Finite Group Databasebeta

← #15625866

Subgroups — #15625866

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
1#13081912C211yesmaximal, characteristic
2#13079795C214yesmaximal, complemented
3#13079784C214yesmaximal, complemented
4#13079775C212yesmaximal, complemented
5#13079767C211yesmaximal, characteristic, complemented
6#13079760C211yesmaximal, characteristic, complemented
7#13079752C212yesmaximal, complemented
8#13079744C211yesmaximal, characteristic, complemented
9#13079737C211yesmaximal, characteristic, complemented
10#13079126C212yesmaximal, complemented
11#13078941C212yesmaximal, complemented
12#13078529C214yesmaximal, complemented
13#13078398C214yesmaximal, complemented
14C2×#10622538C211yesmaximal, characteristic, complemented
15C2×C11×#533C211yesmaximal, characteristic, complemented
16C11×#533—21no—
17C11×#533—21no—
18C11×#533—21no—
19C11×#533—21no—
20C11×#533C2212yes—
21C11×#533C2212yes—
22C11×#533C2212yes—
23C11×#533C2212yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#125C2212yes—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8—21no—
29C2×C4×Q8×C11—21no—
30C2×C4×Q8×C11—21no—
31C2×C11×#117C2212yes—
32C22×C42×C11C2211yescharacteristic
33#10623322—21no—
34#10623322—21no—
35#10623322C2212yes—
36#10623010—21no—
37#10623010—21no—
38#10623010—21no—
39#10623010—21no—
40#10623010C2212yes—
41#10623010C2212yes—
42#10623008C2211yescharacteristic
43#10623008C2211yescharacteristic
44#10623008C2211yescharacteristic
45C4×#4339—21no—
46C4×#4339—21no—
47C4×#4339C2212yes—
48#10623001C2211yescharacteristic
49#10623001C2211yescharacteristic
50#10623001C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2212yes—
52#10622707C2214yescomplemented
53#10622706C2212yescomplemented
54#10622706C2212yescomplemented
55#10622704C2214yescomplemented
56#10622701C2212yescomplemented
57#10622701C2212yescomplemented
58#10622700C2214yescomplemented
59#10622697C2214yescomplemented
60#10622692C2212yescomplemented
61#10622692C2212yescomplemented
62#10622691C2212yescomplemented
63#10622691C2212yescomplemented
64#10622681C2218yescomplemented
65#10622679C2218yescomplemented
66#10622677C2218yescomplemented
67#10622676C2218yescomplemented
68#10622616C2218yes—
69#10622615C2218yes—
70#10622611C2218yes—
71#10622609C2218yes—
72#10622584C2214yes—
73#10622583C2214yes—
74#10622581C2214yes—
75#10622580C2214yes—
76#10622538C2211yescharacteristic
77#10622538C2211yescharacteristic
78#10622538C2212yes—
79#10622538C2212yes—
80#10622538C2212yes—
81C2×C4⋊(C11⋊C8)C2212yes—
82C2×C4×C11⋊C8C2212yes—
83C22×Q8×C11—21no—
84C22×Q8×C11—21no—
85C23×C4×C11D411yescharacteristic
86C23×C4×C11D411yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C2×#4339—21no—
89C2×#4339—21no—
90C2×#4339C2312yes—
91C11×C4⋊Q8—21no—
92C11×C4⋊Q8—21no—
93C11×C4⋊Q8—21no—
94C11×C4⋊Q8—21no—
95C11×C4⋊Q8C2312yes—
96C11×C4⋊Q8C2312yes—
97C11×C4⋊Q8C2312yes—
98C11×C4⋊Q8C2312yes—
99C11×#125—22no—
100C11×#125—22no—
101C11×#125C2314yes—
102C11×#125C2314yes—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C4×Q8×C11—22no—
112C4×Q8×C11—22no—
113C4×Q8×C11—22no—
114C4×Q8×C11—22no—
115C4×Q8×C11—22no—
116C4×Q8×C11—22no—
117C4×Q8×C11—22no—
118C4×Q8×C11—22no—
119C11×#117—22no—
120C11×#117—22no—
121C11×#117C2314yes—
122C11×#117C2314yes—
123C2×C11×C4⋊C4—22no—
124C2×C11×C4⋊C4—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4C2312yes—
