Finite Group Databasebeta

← #14720823

Subgroups — #14720823

Order 2816.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082231C211yesmaximal, characteristic
2#13077741C211yesmaximal, characteristic, complemented
3#13067090C211yesmaximal, characteristic, complemented
4#13067082C211yesmaximal, characteristic, complemented
5#13067077C211yesmaximal, characteristic, complemented
6#13067064C211yesmaximal, characteristic, complemented
7#13067051C211yesmaximal, characteristic, complemented
8#13067046C211yesmaximal, characteristic, complemented
9#13067030C211yesmaximal, characteristic, complemented
10#13067025C211yesmaximal, characteristic, complemented
11#13067020C211yesmaximal, characteristic, complemented
12#13067012C211yesmaximal, characteristic, complemented
13#13067004C211yesmaximal, characteristic, complemented
14C2×#10622094C211yesmaximal, characteristic, complemented
15C11×#2922C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623355—21no—
18#10623115C411yescharacteristic
19#10623109—21no—
20#10623098C411yescharacteristic
21#10623086C411yescharacteristic
22#10623083C411yescharacteristic
23#10623083C411yescharacteristic
24#10623072C411yescharacteristic
25#10623072C411yescharacteristic
26#10623069—21no—
27#10623069—21no—
28D4×Dic22C411yescharacteristic
29C4×#4341—21no—
30#10623064—21no—
31#10623062—21no—
32#10623062—21no—
33#10623010C2211yescharacteristic
34#10623010C2211yescharacteristic
35C4×#4339C2211yescharacteristic
36#10623001C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#433—21no—
40C11×#433—21no—
41C11×#431C2211yescharacteristic
42C11×#431C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C11×#431C2211yescharacteristic
45C11×#424—21no—
46C11×#408—21no—
47C4×C11×M16C2211yescharacteristic
48C2×C4×C8×C11C2211yescharacteristic
49#10622637—21no—
50#10622624—21no—
51#10622624—21no—
52D4×C11⋊C8—21no—
53#10622539C2211yescharacteristic
54#10622539C2211yescharacteristic
55#10622538C2211yescharacteristic
56#10622537C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67#10622094C2211yescharacteristic
68#10622094C2211yescharacteristic
69#10622094C2211yescharacteristic
70#10622094C2211yescharacteristic
71#10622094C2211yescharacteristic
72#10622094C2211yescharacteristic
73#10622094C2211yescharacteristic
74#10622094C2211yescharacteristic
75C2×C11×#41D411yescharacteristic
76C2×#4341—21no—
77C2×#4339C2×C411yescharacteristic
78C22×Dic22C2×C411yescharacteristic
79C22×Dic22C2×C411yescharacteristic
80C2×C11×M16—21no—
81C22×C8×C11—21no—
82C4×Q8×C11C2×C411yescharacteristic
83C4×Q8×C11D411yescharacteristic
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2×C411yescharacteristic
86C4×D4×C11C2×C411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C4×D4×C11D411yescharacteristic
89C4×D4×C11D411yescharacteristic
90C11×#117D411yescharacteristic
91C11×#117D411yescharacteristic
92C11×#117D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96#66999—21no—
