Finite Group Databasebeta

← #14721929

Subgroups — #14721929

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082594C211yesmaximal, characteristic
2#13077630C211yesmaximal, characteristic, complemented
3#13067253C211yesmaximal, characteristic, complemented
4#13067248C211yesmaximal, characteristic, complemented
5#13067245C211yesmaximal, characteristic, complemented
6#13067242C211yesmaximal, characteristic, complemented
7#13067237C211yesmaximal, characteristic, complemented
8#13067234C211yesmaximal, characteristic, complemented
9#13067232C211yesmaximal, characteristic, complemented
10#13067224C211yesmaximal, characteristic, complemented
11#13067219C211yesmaximal, characteristic, complemented
12#13067217C211yesmaximal, characteristic, complemented
13#13067205C211yesmaximal, characteristic, complemented
14C2×#10622103C211yesmaximal, characteristic, complemented
15C11×#2923C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623355—21no—
18#10623114—21no—
19#10623110C411yescharacteristic
20#10623098C411yescharacteristic
21#10623096C411yescharacteristic
22#10623096C411yescharacteristic
23#10623095—21no—
24#10623095—21no—
25#10623086C411yescharacteristic
26#10623077—21no—
27#10623074C411yescharacteristic
28#10623072C411yescharacteristic
29#10623072C411yescharacteristic
30#10623062—21no—
31#10623062—21no—
32#10623060—21no—
33#10623010C2211yescharacteristic
34#10623010C2211yescharacteristic
35#10623010C2211yescharacteristic
36#10623001C2211yescharacteristic
37C2×#66923C2211yescharacteristic
38C2×#66923C2211yescharacteristic
39C11×#433—21no—
40C11×#433—21no—
41C11×#432C2211yescharacteristic
42C11×#432C2211yescharacteristic
43C11×#432C2211yescharacteristic
44C11×#432C2211yescharacteristic
45C11×#424—21no—
46C11×#408—21no—
47C4×C11×M16C2211yescharacteristic
48C2×C11×#97C2211yescharacteristic
49#10622637—21no—
50#10622624—21no—
51#10622624—21no—
52D4×C11⋊C8—21no—
53#10622539C2211yescharacteristic
54#10622539C2211yescharacteristic
55#10622539C2211yescharacteristic
56C4×#4318C2211yescharacteristic
57C2×#66867C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622103C2211yescharacteristic
60#10622103C2211yescharacteristic
61#10622103C2211yescharacteristic
62#10622103C2211yescharacteristic
63#10622103C2211yescharacteristic
64#10622103C2211yescharacteristic
65#10622103C2211yescharacteristic
66#10622103C2211yescharacteristic
67#10622103C2211yescharacteristic
68#10622103C2211yescharacteristic
69#10622103C2211yescharacteristic
70#10622103C2211yescharacteristic
71#10622102C2211yescharacteristic
72#10622102C2211yescharacteristic
73#10622102C2211yescharacteristic
74#10622102C2211yescharacteristic
75C2×C11×#41D411yescharacteristic
76C2×#4341—21no—
77C2×C11×M16—21no—
78C22×C8×C11—21no—
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11D411yescharacteristic
81C4×D4×C11C2×C411yescharacteristic
82C4×D4×C11C2×C411yescharacteristic
83C4×D4×C11C2×C411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C11×#117D411yescharacteristic
88C11×#117D411yescharacteristic
89C11×#117D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93#66999—21no—
94#66997—21no—
95#66992—21no—
96#66992—21no—
97#66988—21no—
98#66988—21no—
99D4×Dic11—21no—
100#66983C2×C411yescharacteristic
101#66983C2×C411yescharacteristic
102#66983C2×C411yescharacteristic
103#66982—21no—
104#66982—21no—
105#66982—21no—
106C4×C22⋊D11—21no—
107C4×C22⋊D11—21no—