128C2×C11×C4⋊C4C2312yes—
129C2×C11×C22⋊C4—22no—
130C2×C42×C11—22no—
131C2×C42×C11D411yescharacteristic
132C2×C42×C11D411yescharacteristic
133C2×C42×C11D411yescharacteristic
134C2×C42×C11D411yescharacteristic
135C2×C42×C11D411yescharacteristic
136C2×C42×C11D411yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143#67006—22no—
144#66983—21no—
145#66983—21no—
146#66983—21no—
147#66983—21no—
148#66983C2312yes—
149#66983C2312yes—
150#66982—22no—
151#66982—22no—
152#66982—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159#66979—21no—
160#66979—21no—
161#66979C2312yes—
162#66977—21no—
163#66977—21no—
164#66977—21no—
165#66977—21no—
166#66977C2312yes—
167#66977C2312yes—
168C22×C11⋊C8C2314yes—
169#66929—22no—
170#66929—22no—
171#66928—21no—
172#66928—21no—
173#66928C2312yes—
174#66927C2311yescharacteristic
175C4×D44—21no—
176C4×D44—21no—
177C4×D44—21no—
178C4×D44—21no—
179C4×D44C2312yes—
180C4×D44C2312yes—
181#66925—22no—
182#66925—22no—
183#66925—22no—
184C42×D11—22no—
185#66923—21no—
186#66923—21no—
187#66923C2312yes—
188#66922C2311yescharacteristic
189#66922C2311yescharacteristic
190#66922C2311yescharacteristic
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22—21no—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197C22⋊(C11⋊C8)C2312yes—
198C22⋊(C11⋊C8)C2312yes—
199C22⋊(C11⋊C8)C2314yes—
200#66874C2318yes—
201#66874C2318yes—
202#66873C2318yes—
203#66873C2318yes—
204#66872C2318yes—
205#66872C2318yes—
206#66871C2318yes—
207#66871C2318yes—
208C4⋊(C11⋊C8)C2314yes—
209C4⋊(C11⋊C8)C2312yes—
210C4⋊(C11⋊C8)C2312yes—
211C4×C11⋊C8C2314yes—
212C4×C11⋊C8C2312yes—
213C4×C11⋊C8C2312yes—
214#60846—111nomaximal, Sylow
215C24×C11C2×D411yescharacteristic
216C2×Q8×C11—22no—
217C2×Q8×C11—22no—
218C2×Q8×C11—22no—
219C2×Q8×C11—22no—
220C2×Q8×C11—44no—
221C2×Q8×C11—44no—
222C22×C4×C11—24no—
223C22×C4×C11—24no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—42no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—22no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248#4339—28no—
249#4339—44no—
250#4339—44no—
251C2×D44—21no—
252C2×D44—21no—
253C2×D44C2412yes—
254C2×C4×D11—22no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×Dic22—21no—
258C2×Dic22—21no—
259C2×Dic22C2412yes—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—24no—
263C11×C4⋊C4—24no—
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⋊C4C2414yes—
271C11×C4⋊C4C2414yes—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C42×C11—24no—
275C42×C11—24no—
276C42×C11C2×D411yescharacteristic
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2411yescharacteristic
289C42×C11C2411yescharacteristic
290C42×C11C2411yescharacteristic
291C42×C11C2411yescharacteristic
292C22⋊Dic11—22no—
293C22⋊Dic11—22no—
294C22⋊Dic11—22no—
295(C2×D11)⋊C4—22no—
296(C2×D11)⋊C4—22no—
297(C2×D11)⋊C4—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301C4⋊Dic11—21no—
302C4⋊Dic11—21no—
303C4⋊Dic11—21no—
304C4⋊Dic11—21no—
305C4⋊Dic11C2412yes—
306C4⋊Dic11C2412yes—
307Dic11⋊C4—22no—
308Dic11⋊C4—22no—
309Dic11⋊C4—22no—
310Dic11⋊C4—22no—
311Dic11⋊C4—22no—
312Dic11⋊C4—22no—
313C4×Dic11—22no—
314C4×Dic11—22no—
315C4×Dic11—22no—
316C2×C11⋊C8—28no—
317C2×C11⋊C8C2414yes—
318C2×C11⋊C8C2414yes—
319#3444—111no—
320C2×#533D1111yescharacteristic, complemented
