Finite Group Databasebeta

← #15625953

Subgroups — #15625953

Order 2816.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2C2×#10623001C211yesmaximal, characteristic, complemented
3#13079858C214yesmaximal, complemented
4#13079848C212yesmaximal, complemented
5#13079839C212yesmaximal, complemented
6#13079832C212yesmaximal, complemented
7#13079824C212yesmaximal, complemented
8#13079816C212yesmaximal, complemented
9#13079808C212yesmaximal, complemented
10#13079140C212yesmaximal, complemented
11#13078962C212yesmaximal, complemented
12#13078531C214yesmaximal, complemented
13#13078406C214yesmaximal, complemented
14C2×C11×#432C211yesmaximal, characteristic, complemented
15C22×C42×C11C2211yescharacteristic
16#10623322—21no—
17#10623322—21no—
18#10623322C2212yes—
19C2×#66979C2212yes—
20C2×#66977—21no—
21C2×#66977—21no—
22#10623010—21no—
23#10623010—21no—
24#10623010—21no—
25#10623010—21no—
26#10623010C2212yes—
27#10623010C2212yes—
28#10623008C2211yescharacteristic
29#10623008C2211yescharacteristic
30#10623008C2211yescharacteristic
31C4×#4339—21no—
32C4×#4339—21no—
33C4×#4339C2212yes—
34#10623001—21no—
35#10623001—21no—
36#10623001—21no—
37#10623001—21no—
38#10623001C2212yes—
39#10623001C2212yes—
40#10623001C2212yes—
41#10623001C2212yes—
42#10623001C2211yescharacteristic
43#10623001C2211yescharacteristic
44#10623001C2211yescharacteristic
45C2×#66923C2212yes—
46C2×#66922C2211yescharacteristic
47C2×#66922C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22—21no—
50C11×#432C2212yes—
51C11×#432C2212yes—
52C11×#432C2212yes—
53C11×#432C2212yes—
54C2×C11×C4⋊C8C2212yes—
55C2×C11×C22⋊C8C2212yes—
56C2×C11×#97C2212yes—
57#10622726C2218yes—
58#10622719C2218yes—
59#10622464C2214yescomplemented
60#10622463C2214yescomplemented
61#10622460C2218yescomplemented
62#10622459C2214yescomplemented
63#10622455C2214yescomplemented
64#10622442C2218yescomplemented
65#10622350C2218yes—
66#10622349C2214yes—
67#10622348C2214yes—
68#10622336C2218yes—
69#10622335C2214yes—
70#10622334C2214yes—
71#10622327C2214yescomplemented
72#10622327C2214yescomplemented
73#10622326C2214yescomplemented
74#10622316C2214yescomplemented
75#10622315C2214yescomplemented
76#10622315C2214yescomplemented
77#10622315C2214yescomplemented
78#10622315C2214yescomplemented
79C23×C4×C11D411yescharacteristic
80C23×C4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C2×#4339—21no—
83C2×#4339—21no—
84C2×#4339C2312yes—
85C22×Dic22—21no—
86C22×Dic22—21no—
87C22×C8×C11C2314yes—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11D411yescharacteristic
91C2×C42×C11D411yescharacteristic
92C2×C42×C11D411yescharacteristic
93C2×C42×C11D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100#67006—22no—
101C2×C22⋊Dic11—22no—
102#66983—21no—
103#66983—21no—
104#66983—21no—
105#66983—21no—
106#66983C2312yes—
107#66983C2312yes—
108#66982—22no—
109#66982—22no—
110#66982—22no—
111C4×C22⋊D11—22no—
112C4×C22⋊D11—22no—
113C4×C22⋊D11—22no—
114C4×C22⋊D11—22no—
115C4×C22⋊D11—22no—
116C4×C22⋊D11—22no—
117#66979—22no—
118#66979—22no—
119#66979—21no—
120#66979—21no—
121#66979C2314yes—
122#66979C2314yes—
123#66979C2312yes—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2312yes—