108C4×C22⋊D11—21no—
109#66979C2×C411yescharacteristic
110#66979C2×C411yescharacteristic
111C2×C4⋊Dic11C2×C411yescharacteristic
112C2×C4⋊Dic11C2×C411yescharacteristic
113C2×C4⋊Dic11C2×C411yescharacteristic
114C2×C4⋊Dic11C2×C411yescharacteristic
115#66977—21no—
116#66977—21no—
117#66977C2×C411yescharacteristic
118#66977C2×C411yescharacteristic
119#66977C2×C411yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×#4318—21no—
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127#66951—21no—
128#66951—21no—
129#66950—21no—
130#66949—21no—
131#66949—21no—
132C4⋊C4×D11—21no—
133#66943—21no—
134#66942—21no—
135#66942—21no—
136#66942—21no—
137#66942—21no—
138#66940—21no—
139#66939—21no—
140#66939—21no—
141#66936—21no—
142#66936—21no—
143(C22⋊D11)⋊C4—21no—
144(C22⋊D11)⋊C4—21no—
145#66932—21no—
146#66932—21no—
147#66931—21no—
148#66931—21no—
149#66930—21no—
150#66930—21no—
151#66929—21no—
152#66929—21no—
153#66929—21no—
154#66928C2311yescharacteristic
155C4×D44C2×C411yescharacteristic
156C4×D44C2×C411yescharacteristic
157C4×D44C2×C411yescharacteristic
158#66925—21no—
159#66925—21no—
160#66925—21no—
161#66923—21no—
162#66923—21no—
163#66923—21no—
164#66923—21no—
165#66923C2×C411yescharacteristic
166#66923C2×C411yescharacteristic
167#66923C2×C411yescharacteristic
168#66923C2×C411yescharacteristic
169#66923C2311yescharacteristic
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
179C11×C4⋊C8—21no—
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×C22⋊C8—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#17680—111nomaximal, Sylow
207C11×#41—42no—
208C2×Q8×C11C22⋊C411yescharacteristic
209C2×D4×C11C22⋊C411yescharacteristic
210C2×D4×C11C22⋊C411yescharacteristic
211C2×D4×C11C22⋊C411yescharacteristic
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C2×C22⋊D11—21no—
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228#4341—44no—
229C2×D44C22×C411yescharacteristic
230C2×C4×D11—21no—
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22C22×C411yescharacteristic
236C11×M16—42no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—42no—
242C11×C4⋊C4C22⋊C411yescharacteristic
243C11×C4⋊C4C22⋊C411yescharacteristic
244C11×C4⋊C4C22⋊C411yescharacteristic
245C11×C4⋊C4C22⋊C411yescharacteristic
246C11×C4⋊C4C22⋊C411yescharacteristic
247C11×C4⋊C4C22⋊C411yescharacteristic
248C11×C22⋊C4C22⋊C411yescharacteristic
249C11×C22⋊C4C22⋊C411yescharacteristic
250C11×C22⋊C4C22⋊C411yescharacteristic
251C11×C22⋊C4C22⋊C411yescharacteristic
252C11×C22⋊C4C22⋊C411yescharacteristic
253C11×C22⋊C4C22⋊C411yescharacteristic
254C42×C11C22×C411yescharacteristic
255C42×C11C22×C411yescharacteristic
256C42×C11C22×C411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261C42×C11C2×D411yescharacteristic
262C42×C11C2×D411yescharacteristic
263C42×C11C2411yescharacteristic
264C22⋊Dic11—21no—
265C22⋊Dic11—21no—
266C22⋊Dic11—21no—
267C22⋊Dic11—21no—
268C22⋊Dic11—21no—
269(C2×D11)⋊C4—21no—
270(C2×D11)⋊C4—21no—
271(C2×D11)⋊C4—21no—
272(C2×D11)⋊C4—21no—
273(C2×D11)⋊C4—21no—
274(C2×D11)⋊C4—21no—
275(C2×D11)⋊C4—21no—
276(C2×D11)⋊C4—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11C22×C411yescharacteristic
284C4⋊Dic11C22×C411yescharacteristic
285C4⋊Dic11C22×C411yescharacteristic
286C4⋊Dic11C22×C411yescharacteristic
287C4⋊Dic11C22×C411yescharacteristic
288C4⋊Dic11C22×C411yescharacteristic
289Dic11⋊C4—21no—
290Dic11⋊C4—21no—
291Dic11⋊C4—21no—
292Dic11⋊C4—21no—