97#66997—21no—
98#66992—21no—
99#66992—21no—
100#66988—21no—
101#66988—21no—
102D4×Dic11—21no—
103#66983C2×C411yescharacteristic
104#66983C2×C411yescharacteristic
105#66982—21no—
106#66982—21no—
107C4×C22⋊D11—21no—
108C4×C22⋊D11—21no—
109C4×C22⋊D11—21no—
110C4×C22⋊D11—21no—
111#66979—21no—
112#66979C2×C411yescharacteristic
113C2×C4⋊Dic11C2×C411yescharacteristic
114C2×C4⋊Dic11C2×C411yescharacteristic
115#66977—21no—
116#66977C2×C411yescharacteristic
117#66977C2×C411yescharacteristic
118#66977C2×C411yescharacteristic
119#66977C2×C411yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—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—
132#66945—21no—
133#66942—21no—
134#66942—21no—
135#66942—21no—
136#66942—21no—
137#66941—21no—
138#66940—21no—
139#66939—21no—
140#66939—21no—
141#66938—21no—
142#66938—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#66928C2×C411yescharacteristic
154#66928C2×C411yescharacteristic
155C4×D44C2×C411yescharacteristic
156C4×D44C2311yescharacteristic
157#66925—21no—
158#66925—21no—
159#66925—21no—
160C42×D11—21no—
161#66923—21no—
162#66923C2×C411yescharacteristic
163#66923C2×C411yescharacteristic
164#66922C2×C411yescharacteristic
165#66922C2×C411yescharacteristic
166C4×Dic22—21no—
167C4×Dic22—21no—
168C4×Dic22—21no—
169C4×Dic22—21no—
170C4×Dic22—21no—
171C4×Dic22C2×C411yescharacteristic
172C4×Dic22C2×C411yescharacteristic
173C4×Dic22C2×C411yescharacteristic
174C4×Dic22C2×C411yescharacteristic
175C4×Dic22C2×C411yescharacteristic
176C4×Dic22C2311yescharacteristic
177C4×Dic22C2311yescharacteristic
178C4×Dic22C2311yescharacteristic
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—
188C4×C8×C11—21no—
189C4×C8×C11C2311yescharacteristic
190C4×C8×C11C2311yescharacteristic
191C4×C8×C11C2311yescharacteristic
192C4×C8×C11C2311yescharacteristic
193C22⋊(C11⋊C8)—21no—
194C22⋊(C11⋊C8)—21no—
195C22⋊(C11⋊C8)—21no—
196C4⋊(C11⋊C8)—21no—
197C4⋊(C11⋊C8)—21no—
198C4⋊(C11⋊C8)—21no—
199C4⋊(C11⋊C8)C2311yescharacteristic
200C4⋊(C11⋊C8)C2311yescharacteristic
201C4⋊(C11⋊C8)C2311yescharacteristic
202C4⋊(C11⋊C8)C2311yescharacteristic
203#66867—21no—
204#66867—21no—
205C4×C11⋊C8—21no—
206#17524—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—
229#4339—22no—
230#4339—41no—
231C2×D44C22×C411yescharacteristic
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×Dic22—22no—
236C2×Dic22—22no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22—41no—
241C2×Dic22—41no—
242C2×Dic22C22×C411yescharacteristic
243C2×Dic22C22×C411yescharacteristic
244C2×Dic22C22×C411yescharacteristic
245C11×M16—42no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—42no—
251C11×C4⋊C4C22⋊C411yescharacteristic
252C11×C4⋊C4C22⋊C411yescharacteristic
253C11×C4⋊C4C22⋊C411yescharacteristic
254C11×C4⋊C4C22⋊C411yescharacteristic
255C11×C4⋊C4C22⋊C411yescharacteristic
256C11×C4⋊C4C22⋊C411yescharacteristic
257C11×C22⋊C4C22⋊C411yescharacteristic
258C11×C22⋊C4C22⋊C411yescharacteristic