128#66977—22no—
129#66977—22no—
130#66977—22no—
131#66977—22no—
132#66977—22no—
133#66977—22no—
134#66977—22no—
135#66977—22no—
136#66977—21no—
137#66977—21no—
138#66977—21no—
139#66977—21no—
140#66977C2312yes—
141#66977C2312yes—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×C4×Dic11—22no—
145#66929—22no—
146#66929—22no—
147#66928—21no—
148#66928—21no—
149#66928C2312yes—
150#66927C2311yescharacteristic
151C4×D44—21no—
152C4×D44—21no—
153C4×D44—21no—
154C4×D44—21no—
155C4×D44C2312yes—
156C4×D44C2312yes—
157#66925—22no—
158#66925—22no—
159#66925—22no—
160C42×D11—22no—
161#66923—22no—
162#66923—22no—
163#66923—21no—
164#66923—21no—
165#66923C2314yes—
166#66923C2314yes—
167#66923C2312yes—
168#66922—21no—
169#66922—21no—
170#66922—21no—
171#66922—21no—
172#66922C2311yescharacteristic
173#66922C2312yes—
174#66922C2312yes—
175#66922C2312yes—
176#66922C2312yes—
177#66922C2311yescharacteristic
178#66922C2311yescharacteristic
179C4×Dic22—22no—
180C4×Dic22—22no—
181C4×Dic22—22no—
182C4×Dic22—22no—
183C4×Dic22—22no—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22—22no—
187C4×Dic22—21no—
188C4×Dic22—21no—
189C4×Dic22—21no—
190C4×Dic22—21no—
191C4×Dic22C2312yes—
192C4×Dic22C2312yes—
193C11×C4⋊C8C2314yes—
194C11×C4⋊C8C2314yes—
195C11×C22⋊C8C2314yes—
196C11×C22⋊C8C2314yes—
197C11×#97C2314yes—
198C11×#97C2314yes—
199#66885C2318yes—
200#66885C2318yes—
201#66882C2318yes—
202#66882C2318yes—
203#66881C2318yes—
204#66881C2318yes—
205#66880C2318yes—
206#66880C2318yes—
207#60854—111nomaximal, Sylow
208C24×C11C2×D411yescharacteristic
209C22×C4×C11—24no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C2×C22⋊D11—22no—
231C2×C22⋊D11—22no—
232C2×C22⋊D11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235#4339—28no—
236#4339—44no—
237#4339—44no—
238C2×D44—21no—
239C2×D44—21no—
240C2×D44C2412yes—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—21no—
249C2×Dic22—21no—
250C2×Dic22—44no—
251C2×Dic22—44no—
252C2×Dic22C2412yes—
253C2×C8×C11—28no—
254C2×C8×C11C2418yes—
255C42×C11C2×D411yescharacteristic
256C42×C11C2×D411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261C42×C11C2×D411yescharacteristic
262C42×C11C2×D411yescharacteristic
263C42×C11C2×D411yescharacteristic
264C42×C11C2×D411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2×D411yescharacteristic
267C42×C11C2411yescharacteristic
268C42×C11C2411yescharacteristic
269C42×C11C2411yescharacteristic
270C42×C11C2411yescharacteristic
271C22⋊Dic11—24no—
272C22⋊Dic11—24no—
273C22⋊Dic11—22no—
274C22⋊Dic11—22no—
275C22⋊Dic11—22no—
276(C2×D11)⋊C4—22no—
277(C2×D11)⋊C4—22no—
278(C2×D11)⋊C4—22no—
279(C2×D11)⋊C4—22no—
280(C2×D11)⋊C4—22no—
281(C2×D11)⋊C4—22no—
282C4⋊Dic11—22no—
283C4⋊Dic11—22no—
284C4⋊Dic11—22no—
285C4⋊Dic11—22no—
286C4⋊Dic11—21no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—22no—
291C4⋊Dic11—22no—
292C4⋊Dic11C2414yes—
293C4⋊Dic11C2414yes—
294C4⋊Dic11C2412yes—
295C4⋊Dic11C2412yes—
296Dic11⋊C4—24no—
297Dic11⋊C4—24no—
298Dic11⋊C4—24no—
299Dic11⋊C4—24no—
300Dic11⋊C4—22no—
301Dic11⋊C4—22no—
302Dic11⋊C4—22no—
303Dic11⋊C4—22no—
304Dic11⋊C4—22no—
305Dic11⋊C4—22no—
306C4×Dic11—24no—
307C4×Dic11—24no—
