Finite Group Databasebeta

← #15625860

Subgroups — #15625860

Order 2816.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13079791C214yesmaximal, complemented
3#13079780C214yesmaximal, complemented
4#13079771C212yesmaximal, complemented
5#13079764C211yesmaximal, characteristic, complemented
6#13079757C211yesmaximal, characteristic, complemented
7#13079748C212yesmaximal, complemented
8#13079741C211yesmaximal, characteristic, complemented
9#13079734C211yesmaximal, characteristic, complemented
10#13079126C212yesmaximal, complemented
11#13078938C212yesmaximal, complemented
12#13078525C214yesmaximal, complemented
13#13078404C214yesmaximal, complemented
14C2×#10622538C211yesmaximal, characteristic, complemented
15C11×#3444C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—21no—
23C11×#529—21no—
24C11×#529—21no—
25C11×#529—21no—
26C11×#529C2212yes—
27C11×#529C2212yes—
28C11×#525—21no—
29C11×#525—21no—
30C11×#525C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41—21no—
33C4×C11×#41C2212yes—
34C22×C42×C11C2211yescharacteristic
35C2×#66979C2212yes—
36C2×#66977—21no—
37C2×#66977—21no—
38#10623001—21no—
39#10623001—21no—
40#10623001—21no—
41#10623001—21no—
42#10623001C2212yes—
43#10623001C2212yes—
44#10623001C2212yes—
45#10623001C2212yes—
46C2×#66923C2212yes—
47C2×#66922C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22—21no—
50C2×C4×Dic22—21no—
51#10622846C2218yes—
52C2×C22⋊(C11⋊C8)C2212yes—
53#10622694C2212yescomplemented
54#10622694C2212yescomplemented
55#10622692C2212yescomplemented
56#10622692C2212yescomplemented
57#10622691C2212yescomplemented
58#10622691C2212yescomplemented
59#10622683C2212yescomplemented
60#10622683C2212yescomplemented
61#10622677C2218yescomplemented
62#10622669C2218yescomplemented
63#10622658C2218yes—
64#10622657C2214yes—
65#10622656C2214yes—
66#10622648C2218yes—
67#10622647C2214yes—
68#10622646C2214yes—
69#10622635C2218yescomplemented
70#10622634C2214yescomplemented
71#10622633C2214yescomplemented
72#10622622C2218yescomplemented
73#10622621C2214yescomplemented
74#10622620C2214yescomplemented
75#10622611C2218yes—
76#10622538C2211yescharacteristic
77#10622538C2211yescharacteristic
78#10622538C2212yes—
79#10622538C2212yes—
80#10622538C2212yes—
81C2×C4⋊(C11⋊C8)C2212yes—
82C2×C4×C11⋊C8C2212yes—
83C2×C11×#41—21no—
84C2×C11×#41—21no—
85C2×C11×#41C2312yes—
86C23×C4×C11D411yescharacteristic
87C23×C4×C11D411yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×Dic22—21no—
90C22×Dic22—21no—
91C11×C4⋊Q8C2311yescharacteristic
92C11×C4⋊Q8C2311yescharacteristic
93C11×C4⋊Q8C2311yescharacteristic
94C11×#127C2311yescharacteristic
95C11×#126—22no—
96C11×#126—22no—
97C11×#125—21no—
98C11×#125—21no—
99C11×#125C2312yes—
100C11×#124—21no—
101C11×#124—21no—
102C11×#124C2312yes—
103C11×#123—22no—
104C11×#123—22no—
105C11×#123—22no—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8C2312yes—
111C11×C22⋊Q8C2312yes—
112C11×#121—21no—
113C11×#121—21no—
114C11×#121—21no—
115C11×#121—21no—
116C11×#121C2312yes—
117C11×#121C2312yes—
118C11×#120—22no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11C2312yes—