259C11×C22⋊C4C22⋊C411yescharacteristic
260C11×C22⋊C4C22⋊C411yescharacteristic
261C11×C22⋊C4C22⋊C411yescharacteristic
262C11×C22⋊C4C22⋊C411yescharacteristic
263C42×C11C22×C411yescharacteristic
264C42×C11C22×C411yescharacteristic
265C42×C11C22×C411yescharacteristic
266C42×C11C2×D411yescharacteristic
267C42×C11C2×D411yescharacteristic
268C42×C11C2×D411yescharacteristic
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2411yescharacteristic
273C22⋊Dic11—21no—
274C22⋊Dic11—21no—
275C22⋊Dic11—21no—
276C22⋊Dic11—21no—
277C22⋊Dic11—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—
286C4⋊Dic11—21no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—21no—
291C4⋊Dic11C22×C411yescharacteristic
292C4⋊Dic11C22×C411yescharacteristic
293C4⋊Dic11C22×C411yescharacteristic
294C4⋊Dic11C22×C411yescharacteristic
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—
309Dic11⋊C4—21no—
310Dic11⋊C4—21no—
311C4×Dic11—21no—
312C4×Dic11—21no—
313C4×Dic11—21no—
314C4×Dic11—21no—
315C4×Dic11—21no—
316C4×Dic11—21no—
317C4×Dic11—21no—
318C4×Dic11—21no—
319C4×Dic11—21no—
320#4318—81no—
321C2×C11⋊C8—21no—
322C2×C11⋊C8—21no—
323C2×C11⋊C8—21no—
324C2×C11⋊C8—21no—
325C2×C11⋊C8—81no—
326C2×C11⋊C8—81no—
327#3482—111no—
328#2990—111no—
329#2922D1111yescharacteristic, complemented
330#1497—111no—
331#1495—111no—
332#1494—111no—
333#1491—111no—
334#1488—111no—
335#1487—111no—
336#1483—111no—
337#1482—111no—
338#1481—111no—
339#1479—111no—
340#1477—111no—
341C2×Q8⋊C8—111no—
342C23×C11C2×C22⋊C411yescharacteristic
343C23×C11C2×C22⋊C411yescharacteristic
344C23×C11C2×C22⋊C411yescharacteristic
345C22×D11—21no—
346Q8×C11—41no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—41no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11C2×C22⋊C411yescharacteristic
366C2×C4×C11C2×C22⋊C411yescharacteristic
367C2×C4×C11C2×C22⋊C411yescharacteristic
368C2×C4×C11C2×C22⋊C411yescharacteristic
369C2×C4×C11C2×C22⋊C411yescharacteristic
370C2×C4×C11C2×C22⋊C411yescharacteristic
371C2×C4×C11C2×C22⋊C411yescharacteristic
372C2×C4×C11C2×C22⋊C411yescharacteristic
373C2×C4×C11C2×C22⋊C411yescharacteristic
374C2×C4×C11C23×C411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C22⋊D11—42no—
378C22⋊D11—42no—
379C22⋊D11—42no—
380C2×Dic11—21no—
381C2×Dic11—21no—
382C2×Dic11—21no—
383C2×Dic11—21no—
384C2×Dic11—21no—
385C2×Dic11—21no—
386C2×Dic11—21no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391D44—21no—
392D44—21no—
393C4×D11—42no—
394C4×D11—42no—
395C4×D11—41no—
396C4×D11—41no—
397Dic22—21no—
398Dic22—21no—
399Dic22—21no—
400Dic22—21no—
401Dic22—21no—
402Dic22—42no—
403Dic22—42no—
404Dic22—42no—
405Dic22#13112yes—
406C8×C11—41no—
407C8×C11—41no—
408C8×C11—41no—
409C8×C11—41no—
410C11⋊C8—41no—
411C11⋊C8—41no—
412C11⋊C8—41no—
413C11⋊C8—41no—
414#557—111no—
415#556—111no—
416#556—221no—
417#552—111no—
418#552—111no—
419#552—221no—
420#552—221no—
421D4×Q8—111no—
422#548—111no—
423#548—111no—
424#547—111no—
425#547—221no—
426#533—111no—