308C4×Dic11—22no—
309C4×Dic11—22no—
310C4×Dic11—22no—
311#3444—111no—
312C2×#533—111no—
313#3240—114no—
314#3239—112no—
315#3238—112no—
316#3237—112no—
317#3236—112no—
318#3235—112no—
319#3234—112no—
320#3162—112no—
321#3135—112no—
322#3091—114no—
323#3076—114no—
324C2×#432D1111yescharacteristic, complemented
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—41no—
328C23×C11C22×D411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C112−1+414yes—
361C2×C4×C11C2511yescharacteristic
362C22⋊D11—44no—
363C22⋊D11—44no—
364C22⋊D11—44no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372D44—24no—
373D44—42no—
374D44—42no—
375C4×D11—44no—
376C4×D11—44no—
377C4×D11—44no—
378Dic22—24no—
379Dic22—44no—
380Dic22—44no—
381Dic22—44no—
382Dic22—42no—
383Dic22—42no—
384Dic22—44no—
385C8×C11—28no—
386#533—112no—
387#533—112no—
388#533—111no—
389#533—112no—
390#533—112no—
391#533—111no—
392#533—111no—
393#533—221no—
394#533—221no—
395#533—221no—
396#533—221no—
397#532—111no—
398#532—111no—
399#532—111no—
400C2×C4⋊Q8—111no—
401C2×C4⋊Q8—111no—
402#529—112no—
403#529—112no—
404#529—221no—
405#529—221no—
406#529—221no—
407#529—221no—
408C2×#125—112no—
409#525—112no—
410#525—221no—
411#525—221no—
412C2×C22⋊Q8—221no—
413C2×C22⋊Q8—221no—
414C4×#41—112no—
415C4×#41—221no—
416C4×#41—221no—
417C2×C4×Q8—221no—
418C2×C4×Q8—221no—
419C2×#117—112no—
420C22×C42C2×D1111yescharacteristic
421#501—114no—
422#501—114no—
423#501—114no—
424#501—114no—
425#491—114no—
426#490—114no—
427#489—114no—
428#489—114no—
429#485—118no—
430#484—114no—
431#483—114no—
432#482—118no—
433#481—114no—
434#480—114no—
435#479—118no—
436#478—118no—
437#477—114no—
438#476—114no—
439#475—114no—
440#474—114no—
441#432C2×D1112yes—
442#432C2×D1112yes—
443#432C2×D1112yes—
444#432C2×D1112yes—
445#427—118no—
446C2×C4⋊C8C2×D1112yes—
447#416—118no—
448C2×C22⋊C8C2×D1112yes—
449C2×#97C2×D1112yes—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—21no—
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—44no—
458C22×C11#53612yes—
459C22×C11#57512yes—
460C22×C11C23×D411yescharacteristic
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—21no—
471C4×C11—21no—
472C4×C11—21no—
473C4×C11#53612yes—
474C4×C11#57512yes—
475C4×C11C2×2−1+412yes—
476Dic11—42no—
477Dic11—44no—
478Dic11—44no—
479Dic11—42no—
480Dic11—42no—
481C2×#41—112no—
482C2×#41—221no—
483C2×#41—221no—
484C22×Q8—221no—
485C22×Q8—221no—
486C23×C4D4411yescharacteristic
487C23×C4D4411yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C22×C8C22×D1114yes—
490C4⋊Q8—112no—
491C4⋊Q8—112no—
492C4⋊Q8—112no—
493C4⋊Q8—112no—
494C4⋊Q8—111no—
495C4⋊Q8—111no—
496C4⋊Q8—111no—
497C4⋊Q8—221no—
498C4⋊Q8—221no—
499C4⋊Q8—221no—
500C4⋊Q8—221no—
501#127—111no—
502#126—222no—
503#126—222no—
504#125—114no—
505#125—114no—
506#125—112no—
507#125—222no—
508#125—222no—
509#125—221no—
510#125—221no—
511#124—112no—
512#124—221no—
513#124—221no—
514#123—222no—
515#123—222no—
516#123—222no—
517C22⋊Q8—112no—
518C22⋊Q8—112no—
519C22⋊Q8—222no—
520C22⋊Q8—222no—
521C22⋊Q8—222no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526C22⋊Q8—222no—
527C22⋊Q8—221no—
528C22⋊Q8—221no—
529C22⋊Q8—221no—
530C22⋊Q8—221no—
531#121—112no—
