Finite Group Databasebeta

← #15626420

Subgroups — #15626420

Order 2816.

1678 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082538C211yesmaximal, characteristic
2#13079884C214yesmaximal, complemented
3#13079869C214yesmaximal, complemented
4#13079856C212yesmaximal, complemented
5#13079856C212yesmaximal, complemented
6#13079846C212yesmaximal, complemented
7#13079837C212yesmaximal, complemented
8#13079169C211yesmaximal, characteristic, complemented
9C2×#10622693C211yesmaximal, characteristic, complemented
10#13079012C211yesmaximal, characteristic, complemented
11#13078964C211yesmaximal, characteristic, complemented
12#13078605C212yesmaximal, complemented
13#13078594C212yesmaximal, complemented
14#13078474C212yesmaximal, complemented
15#13078463C212yesmaximal, complemented
16#13077267C211yesmaximal, characteristic, complemented
17C11×#3503C211yesmaximal, characteristic, complemented
18Q82×C11—21no—
19C11×#557—21no—
20C11×#554—22no—
21C11×#554—21no—
22D4×Q8×C11—22no—
23D4×Q8×C11—21no—
24C11×#544C2214yes—
25C11×#544C2212yes—
26C11×#533C2212yes—
27C11×#533C2211yescharacteristic
28C2×C11×C4⋊Q8C2212yes—
29C2×C11×C4⋊Q8C2211yescharacteristic
30C11×#520C2212yes—
31C4×C11×#41C2211yescharacteristic
32#10623364C2211yescharacteristic
33#10623364C2211yescharacteristic
34#10623112—21no—
35#10623112—21no—
36#10623089—21no—
37#10623089—21no—
38#10623071—22no—
39#10623071—22no—
40#10623066C2212yes—
41#10623054C2211yescharacteristic
42#10623054C2211yescharacteristic
43#10623049C2212yes—
44#10623010C2212yes—
45#10623010C2212yes—
46#10623008C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48#10622847C2212yes—
49#10622707C2214yes—
50#10622706C2212yes—
51#10622704C2214yes—
52#10622702C2211yescharacteristic
53#10622702C2212yes—
54#10622702C2211yescharacteristic
55#10622702C2212yes—
56#10622702C2211yescharacteristic
57#10622702C2211yescharacteristic
58#10622701C2212yes—
59#10622700C2214yes—
60#10622697C2214yes—
61#10622693C2212yes—
62#10622693C2212yes—
63#10622693C2212yes—
64#10622693C2212yes—
65#10622693C2214yes—
66#10622682C2212yes—
67#10622680C2212yes—
68#10622679C2214yes—
69#10622679C2214yes—
70#10622677C2214yes—
71#10622676C2214yes—
72#10622676C2214yes—
73#10622616C2214yes—
74#10622616C2214yes—
75#10622615C2212yes—
76#10622615C2212yes—
77#10622613C2214yes—
78#10622612C2212yes—
79#10622609C2214yes—
80#10622609C2214yes—
81#10622608C2212yes—
82#10622608C2212yes—
83#10622584C2214yes—
84#10622583C2214yes—
85#10622581C2214yes—
86#10622580C2214yes—
87#10622579C2212yes—
88#10622579C2212yes—
89C2×#66872C2212yes—
90C2×#66871C2212yes—
91#10622539C2212yes—
92#10622539C2212yes—
93C4×#4318C2211yescharacteristic
94C2×#66867C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11—21no—
97C22×Q8×C11—22no—
98C2×#4339C2311yescharacteristic
99C2×#4339C2311yescharacteristic
100C11×C4⋊Q8—24no—
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—22no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8C2311yescharacteristic
107C11×C4⋊Q8C2312yes—
108C11×C4⋊Q8C2312yes—
109C11×C4⋊Q8C2314yes—
110C11×C4⋊Q8C2311yescharacteristic
111C11×#125—24no—
112C11×#125—22no—
113C11×#125C2314yes—
114C11×#125C2312yes—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—24no—
120C11×C22⋊Q8—24no—
121C11×C22⋊Q8—24no—
122C4×Q8×C11—22no—
123C4×Q8×C11—21no—
124C4×Q8×C11—22no—
125C4×Q8×C11—21no—
126C4×Q8×C11—22no—
127C4×Q8×C11D411yescharacteristic
128C4×Q8×C11D411yescharacteristic
129C4×D4×C11—22no—