427#533—221no—
428#529—111no—
429#529—111no—
430#529—221no—
431#529—221no—
432C4×#41—111no—
433C4×#41—221no—
434C4×#41C2×D1111yescharacteristic
435C2×C4×Q8—111no—
436C2×C4×Q8—111no—
437#446—221no—
438#435—221no—
439#435—221no—
440C8×D4—221no—
441#433—21no—
442#433—21no—
443#432—111no—
444#432—111no—
445#431—111no—
446#431C2×D1111yescharacteristic
447#431C2×D1111yescharacteristic
448#431C2×D1111yescharacteristic
449#431C2×D1111yescharacteristic
450#424—21no—
451#423—111no—
452C2×C4⋊C8—111no—
453C2×C4⋊C8—111no—
454#408—21no—
455C4×M16C2×D1111yescharacteristic
456C2×C4×C8C2×D1111yescharacteristic
457Q8⋊C8—111no—
458Q8⋊C8—111no—
459Q8⋊C8—111no—
460Q8⋊C8—111no—
461Q8⋊C8—111no—
462Q8⋊C8—111no—
463Q8⋊C8—111no—
464Q8⋊C8—111no—
465Q8⋊C8—111no—
466Q8⋊C8—111no—
467Q8⋊C8—111no—
468Q8⋊C8—111no—
469D4⋊C8—111no—
470D4⋊C8—111no—
471D4⋊C8—111no—
472D4⋊C8—111no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—21no—
479C22×C11—21no—
480C22×C11—21no—
481C22×C11#42112yes—
482C22×C11C22×C22⋊C411yescharacteristic
483C2×D11—41no—
484C2×D11—41no—
485C2×D11—41no—
486C4×C11—21no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—21no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—21no—
493C4×C11—21no—
494C4×C11—21no—
495C4×C11—21no—
496C4×C11C2×#13111yescharacteristic
497C4×C11#56811yescharacteristic
498C4×C11#57711yescharacteristic
499C4×C11#57811yescharacteristic
500Dic11—22no—
501Dic11—41no—
502Dic11—41no—
503Dic11—41no—
504Dic11—41no—
505Dic11—41no—
506Dic11—41no—
507C2×#41—111no—
508C2×#41—221no—
509C2×#41C22⋊D1111yescharacteristic
510C22×Q8—111no—
511C22×Q8—111no—
512C2×M16—21no—
513C2×M16—221no—
514C22×C8—21no—
515C22×C8—221no—
516C22×C8—221no—
517C4⋊Q8—111no—
518C4⋊Q8—111no—
519C4⋊Q8—221no—
520C4⋊Q8—221no—
521#126—221no—
522#126—221no—
523#126—221no—
524#126—221no—
525#126—221no—
526#126—221no—
527#125—111no—
528#125—111no—
529#125—221no—
530#125—221no—
531#125—221no—
532#125—221no—
533#125—221no—
534#124—111no—
535#124—111no—
536#124—221no—
537#124—221no—
538#123—221no—
539#123—221no—
540#123—221no—
541#123—221no—
542#123—221no—
543#123—221no—
544C22⋊Q8—111no—
545C22⋊Q8—111no—
546C22⋊Q8—111no—
547C22⋊Q8—111no—
548C22⋊Q8—221no—
549C22⋊Q8—221no—
550C22⋊Q8—221no—
551C22⋊Q8—221no—
552C22⋊Q8—221no—
553C22⋊Q8—221no—
554C22⋊Q8—221no—
555#121—111no—
556#121—111no—
557#121—221no—
558#121—221no—
559C4×Q8—111no—
560C4×Q8—111no—
561C4×Q8—111no—
562C4×Q8—111no—
563C4×Q8—111no—
564C4×Q8—111no—
565C4×Q8—111no—
566C4×Q8—111no—
567C4×Q8—221no—
568C4×Q8—221no—
569C4×Q8—221no—
570C4×Q8—221no—
571C4×Q8—221no—
572C4×Q8—221no—
573C4×Q8C4×D1111yescharacteristic
574C4×Q8D4411yescharacteristic
575C4×D4—111no—
576C4×D4—111no—
577C4×D4—221no—
578C4×D4—221no—
579C4×D4—221no—
580C4×D4—221no—
581C4×D4—221no—
582C4×D4—221no—
583C4×D4—221no—
584C4×D4C4×D1111yescharacteristic
585C4×D4C4×D1111yescharacteristic
586C4×D4C4×D1111yescharacteristic
587C4×D4D4411yescharacteristic
588C4×D4D4411yescharacteristic