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—41no—
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C22×D11—22no—
341Q8×C11—44no—
342Q8×C11—44no—
343Q8×C11—44no—
344Q8×C11—44no—
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—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—24no—
359C2×C4×C11—24no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11#13514yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C112−1+414yes—
378C2×C4×C11C2511yescharacteristic
379C22⋊D11—44no—
380C22⋊D11—44no—
381C22⋊D11—44no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385D44—24no—
386D44—42no—
387D44—42no—
388C4×D11—44no—
389C4×D11—44no—
390C4×D11—44no—
391Dic22—24no—
392Dic22—42no—
393Dic22—42no—
394C11⋊C8—24no—
395C11⋊C8—24no—
396#533—21no—
397#533—21no—
398#533—21no—
399#533—21no—
400#533—111no—
401#533—111no—
402#533—111no—
403#533C2×D1112yes—
404#533C2×D1112yes—
405#533C2×D1112yes—
406#533C2×D1112yes—
407#532—111no—
408#532—111no—
409#532—111no—
410C2×C4⋊Q8C2×D1111yescharacteristic
411C2×C4⋊Q8C2×D1111yescharacteristic
412#529—112no—
413#529—112no—
414#529—221no—
415#529—221no—
416#529—221no—
417#529—221no—
418C2×#125C2×D1112yes—
419#525—112no—
420#525—221no—
421#525—221no—
422C2×C22⋊Q8—21no—
423C2×C22⋊Q8—21no—
424C4×#41—112no—
425C4×#41—221no—
426C4×#41—221no—
427C2×C4×Q8—21no—
428C2×C4×Q8—21no—
429C2×#117C2×D1112yes—
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#53612yes—
472C22×C11C2×#13512yes—
473C22×C11C23×D411yescharacteristic
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C4×C11—21no—
478C4×C11—21no—
479C4×C11—21no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—44no—
485C4×C11—44no—
486C4×C11#53612yes—
487C4×C11C2×#13512yes—
488C4×C11C2×#13512yes—
489C4×C11#57512yes—
490C4×C11C2×2−1+412yes—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C2×#41—112no—
495C2×#41—221no—
496C2×#41—221no—
497C22×Q8—21no—
498C22×Q8—21no—
499C23×C4C22⋊D1111yescharacteristic
500C23×C4C22⋊D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C22×C8—114no—
503C4⋊Q8—21no—
504C4⋊Q8—21no—
505C4⋊Q8—21no—
506C4⋊Q8—21no—
507C4⋊Q8—111no—
508C4⋊Q8—111no—
509C4⋊Q8—111no—
510C4⋊Q8C22×D1112yes—
511C4⋊Q8C22×D1112yes—
512C4⋊Q8C22×D1112yes—
513C4⋊Q8C22×D1112yes—
514#127—111no—
515#126—222no—
516#126—222no—
517#125—22no—
518#125—22no—
519#125—112no—
520#125—221no—
521#125—221no—
522#125C22×D1114yes—
523#125C22×D1114yes—
524#124—112no—
525#124—221no—
526#124—221no—
527#123—222no—
528#123—222no—
529#123—222no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—112no—
539C22⋊Q8—112no—
540C22⋊Q8—221no—
541C22⋊Q8—221no—
542C22⋊Q8—221no—
543C22⋊Q8—221no—
544#121—112no—
545#121—112no—
546#121—221no—
547#121—221no—
548#121—221no—
549#121—221no—
550#120—222no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—112no—
560C4×Q8—112no—
561C4×Q8—221no—
562C4×Q8—221no—
563C4×Q8—221no—
564C4×Q8—221no—
565C4×D4—112no—
566C4×D4—112no—
567C4×D4—222no—
568C4×D4—222no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4—221no—
574C4×D4—221no—
575C4×D4—221no—
576C4×D4—221no—
577#117—22no—
578#117—22no—
579#117—112no—
580#117—221no—
581#117—221no—
582#117—222no—
583#117—222no—
584#117—222no—
585#117C22×D1114yes—
586#117C22×D1114yes—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C22×D1112yes—
592C2×C4⋊C4C22×D1112yes—
593C2×C22⋊C4—22no—