130C4×D4×C11—24no—
131C4×D4×C11D412yes—
132C4×D4×C11D412yes—
133C4×D4×C11D411yescharacteristic
134C4×D4×C11D411yescharacteristic
135C11×#117C2312yes—
136C11×#117C2314yes—
137C11×#117C2312yes—
138C11×#117C2311yescharacteristic
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4—22no—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2314yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2312yes—
145#66999—21no—
146#66999—21no—
147#66992—22no—
148#66992—22no—
149#66991—21no—
150#66991—21no—
151#66983—21no—
152#66983—21no—
153#66983C2312yes—
154#66983C2312yes—
155#66982—22no—
156#66982—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159C2×C4⋊Dic11C2311yescharacteristic
160C2×C4⋊Dic11C2311yescharacteristic
161#66977C2312yes—
162#66977C2312yes—
163C2×Dic11⋊C4—21no—
164C2×Dic11⋊C4—21no—
165C2×#4318C2312yes—
166C22×C11⋊C8C2312yes—
167#66947—22no—
168#66947—22no—
169#66945—21no—
170#66945—21no—
171C4⋊C4×D11—21no—
172C4⋊C4×D11—21no—
173#66942—22no—
174#66942—22no—
175#66937—22no—
176#66937—22no—
177(C22⋊D11)⋊C4—22no—
178(C22⋊D11)⋊C4—22no—
179#66932—22no—
180#66932—22no—
181#66929—22no—
182#66929—22no—
183#66928C2311yescharacteristic
184#66928C2311yescharacteristic
185#66927C2311yescharacteristic
186C4×D44—21no—
187C4×D44—21no—
188C4×D44C2312yes—
189C4×D44C2312yes—
190#66925—22no—
191#66925—22no—
192#66923—21no—
193#66923—21no—
194#66923C2312yes—
195#66923C2312yes—
196#66922C2311yescharacteristic
197C4×Dic22C2312yes—
198C4×Dic22C2312yes—
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2314yes—
202#66874C2314yes—
203#66874C2312yes—
204#66874C2312yes—
205#66874C2312yes—
206#66874C2312yes—
207#66873C2314yes—
208#66873C2314yes—
209#66873C2312yes—
210#66873C2312yes—
211#66873C2312yes—
212#66873C2312yes—
213#66872C2314yes—
214#66872C2314yes—
215#66872C2314yes—
216#66872C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2314yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2314yes—
222C4⋊(C11⋊C8)C2314yes—
223#66867C2311yescharacteristic
224#66867C2311yescharacteristic
225#66867C2312yes—
226#66867C2312yes—
227C4×C11⋊C8C2312yes—
228#60887—111nomaximal, Sylow
229C11×#41—24no—
230C2×Q8×C11—21no—
231C2×Q8×C11—21no—
232C2×Q8×C11—22no—
233C2×Q8×C11—24no—
234C2×Q8×C11—22no—
235C2×Q8×C11—84no—
236C2×Q8×C11—82no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×D4×C11C2×D411yescharacteristic
239C2×D4×C11C2×D412yes—
240C22×C4×C11—24no—
241C22×C4×C11—22no—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2411yescharacteristic
248C2×C22⋊D11—21no—
249C2×C22⋊D11—21no—
250C2×C22⋊D11—22no—
251C2×C22⋊D11—22no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254#4339—24no—
255#4339—24no—
256C2×D44—21no—
257C2×D44—21no—
258C2×D44C2411yescharacteristic
259C2×D44C2411yescharacteristic
260C2×C4×D11—21no—
261C2×C4×D11—21no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×Dic22C2411yescharacteristic
265C2×Dic22C2411yescharacteristic
266C11×C4⋊C4—22no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—22no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4C2×D412yes—
278C11×C4⋊C4C2×D412yes—
279C11×C4⋊C4C2×D411yescharacteristic
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2414yes—
282C11×C4⋊C4C2412yes—
283C11×C4⋊C4C2412yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—22no—
286C11×C22⋊C4C2×D412yes—
287C11×C22⋊C4C2×D412yes—
288C11×C22⋊C4C2×D412yes—
289C42×C11—24no—
290C42×C11—22no—
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D412yes—