589C4×D4D4411yescharacteristic
590#117—111no—
591#117—221no—
592#117—221no—
593#117—221no—
594#117—221no—
595#117—221no—
596#117—221no—
597#117—221no—
598#117C22⋊D1111yescharacteristic
599#117C22⋊D1111yescharacteristic
600#117C22⋊D1111yescharacteristic
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C42—221no—
606C2×C42—221no—
607C2×C42—221no—
608C2×C42C22×D1111yescharacteristic
609C2×C42C22×D1111yescharacteristic
610C2×C42C22×D1111yescharacteristic
611C4⋊C8—21no—
612C4⋊C8—21no—
613C4⋊C8—21no—
614C4⋊C8—21no—
615C4⋊C8—111no—
616C4⋊C8—111no—
617C4⋊C8—111no—
618C4⋊C8—111no—
619C4⋊C8—221no—
620C4⋊C8—221no—
621C4⋊C8—221no—
622C22⋊C8—21no—
623C22⋊C8—21no—
624C22⋊C8—21no—
625C22⋊C8—21no—
626C22⋊C8—221no—
627C22⋊C8—221no—
628C22⋊C8—221no—
629#97—21no—
630#97—221no—
631#97—221no—
632C4×C8—21no—
633C4×C8—221no—
634C4×C8C22×D1111yescharacteristic
635C4×C8C22×D1111yescharacteristic
636C4×C8C22×D1111yescharacteristic
637C4×C8C22×D1111yescharacteristic
638C2×C11—22no—
639C2×C11—41no—
640C2×C11—41no—
641C2×C11#288011yescharacteristic
642C2×C11#289811yescharacteristic
643C2×C11C2×#42111yescharacteristic
644D11—81no—
645#41—42no—
646#41—222no—
647#41—441no—
648#41—444no—
649C2×Q8—111no—
650C2×Q8—111no—
651C2×Q8—111no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8—221no—
655C2×Q8—221no—
656C2×Q8—221no—
657C2×Q8—441no—
658C2×Q8—441no—
659C2×Q8(C2×D11)⋊C411yescharacteristic
660C2×D4—111no—
661C2×D4—221no—
662C2×D4—221no—
663C2×D4—221no—
664C2×D4(C2×D11)⋊C411yescharacteristic
665C2×D4(C2×D11)⋊C411yescharacteristic
666C2×D4(C2×D11)⋊C411yescharacteristic
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4C2×C4×D1111yescharacteristic
675C22×C4C2×C4×D1111yescharacteristic
676C22×C4C2×C4×D1111yescharacteristic
677C22×C4C2×D4411yescharacteristic
678C22×C4C2×D4411yescharacteristic
679C22×C4C2×D4411yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683M16—42no—
684M16—881no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—881no—
695C2×C8—881no—
696C4⋊C4—111no—
697C4⋊C4—111no—
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4—221no—
712C4⋊C4—221no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4(C2×D11)⋊C411yescharacteristic
722C4⋊C4(C2×D11)⋊C411yescharacteristic
723C4⋊C4(C2×D11)⋊C411yescharacteristic
724C4⋊C4(C2×D11)⋊C411yescharacteristic
725C4⋊C4(C2×D11)⋊C411yescharacteristic
726C4⋊C4(C2×D11)⋊C411yescharacteristic
727C22⋊C4—221no—
728C22⋊C4—221no—
729C22⋊C4—221no—
730C22⋊C4—221no—
731C22⋊C4—221no—
732C22⋊C4—221no—
733C22⋊C4—221no—
734C22⋊C4—221no—
735C22⋊C4—221no—
736C22⋊C4—221no—
737C22⋊C4—221no—
738C22⋊C4—221no—
739C22⋊C4—221no—
740C22⋊C4(C2×D11)⋊C411yescharacteristic
741C22⋊C4(C2×D11)⋊C411yescharacteristic
742C22⋊C4(C2×D11)⋊C411yescharacteristic
743C22⋊C4(C2×D11)⋊C411yescharacteristic
744C22⋊C4(C2×D11)⋊C411yescharacteristic
745C22⋊C4(C2×D11)⋊C411yescharacteristic
746C42—221no—
747C42—221no—
748C42—221no—
749C42—221no—
750C42—221no—
751C42—221no—
752C42—221no—