532#121—112no—
533#121—221no—
534#121—221no—
535#121—221no—
536#121—221no—
537#120—222no—
538C4×Q8—112no—
539C4×Q8—112no—
540C4×Q8—222no—
541C4×Q8—222no—
542C4×Q8—222no—
543C4×Q8—222no—
544C4×Q8—222no—
545C4×Q8—222no—
546C4×Q8—222no—
547C4×Q8—222no—
548C4×Q8—221no—
549C4×Q8—221no—
550C4×Q8—221no—
551C4×Q8—221no—
552C4×D4—112no—
553C4×D4—112no—
554C4×D4—222no—
555C4×D4—222no—
556C4×D4—222no—
557C4×D4—222no—
558C4×D4—222no—
559C4×D4—222no—
560C4×D4—221no—
561C4×D4—221no—
562C4×D4—221no—
563C4×D4—221no—
564#117—114no—
565#117—114no—
566#117—112no—
567#117—222no—
568#117—222no—
569#117—221no—
570#117—221no—
571#117—222no—
572#117—222no—
573#117—222no—
574C2×C4⋊C4—112no—
575C2×C4⋊C4—112no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C22⋊C4—222no—
581C2×C42—222no—
582C2×C42—222no—
583C2×C42D4411yescharacteristic
584C2×C42D4411yescharacteristic
585C2×C42D4411yescharacteristic
586C2×C42D4411yescharacteristic
587C2×C42D4411yescharacteristic
588C2×C42D4411yescharacteristic
589C2×C42C22×D1111yescharacteristic
590C2×C42C22×D1111yescharacteristic
591C2×C42C22×D1111yescharacteristic
592C2×C42C22×D1111yescharacteristic
593C2×C42C22×D1111yescharacteristic
594C2×C42C22×D1111yescharacteristic
595#107—118no—
596#107—118no—
597#106—118no—
598#106—118no—
599C4⋊C8C22×D1114yes—
600C4⋊C8C22×D1114yes—
601#103—118no—
602#103—118no—
603#102—118no—
604#102—118no—
605C22⋊C8C22×D1114yes—
606C22⋊C8C22×D1114yes—
607#97C22×D1114yes—
608#97C22×D1114yes—
609C2×C11—22no—
610C2×C11—22no—
611C2×C11—41no—
612C2×C11C2×#53611yescharacteristic
613C2×C11C2×#57511yescharacteristic
614C2×C11C2×#57511yescharacteristic
615D11—82no—
616C24C2×D4411yescharacteristic
617#41—228no—
618#41—444no—
619#41—444no—
620C2×Q8—112no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—222no—
624C2×Q8—222no—
625C2×Q8—222no—
626C2×Q8—222no—
627C2×Q8—444no—
628C2×Q8—444no—
629C2×D4—112no—
630C2×D4—222no—
631C2×D4—222no—
632C2×D4—222no—
633C2×D4—221no—
634C2×D4—221no—
635C22×C4—24no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4C2×D4411yescharacteristic
644C22×C4C2×D4411yescharacteristic
645C22×C4C2×D4411yescharacteristic
646C22×C4C2×D4411yescharacteristic
647C22×C4C2×D4411yescharacteristic
648C22×C4C2×D4411yescharacteristic
649C22×C4C2×D4411yescharacteristic
650C22×C4C2×D4411yescharacteristic
651C22×C4C2×D4411yescharacteristic
652C22×C4C2×D4411yescharacteristic
653C22×C4C2×D4411yescharacteristic
654C22×C4C2×D4411yescharacteristic
655C22×C4C2×D4411yescharacteristic
656C22×C4C2×D4411yescharacteristic
657C22×C4C2×D4411yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C2×C8—28no—
662C2×C8C23×D1118yes—
663C4⋊C4—114no—
664C4⋊C4—114no—
665C4⋊C4—112no—
666C4⋊C4—112no—
667C4⋊C4—222no—
668C4⋊C4—222no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—222no—
674C4⋊C4—222no—
675C4⋊C4—222no—
676C4⋊C4—222no—
677C4⋊C4—222no—
678C4⋊C4—222no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—221no—
682C4⋊C4—221no—
683C4⋊C4—222no—
684C4⋊C4—222no—
685C4⋊C4—222no—
686C4⋊C4—222no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—222no—
690C22⋊C4—222no—
691C22⋊C4—222no—
692C22⋊C4—222no—
693C22⋊C4—222no—
694C22⋊C4—222no—
695C22⋊C4—222no—