293Dic11⋊C4—21no—
294Dic11⋊C4—21no—
295Dic11⋊C4—21no—
296Dic11⋊C4—21no—
297Dic11⋊C4—21no—
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—
309C4×Dic11—21no—
310C4×Dic11—21no—
311C4×Dic11—21no—
312C4×Dic11—21no—
313C4×Dic11—21no—
314#4318—42no—
315C2×C11⋊C8—21no—
316C2×C11⋊C8—21no—
317C2×C11⋊C8—21no—
318C2×C11⋊C8—21no—
319C2×C11⋊C8—42no—
320C2×C11⋊C8—42no—
321#3515—111no—
322#2970—111no—
323#2923D1111yescharacteristic, complemented
324#1537—111no—
325#1535—111no—
326#1535—111no—
327#1534—111no—
328#1532—111no—
329#1532—111no—
330#1531—111no—
331#1529—111no—
332#1528—111no—
333#1528—111no—
334#1524—111no—
335C2×#330—111no—
336C23×C11C2×C22⋊C411yescharacteristic
337C23×C11C2×C22⋊C411yescharacteristic
338C23×C11C2×C22⋊C411yescharacteristic
339C22×D11—21no—
340Q8×C11—41no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—41no—
344C2×C4×C11—22no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11C2×C22⋊C411yescharacteristic
354C2×C4×C11C2×C22⋊C411yescharacteristic
355C2×C4×C11C2×C22⋊C411yescharacteristic
356C2×C4×C11C2×C22⋊C411yescharacteristic
357C2×C4×C11C2×C22⋊C411yescharacteristic
358C2×C4×C11C2×C22⋊C411yescharacteristic
359C2×C4×C11C2×C22⋊C411yescharacteristic
360C2×C4×C11C2×C22⋊C411yescharacteristic
361C2×C4×C11C2×C22⋊C411yescharacteristic
362C2×C4×C11C23×C411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C22⋊D11—42no—
366C22⋊D11—42no—
367C22⋊D11—81no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11—81no—
378C2×Dic11—81no—
379D44—41no—
380C4×D11—42no—
381C4×D11—81no—
382C4×D11—81no—
383Dic22—42no—
384Dic22—41no—
385Dic22—81no—
386C8×C11—41no—
387C8×C11—41no—
388C8×C11—41no—
389C8×C11—41no—
390C11⋊C8—22no—
391C11⋊C8—41no—
392C11⋊C8—41no—
393C11⋊C8—41no—
394#557—111no—
395#554—111no—
396#554—111no—
397#553—111no—
398#553—111no—
399#552—111no—
400#552—111no—
401#552—221no—
402#552—221no—
403#552—221no—
404#547—111no—
405#547—221no—
406#541—221no—
407#539—221no—
408#539—221no—
409#533—111no—
410#529—111no—
411#529—111no—
412#529—111no—
413C2×#125—111no—
414C2×#125—111no—
415#520—221no—
416C4×#41C2×D1111yescharacteristic
417#446—221no—
418#435—221no—
419#435—221no—
420C8×D4—221no—
421#433—21no—
422#433—21no—
423#432—111no—
424#432—111no—
425#432—111no—
426#432C2×D1111yescharacteristic
427#432C2×D1111yescharacteristic
428#432C2×D1111yescharacteristic
429#432C2×D1111yescharacteristic
430#424—21no—
431#408—21no—
432C4×M16—111no—
433C4×M16C2×D1111yescharacteristic
434C2×#97—111no—
435C2×#97—111no—
436C2×#97C2×D1111yescharacteristic
437#330—111no—
438#330—111no—
439#330—111no—
440#330—111no—
441#330—111no—
442#330—111no—
443#330—111no—
444#330—111no—
445#330—111no—
446#330—111no—
447#330—111no—
448#330—111no—
449#329—111no—
450#329—111no—
451#329—111no—
452#329—111no—
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—21no—
461C22×C11#42112yes—
462C22×C11C22×C22⋊C411yescharacteristic
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—41no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—21no—
471C4×C11—21no—
472C4×C11—21no—
473C4×C11—21no—
474C4×C11—21no—
475C4×C11—21no—
476C4×C11—21no—
477C4×C11—21no—
478Dic11—41no—
479Dic11—41no—
480Dic11—41no—
481Dic11—41no—
482Dic11—41no—
483Dic11—41no—
484Dic11—41no—
485C2×#41—221no—
486C2×#41C22⋊D1111yescharacteristic
487C2×M16—21no—
488C2×M16—221no—
489C22×C8—21no—
490C22×C8—221no—
491C22×C8—221no—
492C4⋊Q8—111no—
493C4⋊Q8—111no—