136C4×D4×C11C2312yes—
137C11×#117—21no—
138C11×#117—21no—
139C11×#117—22no—
140C11×#117—22no—
141C11×#117—22no—
142C11×#117C2312yes—
143C2×C42×C11—22no—
144C2×C42×C11D411yescharacteristic
145C2×C42×C11D411yescharacteristic
146C2×C42×C11D411yescharacteristic
147C2×C42×C11D411yescharacteristic
148C2×C42×C11D411yescharacteristic
149C2×C42×C11D411yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C2×C22⋊Dic11—22no—
157#66979—22no—
158#66979—22no—
159#66979C2314yes—
160#66979C2314yes—
161C2×C4⋊Dic11—21no—
162C2×C4⋊Dic11—21no—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2312yes—
165#66977—22no—
166#66977—22no—
167#66977—22no—
168#66977—22no—
169#66977—22no—
170#66977—22no—
171#66977—22no—
172#66977—22no—
173C2×Dic11⋊C4—22no—
174C2×Dic11⋊C4—22no—
175C2×C4×Dic11—22no—
176C22×C11⋊C8C2314yes—
177#66923—22no—
178#66923—22no—
179#66923C2314yes—
180#66923C2314yes—
181#66922—21no—
182#66922—21no—
183#66922—21no—
184#66922—21no—
185#66922C2312yes—
186#66922C2312yes—
187#66922C2312yes—
188#66922C2312yes—
189C4×Dic22—22no—
190C4×Dic22—22no—
191C4×Dic22—22no—
192C4×Dic22—22no—
193C4×Dic22—22no—
194C4×Dic22—22no—
195C4×Dic22—22no—
196C4×Dic22—22no—
197#66899C2318yes—
198#66899C2318yes—
199#66896C2318yes—
200#66896C2318yes—
201C22⋊(C11⋊C8)C2312yes—
202C22⋊(C11⋊C8)C2312yes—
203C22⋊(C11⋊C8)C2314yes—
204#66872C2318yes—
205#66872C2318yes—
206#66871C2318yes—
207#66871C2318yes—
208C4⋊(C11⋊C8)C2312yes—
209C4⋊(C11⋊C8)C2312yes—
210C4⋊(C11⋊C8)C2314yes—
211C4×C11⋊C8C2314yes—
212C4×C11⋊C8C2312yes—
213C4×C11⋊C8C2312yes—
214#60846—111nomaximal, Sylow
215C24×C11C2×D411yescharacteristic
216C11×#41—28no—
217C11×#41—44no—
218C11×#41—44no—
219C2×Q8×C11—21no—
220C2×Q8×C11—21no—
221C2×Q8×C11C2412yes—
222C2×D4×C11—22no—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11C2412yes—
228C22×C4×C11—24no—
229C22×C4×C11—24no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—42no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×Dic11—22no—
253C22×Dic11—22no—
254C2×Dic22—22no—
255C2×Dic22—22no—
256C2×Dic22—22no—
257C2×Dic22—22no—
258C2×Dic22—44no—
259C2×Dic22—44no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—22no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—22no—
270C11×C4⋊C4C2412yes—
271C11×C4⋊C4C2412yes—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C42×C11—22no—
282C42×C11—22no—
283C42×C11—22no—
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299C42×C11C2411yescharacteristic
300C22⋊Dic11—24no—
301C22⋊Dic11—24no—
302C4⋊Dic11—22no—
303C4⋊Dic11—22no—
304C4⋊Dic11—22no—
305C4⋊Dic11—22no—
306C4⋊Dic11—22no—
307C4⋊Dic11—22no—
308C4⋊Dic11C2414yes—
309C4⋊Dic11C2414yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314C4×Dic11—24no—
315C4×Dic11—24no—
316C2×C11⋊C8—28no—
317C2×C11⋊C8C2414yes—
318C2×C11⋊C8C2414yes—
319#3444D1111yescharacteristic
320C2×#533—111no—
321#3233—114no—
322#3232—114no—
323#3231—112no—
324#3230—111no—
325#3229—111no—
326#3228—112no—
327#3227—111no—
328#3226—111no—
329#3160—112no—
330#3131—112no—
331#3091—114no—
332#3076—114no—
333C2×#431—111no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—41no—