753C42—221no—
754C42—221no—
755C42C2×C4×D1111yescharacteristic
756C42C2×C4×D1111yescharacteristic
757C42C2×C4×D1111yescharacteristic
758C42C2×D4411yescharacteristic
759C42C2×D4411yescharacteristic
760C42C2×D4411yescharacteristic
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1111yescharacteristic
764C42C23×D1111yescharacteristic
765C11#1752411yescharacteristic, complemented, Sylow
766C23—221no—
767C23C2×(C2×D11)⋊C411yescharacteristic
768C23C2×(C2×D11)⋊C411yescharacteristic
769C23C2×(C2×D11)⋊C411yescharacteristic
770Q8—41no—
771Q8—112no—
772Q8—221no—
773Q8—221no—
774Q8—221no—
775Q8—221no—
776Q8—221no—
777Q8—442no—
778Q8—442no—
779Q8—442no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—221no—
784D4—221no—
785D4—442no—
786D4—442no—
787D4—442no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—221no—
807C2×C4—221no—
808C2×C4—221no—
809C2×C4—221no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4C2×(C2×D11)⋊C411yescharacteristic
819C2×C4C2×(C2×D11)⋊C411yescharacteristic
820C2×C4C2×(C2×D11)⋊C411yescharacteristic
821C2×C4C2×(C2×D11)⋊C411yescharacteristic
822C2×C4C2×(C2×D11)⋊C411yescharacteristic
823C2×C4C2×(C2×D11)⋊C411yescharacteristic
824C2×C4C2×(C2×D11)⋊C411yescharacteristic
825C2×C4C2×(C2×D11)⋊C411yescharacteristic
826C2×C4C2×(C2×D11)⋊C411yescharacteristic
827C2×C4C22×C4×D1111yescharacteristic
828C2×C4C22×D4411yescharacteristic
829C2×C4C22×C22⋊D1111yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—441no—
835C8—441no—
836C8—441no—
837C8—441no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—441no—
847C22—441no—
848C22—441no—
849C22#1062261812yes—
850C22C22×(C2×D11)⋊C411yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—222no—
862C4—441no—
863C4—441no—
864C4—441no—
865C4—441no—
866C4—441no—
867C4—441no—
868C4D11×#13111yescharacteristic
869C4#1062328111yescharacteristic
870C4#1062328211yescharacteristic
871C4#1062328411yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—881no—
876C2#1307706311yescharacteristic
877C2#1307715011yescharacteristic
878C2C2×#1062261811yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2922C2
socleC22×C11C22×C22⋊C4
prime radical#13082231C2
cosocleC42×C11C24
hypercenter#2922D11
hypocenterC11#17524
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13077741C2semidirect
3. #13067090C2semidirect
4. #13067082C2semidirect
5. #13067077C2semidirect
6. #13067064C2semidirect
7. #13067051C2semidirect
8. #13067046C2semidirect
9. #13067030C2semidirect
10. #13067025C2semidirect
11. #13067020C2semidirect
12. #13067012C2semidirect
13. #13067004C2semidirect
14. C2×#10622094C2semidirect
15. C11×#2922C2semidirect
329. #2922D11semidirect
765. C11#17524semidirect

Maximal subgroups

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

subgroupindex
#130822312
#130777412
#130670902
#130670822
#130670772
#130670642
#130670512
#130670462
#130670302
#130670252
#130670202
#130670122
#130670042
C2×#106220942
C11×#29222
#1752411