494C4⋊Q8—221no—
495#126—221no—
496#126—221no—
497#126—221no—
498#126—221no—
499#126—221no—
500#126—221no—
501#126—221no—
502#125—111no—
503#125—111no—
504#125—111no—
505#125—111no—
506#125—111no—
507#125—111no—
508#125—111no—
509#125—221no—
510#125—221no—
511#125—221no—
512#125—221no—
513#125—221no—
514#125—221no—
515#125—221no—
516#125—221no—
517#125—221no—
518#124—111no—
519#123—221no—
520#123—221no—
521#123—221no—
522#123—221no—
523#123—221no—
524#123—221no—
525#123—221no—
526#123—221no—
527#123—221no—
528C22⋊Q8—111no—
529C22⋊Q8—111no—
530C22⋊Q8—111no—
531C22⋊Q8—221no—
532C22⋊Q8—221no—
533C22⋊Q8—221no—
534C22⋊Q8—221no—
535C22⋊Q8—221no—
536C22⋊Q8—221no—
537C22⋊Q8—221no—
538C22⋊Q8—221no—
539#121—111no—
540#121—111no—
541#121—111no—
542#121—221no—
543#121—221no—
544C4×Q8—111no—
545C4×Q8—111no—
546C4×Q8—111no—
547C4×Q8—221no—
548C4×Q8—221no—
549C4×Q8—221no—
550C4×Q8C4×D1111yescharacteristic
551C4×Q8D4411yescharacteristic
552C4×D4—111no—
553C4×D4—111no—
554C4×D4—111no—
555C4×D4—221no—
556C4×D4—221no—
557C4×D4—221no—
558C4×D4—221no—
559C4×D4—221no—
560C4×D4—221no—
561C4×D4C4×D1111yescharacteristic
562C4×D4C4×D1111yescharacteristic
563C4×D4C4×D1111yescharacteristic
564C4×D4D4411yescharacteristic
565C4×D4D4411yescharacteristic
566C4×D4D4411yescharacteristic
567#117—111no—
568#117—111no—
569#117—221no—
570#117—221no—
571#117—221no—
572#117—221no—
573#117—221no—
574#117C22⋊D1111yescharacteristic
575#117C22⋊D1111yescharacteristic
576#117C22⋊D1111yescharacteristic
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4—221no—
586C2×C42C22×D1111yescharacteristic
587C2×C42C22×D1111yescharacteristic
588C2×C42C22×D1111yescharacteristic
589C4⋊C8—21no—
590C4⋊C8—21no—
591C4⋊C8—21no—
592C4⋊C8—21no—
593C4⋊C8—221no—
594C4⋊C8—221no—
595C4⋊C8—221no—
596C22⋊C8—21no—
597C22⋊C8—21no—
598C22⋊C8—21no—
599C22⋊C8—21no—
600C22⋊C8—221no—
601C22⋊C8—221no—
602C22⋊C8—221no—
603#97—21no—
604#97—111no—
605#97—111no—
606#97—111no—
607#97—111no—
608#97—221no—
609#97—221no—
610#97C22×D1111yescharacteristic
611#97C22×D1111yescharacteristic
612#97C22×D1111yescharacteristic
613#97C22×D1111yescharacteristic
614C4×C8—21no—
615C4×C8—221no—
616C2×C11—22no—
617C2×C11—41no—
618C2×C11—41no—
619C2×C11#288911yescharacteristic
620C2×C11C2×#42111yescharacteristic
621C2×C11#290111yescharacteristic
622D11—81no—
623#41—42no—
624#41—444no—
625C2×Q8—111no—
626C2×Q8—221no—
627C2×Q8—221no—
628C2×Q8(C2×D11)⋊C411yescharacteristic
629C2×D4—111no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4(C2×D11)⋊C411yescharacteristic
634C2×D4(C2×D11)⋊C411yescharacteristic
635C2×D4(C2×D11)⋊C411yescharacteristic
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4C2×C4×D1111yescharacteristic
644C22×C4C2×C4×D1111yescharacteristic
645C22×C4C2×C4×D1111yescharacteristic
646C22×C4C2×D4411yescharacteristic
647C22×C4C2×D4411yescharacteristic
648C22×C4C2×D4411yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652M16—42no—
653M16—442no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—42no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—442no—
664C2×C8—442no—
665C4⋊C4—111no—
666C4⋊C4—111no—
667C4⋊C4—111no—
668C4⋊C4—111no—
669C4⋊C4—111no—
670C4⋊C4—111no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—221no—
682C4⋊C4—221no—
683C4⋊C4—221no—
684C4⋊C4—221no—
685C4⋊C4—221no—
686C4⋊C4—221no—
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(C2×D11)⋊C411yescharacteristic