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341Q8×C11—24no—
342Q8×C11—42no—
343Q8×C11—42no—
344D4×C11—24no—
345D4×C11—44no—
346D4×C11—44no—
347D4×C11—44no—
348D4×C11—42no—
349D4×C11—42no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—44no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11#13514yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C112−1+414yes—
385C2×C4×C11C2511yescharacteristic
386C2×Dic11—24no—
387C2×Dic11—24no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390Dic22—44no—
391Dic22—44no—
392Dic22—44no—
393Dic22—44no—
394C11⋊C8—24no—
395C11⋊C8—24no—
396#533—112no—
397#533—112no—
398#533—112no—
399#533—112no—
400#533—221no—
401#533—221no—
402#533—221no—
403#533—221no—
404#533C2×D1111yescharacteristic
405#533C2×D1111yescharacteristic
406#533C2×D1111yescharacteristic
407#532C2×D1111yescharacteristic
408#532C2×D1111yescharacteristic
409#532C2×D1111yescharacteristic
410C2×C4⋊Q8—111no—
411C2×C4⋊Q8—111no—
412#529—21no—
413#529—21no—
414#529—21no—
415#529—21no—
416#529C2×D1112yes—
417#529C2×D1112yes—
418C2×#125—112no—
419#525—21no—
420#525—21no—
421#525C2×D1112yes—
422C2×C22⋊Q8—221no—
423C2×C22⋊Q8—221no—
424C4×#41—21no—
425C4×#41—21no—
426C4×#41C2×D1112yes—
427C2×C4×Q8—221no—
428C2×C4×Q8—221no—
429C2×#117—112no—
430C22×C42C2×D1111yescharacteristic
431#500—112no—
432#500—112no—
433#499—118no—
434#498—112no—
435#498—112no—
436#488—118no—
437#487—112no—
438#487—112no—
439#486—112no—
440#486—112no—
441#485—118no—
442#484—114no—
443#483—114no—
444#482—118no—
445#481—114no—
446#480—114no—
447#479—118no—
448#478—118no—
449#477—114no—
450#476—114no—
451#475—114no—
452#474—114no—
453#431—111no—
454#431—111no—
455#431—112no—
456#431—112no—
457#431—112no—
458#427—118no—
459C2×C4⋊C8—112no—
460#416—118no—
461C2×C22⋊C8—112no—
462C2×C4×C8—112no—
463C22×C11—21no—
464C22×C11—21no—
465C22×C11—21no—
466C22×C11—21no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—44no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11#53612yes—
475C22×C11C2×#13512yes—
476C22×C11C23×D411yescharacteristic
477C4×C11—21no—
478C4×C11—21no—
479C4×C11—21no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11#53612yes—
488C4×C11C2×#13512yes—
489C4×C11C2×#13512yes—
490C4×C11#57512yes—
491C4×C11C2×2−1+412yes—
492Dic11—44no—
493Dic11—44no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41C22×D1112yes—
497C22×Q8—221no—
498C22×Q8—221no—
499C23×C4C22⋊D1111yescharacteristic
500C23×C4C22⋊D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C22×C8—114no—
503C4⋊Q8—112no—
504C4⋊Q8—112no—
505C4⋊Q8—112no—
506C4⋊Q8—112no—
507C4⋊Q8—221no—
508C4⋊Q8—221no—
509C4⋊Q8—221no—
510C4⋊Q8—221no—
511C4⋊Q8C22×D1111yescharacteristic
512C4⋊Q8C22×D1111yescharacteristic
513C4⋊Q8C22×D1111yescharacteristic
514#127C22×D1111yescharacteristic
515#126—22no—
516#126—22no—
517#125—21no—
518#125—21no—
519#125—114no—
520#125—114no—
521#125—222no—
522#125—222no—
523#125C22×D1112yes—
524#124—21no—
525#124—21no—
526#124C22×D1112yes—
527#123—22no—
528#123—22no—
529#123—22no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—222no—
535C22⋊Q8—222no—
536C22⋊Q8—222no—