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×C11C2×#53611yescharacteristic
629C2×C11C22×#13511yescharacteristic
630C2×C11C2×#57511yescharacteristic
631D11—82no—
632C24C2×C22⋊D1111yescharacteristic
633#41—228no—
634#41—444no—
635#41—444no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—112no—
643C2×Q8—221no—
644C2×Q8—221no—
645C2×D4—112no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—221no—
650C2×D4—221no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—42no—
656C22×C4—222no—
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—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—112no—
691C4⋊C4—112no—
692C4⋊C4—222no—
693C4⋊C4—222no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C4⋊C4—222no—
702C4⋊C4C23×D1114yes—
703C4⋊C4C23×D1114yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—222no—
707C22⋊C4—222no—
708C22⋊C4—222no—
709C22⋊C4—222no—
710C22⋊C4—222no—
711C22⋊C4—222no—
712C22⋊C4—222no—
713C22⋊C4—222no—
714C22⋊C4—222no—
715C42—24no—
716C42—24no—
717C42—222no—
718C42—222no—
719C42—222no—
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—41no—
740C23—222no—
741C23C22×C22⋊D1111yescharacteristic
742C23C22×C22⋊D1111yescharacteristic
743C23C22×C22⋊D1111yescharacteristic
744Q8—44no—
745Q8—44no—
746Q8—44no—
747Q8—44no—
748Q8—224no—
749Q8—442no—
750Q8—442no—
751D4—224no—
752D4—444no—
753D4—444no—
754D4—444no—
755D4—442no—
756D4—442no—
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—24no—
771C2×C4—24no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—444no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4#6700314yes—
784C2×C4#6704014yes—
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—442no—
808C22—442no—
809C22—442no—
810C22#1062334712yes—
811C22C2×#6700312yes—
812C22C23×C22⋊D1111yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—44no—
821C4—44no—
822C4—442no—
823C4—442no—
824C4—442no—
825C4#1062334712yes—
826C4C2×#6700312yes—
827C4C2×#6700312yes—
828C4#1062335312yes—
829C4C2×#6704012yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—882no—
834C2C2×#1062334711yescharacteristic
835C2C22×#6700311yescharacteristic
836C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenterC2×#533D11
hypocenterC11#60846
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079795C2semidirect
3. #13079784C2semidirect
4. #13079775C2semidirect
5. #13079767C2semidirect
6. #13079760C2semidirect
7. #13079752C2semidirect
8. #13079744C2semidirect
9. #13079737C2semidirect
10. #13079126C2semidirect
11. #13078941C2semidirect
12. #13078529C2semidirect
13. #13078398C2semidirect
14. C2×#10622538C2semidirect
15. C2×C11×#533C2semidirect
52. #10622707C22semidirect
53. #10622706C22semidirect
54. #10622706C22semidirect
55. #10622704C22semidirect
56. #10622701C22semidirect
57. #10622701C22semidirect
58. #10622700C22semidirect
59. #10622697C22semidirect
60. #10622692C22semidirect
61. #10622692C22semidirect
62. #10622691C22semidirect
63. #10622691C22semidirect
64. #10622681C22semidirect
65. #10622679C22semidirect
66. #10622677C22semidirect
67. #10622676C22semidirect
320. C2×#533D11semidirect
736. C11#60846semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130797952
#130797842
#130797752
#130797672
#130797602
#130797522
#130797442
#130797372
#130791262
#130789412
#130785292
#130783982
C2×#106225382
C2×C11×#5332
#6084611