698C4⋊C4(C2×D11)⋊C411yescharacteristic
699C4⋊C4(C2×D11)⋊C411yescharacteristic
700C4⋊C4(C2×D11)⋊C411yescharacteristic
701C4⋊C4(C2×D11)⋊C411yescharacteristic
702C4⋊C4(C2×D11)⋊C411yescharacteristic
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
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(C2×D11)⋊C411yescharacteristic
717C22⋊C4(C2×D11)⋊C411yescharacteristic
718C22⋊C4(C2×D11)⋊C411yescharacteristic
719C22⋊C4(C2×D11)⋊C411yescharacteristic
720C22⋊C4(C2×D11)⋊C411yescharacteristic
721C22⋊C4(C2×D11)⋊C411yescharacteristic
722C42—221no—
723C42—221no—
724C42—221no—
725C42—221no—
726C42—221no—
727C42C2×C4×D1111yescharacteristic
728C42C2×C4×D1111yescharacteristic
729C42C2×C4×D1111yescharacteristic
730C42C2×D4411yescharacteristic
731C42C2×D4411yescharacteristic
732C42C2×D4411yescharacteristic
733C42C2×C22⋊D1111yescharacteristic
734C42C2×C22⋊D1111yescharacteristic
735C42C2×C22⋊D1111yescharacteristic
736C42C23×D1111yescharacteristic
737C11#1768011yescharacteristic, complemented, Sylow
738C23—221no—
739C23C2×(C2×D11)⋊C411yescharacteristic
740C23C2×(C2×D11)⋊C411yescharacteristic
741C23C2×(C2×D11)⋊C411yescharacteristic
742Q8—41no—
743Q8—441no—
744Q8—442no—
745Q8—881no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—441no—
750D4—442no—
751D4—442no—
752D4—881no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—221no—
763C2×C4—221no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—881no—
773C2×C4—881no—
774C2×C4—881no—
775C2×C4—881no—
776C2×C4C2×(C2×D11)⋊C411yescharacteristic
777C2×C4C2×(C2×D11)⋊C411yescharacteristic
778C2×C4C2×(C2×D11)⋊C411yescharacteristic
779C2×C4C2×(C2×D11)⋊C411yescharacteristic
780C2×C4C2×(C2×D11)⋊C411yescharacteristic
781C2×C4C2×(C2×D11)⋊C411yescharacteristic
782C2×C4C2×(C2×D11)⋊C411yescharacteristic
783C2×C4C2×(C2×D11)⋊C411yescharacteristic
784C2×C4C2×(C2×D11)⋊C411yescharacteristic
785C2×C4C22×C4×D1111yescharacteristic
786C2×C4C22×D4411yescharacteristic
787C2×C4C22×C22⋊D1111yescharacteristic
788C8—41no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—222no—
793C8—441no—
794C8—441no—
795C8—441no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—441no—
805C22—441no—
806C22—441no—
807C22#1062261812yes—
808C22C22×(C2×D11)⋊C411yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—441no—
822C4—441no—
823C4—441no—
824C4—441no—
825C4—441no—
826C4—441no—
827C4—441no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—881no—
832C2#1307709811yescharacteristic
833C2C2×#1062261811yescharacteristic
834C2#1307716111yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2923C2
socleC22×C11C22×C22⋊C4
prime radical#13082594C2
cosocleC42×C11C24
hypercenter#2923D11
hypocenterC11#17680
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13077630C2semidirect
3. #13067253C2semidirect
4. #13067248C2semidirect
5. #13067245C2semidirect
6. #13067242C2semidirect
7. #13067237C2semidirect
8. #13067234C2semidirect
9. #13067232C2semidirect
10. #13067224C2semidirect
11. #13067219C2semidirect
12. #13067217C2semidirect
13. #13067205C2semidirect
14. C2×#10622103C2semidirect
15. C11×#2923C2semidirect
323. #2923D11semidirect
737. C11#17680semidirect

Maximal subgroups

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

subgroupindex
#130825942
#130776302
#130672532
#130672482
#130672452
#130672422
#130672372
#130672342
#130672322
#130672242
#130672192
#130672172
#130672052
C2×#106221032
C11×#29232
#1768011