537C22⋊Q8—222no—
538C22⋊Q8—222no—
539C22⋊Q8—222no—
540C22⋊Q8—222no—
541C22⋊Q8—222no—
542C22⋊Q8C22×D1112yes—
543C22⋊Q8C22×D1112yes—
544#121—21no—
545#121—21no—
546#121—21no—
547#121—21no—
548#121C22×D1112yes—
549#121C22×D1112yes—
550#120—22no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8—222no—
556C4×Q8—222no—
557C4×Q8—222no—
558C4×Q8—222no—
559C4×Q8—222no—
560C4×Q8—222no—
561C4×Q8—222no—
562C4×Q8—222no—
563C4×Q8C22×D1112yes—
564C4×Q8C22×D1112yes—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4C22×D1112yes—
576C4×D4C22×D1112yes—
577#117—21no—
578#117—21no—
579#117—22no—
580#117—22no—
581#117—22no—
582#117—114no—
583#117—114no—
584#117—222no—
585#117—222no—
586#117C22×D1112yes—
587C2×C4⋊C4—112no—
588C2×C4⋊C4—112no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C22⋊C4—222no—
594C2×C42—22no—
595C2×C42—222no—
596C2×C42C22⋊D1111yescharacteristic
597C2×C42C22⋊D1111yescharacteristic
598C2×C42C22⋊D1111yescharacteristic
599C2×C42C22⋊D1111yescharacteristic
600C2×C42C22⋊D1111yescharacteristic
601C2×C42C22⋊D1111yescharacteristic
602C2×C42C22×D1111yescharacteristic
603C2×C42C22×D1111yescharacteristic
604C2×C42C22×D1111yescharacteristic
605C2×C42C22×D1111yescharacteristic
606C2×C42C22×D1111yescharacteristic
607C2×C42C22×D1111yescharacteristic
608#107—118no—
609#107—118no—
610#106—118no—
611#106—118no—
612C4⋊C8—112no—
613C4⋊C8—112no—
614C4⋊C8—114no—
615#103—118no—
616#103—118no—
617#102—118no—
618#102—118no—
619C22⋊C8—112no—
620C22⋊C8—112no—
621C22⋊C8—114no—
622C4×C8—112no—
623C4×C8—112no—
624C4×C8—114no—
625C2×C11—22no—
626C2×C11—22no—
627C2×C11—41no—
628C2×C11—82no—
629C2×C11C2×#53611yescharacteristic
630C2×C11C22×#13511yescharacteristic
631C2×C11C2×#57511yescharacteristic
632C24C2×C22⋊D1111yescharacteristic
633#41—28no—
634#41—44no—
635#41—44no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—222no—
639C2×Q8—222no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8—444no—
643C2×Q8—444no—
644C2×Q8C23×D1112yes—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4C23×D1112yes—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—42no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4C2×C22⋊D1111yescharacteristic
660C22×C4C2×C22⋊D1111yescharacteristic
661C22×C4C2×C22⋊D1111yescharacteristic
662C22×C4C2×C22⋊D1111yescharacteristic
663C22×C4C2×C22⋊D1111yescharacteristic
664C22×C4C2×C22⋊D1111yescharacteristic
665C22×C4C2×C22⋊D1111yescharacteristic
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C2×C22⋊D1111yescharacteristic
671C22×C4C2×C22⋊D1111yescharacteristic
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C22×C4C23×D1111yescharacteristic
676C22×C4C23×D1111yescharacteristic
677C2×C8—114no—
678C2×C8—114no—
679C2×C8—228no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—114no—
691C4⋊C4—114no—
692C4⋊C4—222no—
693C4⋊C4—222no—
694C4⋊C4—224no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4—224no—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C4⋊C4—222no—
702C4⋊C4C23×D1112yes—
703C4⋊C4C23×D1112yes—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—224no—
719C42—224no—
720C42C2×C22⋊D1111yescharacteristic