696C22⋊C4—222no—
697C22⋊C4—222no—
698C42—224no—
699C42—222no—
700C42—222no—
701C42—222no—
702C42—224no—
703C42C2×D4411yescharacteristic
704C42C2×D4411yescharacteristic
705C42C2×D4411yescharacteristic
706C42C2×D4411yescharacteristic
707C42C2×D4411yescharacteristic
708C42C2×D4411yescharacteristic
709C42C2×D4411yescharacteristic
710C42C2×D4411yescharacteristic
711C42C2×D4411yescharacteristic
712C42C2×D4411yescharacteristic
713C42C2×D4411yescharacteristic
714C42C2×D4411yescharacteristic
715C42C23×D1111yescharacteristic
716C42C23×D1111yescharacteristic
717C42C23×D1111yescharacteristic
718C42C23×D1111yescharacteristic
719C11#6085411yescharacteristic, complemented, Sylow
720C23—22no—
721C23—22no—
722C23—41no—
723C23—222no—
724C23C22×D4411yescharacteristic
725C23C22×D4411yescharacteristic
726C23C22×D4411yescharacteristic
727Q8—224no—
728Q8—444no—
729Q8—444no—
730Q8—444no—
731Q8—442no—
732Q8—442no—
733Q8—444no—
734D4—224no—
735D4—442no—
736D4—442no—
737D4—444no—
738D4—444no—
739D4—444no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—444no—
763C2×C4—444no—
764C2×C4—444no—
765C2×C4—444no—
766C2×C4—444no—
767C2×C4C22×D4411yescharacteristic
768C2×C4C22×D4411yescharacteristic
769C2×C4C22×D4411yescharacteristic
770C2×C4C22×D4411yescharacteristic
771C2×C4C22×D4411yescharacteristic
772C2×C4C22×D4411yescharacteristic
773C2×C4C22×D4411yescharacteristic
774C2×C4C22×D4411yescharacteristic
775C2×C4C22×D4411yescharacteristic
776C2×C4C22×D4411yescharacteristic
777C2×C4C22×D4411yescharacteristic
778C2×C4#6704314yes—
779C2×C4C24×D1111yescharacteristic
780C8—28no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22#1062305712yes—
793C22#1062327912yes—
794C22C23×D4411yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—442no—
805C4—442no—
806C4—442no—
807C4—444no—
808C4—444no—
809C4#1062305712yes—
810C4#1062327912yes—
811C4C2×#6704312yes—
812C2—22no—
813C2—22no—
814C2—41no—
815C2—882no—
816C2C2×#1062305711yescharacteristic
817C2C2×#1062327911yescharacteristic
818C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#432C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenterC2×#432D11
hypocenterC11#60854
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
2. C2×#10623001C2semidirect
3. #13079858C2semidirect
4. #13079848C2semidirect
5. #13079839C2semidirect
6. #13079832C2semidirect
7. #13079824C2semidirect
8. #13079816C2semidirect
9. #13079808C2semidirect
10. #13079140C2semidirect
11. #13078962C2semidirect
12. #13078531C2semidirect
13. #13078406C2semidirect
14. C2×C11×#432C2semidirect
59. #10622464C22semidirect
60. #10622463C22semidirect
61. #10622460C22semidirect
62. #10622459C22semidirect
63. #10622455C22semidirect
64. #10622442C22semidirect
71. #10622327C22semidirect
72. #10622327C22semidirect
73. #10622326C22semidirect
74. #10622316C22semidirect
75. #10622315C22semidirect
76. #10622315C22semidirect
77. #10622315C22semidirect
78. #10622315C22semidirect
324. C2×#432D11semidirect
719. C11#60854semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×#106230012
#130798582
#130798482
#130798392
#130798322
#130798242
#130798162
#130798082
#130791402
#130789622
#130785312
#130784062
C2×C11×#4322
#6085411