—881no—
795C2×C4—881no—
796C2×C4C2×(C2×D11)⋊C411yescharacteristic
797C2×C4C2×(C2×D11)⋊C411yescharacteristic
798C2×C4C2×(C2×D11)⋊C411yescharacteristic
799C2×C4C2×(C2×D11)⋊C411yescharacteristic
800C2×C4C2×(C2×D11)⋊C411yescharacteristic
801C2×C4C2×(C2×D11)⋊C411yescharacteristic
802C2×C4C2×(C2×D11)⋊C411yescharacteristic
803C2×C4C2×(C2×D11)⋊C411yescharacteristic
804C2×C4C2×(C2×D11)⋊C411yescharacteristic
805C2×C4C22×C4×D1111yescharacteristic
806C2×C4C22×D4411yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—222no—
813C8—441no—
814C8—441no—
815C8—441no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—441no—
825C22—441no—
826C22—441no—
827C22—441no—
828C22—441no—
829C22—441no—
830C22—1762no—
831C22#1062274512yes—
832C22C22×(C2×D11)⋊C411yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—441no—
846C4—441no—
847C4—441no—
848C4—441no—
849C4—441no—
850C4—441no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—881no—
855C2—881no—
856C2C2×#1062274511yescharacteristic
857C2#1307716111yescharacteristic
858C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2970C2
socleC22×C11C22×C22⋊C4
prime radical#10623361C4
cosocleC42×C11C24
hypercenter#2970D11
hypocenterC11#17686
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #13077630C2semidirect
3. #13067248C2semidirect
4. #13067245C2semidirect
5. #13067239C2semidirect
6. #13067237C2semidirect
7. #13067234C2semidirect
8. #13067232C2semidirect
9. #13067230C2semidirect
10. #13067224C2semidirect
11. #13067221C2semidirect
12. #13067205C2semidirect
13. #13067202C2semidirect
14. C2×#10622102C2semidirect
15. C11×#2970C2semidirect
44. C11×#432C22semidirect
45. C11×#432C22semidirect
46. C4×C11×M16C22semidirect
48. C2×C11×#97C22semidirect
54. #10622539C22semidirect
55. #10622539C22semidirect
56. C4×#4318C22semidirect
58. C2×#66867C22semidirect
59. #10622103C22semidirect
60. #10622103C22semidirect
61. #10622103C22semidirect
62. #10622103C22semidirect
63. #10622103C22semidirect
64. #10622103C22semidirect
65. #10622103C22semidirect
66. #10622103C22semidirect
325. #2970D11semidirect
437. #432C2×D11semidirect
438. #432C2×D11semidirect
440. C4×M16C2×D11semidirect
444. C2×#97C2×D11semidirect
751. C11#17686semidirect

Maximal subgroups

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

subgroupindex
#130825122
#130776302
#130672482
#130672452
#130672392
#130672372
#130672342
#130672322
#130672302
#130672242
#130672212
#130672052
#130672022
C2×#106221022
C11×#29702
#1768611