721C42C2×C22⋊D1111yescharacteristic
722C42C2×C22⋊D1111yescharacteristic
723C42C2×C22⋊D1111yescharacteristic
724C42C2×C22⋊D1111yescharacteristic
725C42C2×C22⋊D1111yescharacteristic
726C42C2×C22⋊D1111yescharacteristic
727C42C2×C22⋊D1111yescharacteristic
728C42C2×C22⋊D1111yescharacteristic
729C42C2×C22⋊D1111yescharacteristic
730C42C2×C22⋊D1111yescharacteristic
731C42C2×C22⋊D1111yescharacteristic
732C42C23×D1111yescharacteristic
733C42C23×D1111yescharacteristic
734C42C23×D1111yescharacteristic
735C42C23×D1111yescharacteristic
736C11#6084611yescharacteristic, complemented, Sylow
737C23—22no—
738C23—22no—
739C23—22no—
740C23—41no—
741C23C22×C22⋊D1111yescharacteristic
742C23C22×C22⋊D1111yescharacteristic
743C23C22×C22⋊D1111yescharacteristic
744Q8—24no—
745Q8—42no—
746Q8—42no—
747Q8—444no—
748Q8—444no—
749Q8—444no—
750Q8—444no—
751D4—24no—
752D4—44no—
753D4—44no—
754D4—44no—
755D4—42no—
756D4—42no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4#6700314yes—
784C2×C4#6704314yes—
785C2×C4C22×C22⋊D1111yescharacteristic
786C2×C4C22×C22⋊D1111yescharacteristic
787C2×C4C22×C22⋊D1111yescharacteristic
788C2×C4C22×C22⋊D1111yescharacteristic
789C2×C4C22×C22⋊D1111yescharacteristic
790C2×C4C22×C22⋊D1111yescharacteristic
791C2×C4C22×C22⋊D1111yescharacteristic
792C2×C4C22×C22⋊D1111yescharacteristic
793C2×C4C22×C22⋊D1111yescharacteristic
794C2×C4C22×C22⋊D1111yescharacteristic
795C2×C4C22×C22⋊D1111yescharacteristic
796C2×C4C24×D1111yescharacteristic
797C8—224no—
798C8—224no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—44no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22C2×#6700312yes—
811C22#1062335612yes—
812C22C23×C22⋊D1111yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—444no—
824C4—444no—
825C4C2×#6700312yes—
826C4C2×#6700312yes—
827C4#1062335312yes—
828C4#1062335612yes—
829C4C2×#6704312yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—82no—
834C2C2×#1062335611yescharacteristic
835C2C22×#6700311yescharacteristic
836C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60846
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13079791C2semidirect
3. #13079780C2semidirect
4. #13079771C2semidirect
5. #13079764C2semidirect
6. #13079757C2semidirect
7. #13079748C2semidirect
8. #13079741C2semidirect
9. #13079734C2semidirect
10. #13079126C2semidirect
11. #13078938C2semidirect
12. #13078525C2semidirect
13. #13078404C2semidirect
14. C2×#10622538C2semidirect
53. #10622694C22semidirect
54. #10622694C22semidirect
55. #10622692C22semidirect
56. #10622692C22semidirect
57. #10622691C22semidirect
58. #10622691C22semidirect
59. #10622683C22semidirect
60. #10622683C22semidirect
61. #10622677C22semidirect
62. #10622669C22semidirect
69. #10622635C22semidirect
70. #10622634C22semidirect
71. #10622633C22semidirect
72. #10622622C22semidirect
73. #10622621C22semidirect
74. #10622620C22semidirect
736. C11#60846semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130797912
#130797802
#130797712
#130797642
#130797572
#130797482
#130797412
#130797342
#130791262
#130789382
#130785252
#130784042
C2×#106225382
C11×#34442
#6084611