294C42×C11C2×D412yes—
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2412yes—
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313C4⋊Dic11C2412yes—
314Dic11⋊C4—22no—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322C4×Dic11—22no—
323C4×Dic11—22no—
324#4318—24no—
325C2×C11⋊C8—24no—
326C2×C11⋊C8C2414yes—
327C2×C11⋊C8C2412yes—
328C2×C11⋊C8C2412yes—
329#3512—111no—
330#3503D1111yescharacteristic, complemented
331#3242—114no—
332#3241—114no—
333#3240—112no—
334#3240—112no—
335#3239—112no—
336#3238—112no—
337#3166—111no—
338C2×#501—111no—
339#3141—111no—
340#3135—111no—
341#3099—112no—
342#3098—112no—
343#3084—112no—
344#3083—112no—
345#2923—111no—
346C23×C11C22×D412yes—
347C23×C11C22×D411yescharacteristic
348C22×D11—21no—
349C22×D11—21no—
350Q8×C11—22no—
351Q8×C11—42no—
352Q8×C11—44no—
353Q8×C11—42no—
354Q8×C11—84no—
355Q8×C11—82no—
356D4×C11—24no—
357D4×C11—22no—
358C2×C4×C11—24no—
359C2×C4×C11—22no—
360C2×C4×C11—24no—
361C2×C4×C11—22no—
362C2×C4×C11—42no—
363C2×C4×C11—41no—
364C2×C4×C11—42no—
365C2×C4×C11—41no—
366C2×C4×C11—82no—
367C2×C4×C11—84no—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C112−1+414yes—
377C2×C4×C11C2511yescharacteristic
378C22⋊D11—42no—
379C22⋊D11—42no—
380C22⋊D11—82no—
381C22⋊D11—82no—
382C2×Dic11—21no—
383C2×Dic11—21no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—81no—
387C2×Dic11—81no—
388D44—22no—
389D44—22no—
390D44—81no—
391D44—81no—
392C4×D11—42no—
393C4×D11—42no—
394C4×D11—82no—
395C4×D11—82no—
396Dic22—22no—
397Dic22—22no—
398C11⋊C8—22no—
399C11⋊C8—22no—
400C11⋊C8—24no—
401Q82—21no—
402#557—21no—
403#554—22no—
404#554—21no—
405#553—222no—
406#553—222no—
407#553—221no—
408#553—221no—
409#552—221no—
410#552—221no—
411D4×Q8—22no—
412D4×Q8—21no—
413#544C2×D1112yes—
414#544C2×D1114yes—
415#541—112no—
416#540—112no—
417#537—111no—
418#537—111no—
419#533C2×D1111yescharacteristic
420#533C2×D1112yes—
421#532—111no—
422C2×C4⋊Q8C2×D1111yescharacteristic
423C2×C4⋊Q8C2×D1112yes—
424#529—112no—
425#529—112no—
426C2×#125—111no—
427#520—111no—
428#520—111no—
429#520C2×D1112yes—
430C4×#41C2×D1111yescharacteristic
431#501—112no—
432#501—112no—
433#501—114no—
434#501—112no—
435#501—112no—
436#499—114no—
437#491—112no—
438#490—112no—
439#489—111no—
440#489—111no—
441#489—111no—
442#489—111no—
443#489—112no—
444#489—112no—
445#487—112no—
446#486—112no—
447#485—114no—
448#485—114no—
449#484—114no—
450#483—114no—
451#482—114no—
452#482—114no—
453#481—114no—
454#480—114no—
455#479—114no—
456#479—114no—
457#478—114no—
458#478—114no—
459#477—114no—
460#476—114no—
461#475—114no—
462#474—114no—
463#433—114no—
464#432—112no—
465#432—112no—
466#428—112no—
467#428—112no—
468C2×#107—112no—
469C2×#106—112no—
470#424—112no—
471#417—112no—
472#417—112no—
473#416—112no—
474#416—112no—
475#408—112no—
476C4×M16—111no—
477C2×#97—111no—
478C22×C11—21no—
479C22×C11—21no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11#53612yes—
484C22×C11C23×D411yescharacteristic
485C2×D11—41no—
486C2×D11—41no—
487C2×D11—41no—
488C2×D11—41no—
489C2×D11—41no—
490C2×D11—41no—
491C4×C11—21no—
492C4×C11—22no—
493C4×C11—21no—
494C4×C11—21no—
495C4×C11—22no—
496C4×C11—21no—
497C4×C11—22no—
498C4×C11—44no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11#53612yes—
502C4×C11C2×2−1+412yes—
503Dic11—42no—
504Dic11—42no—
505Dic11—41no—
506Dic11—41no—
507C2×#41—111no—
508C2×#41—111no—
509C2×#41C22×D1111yescharacteristic
510C22×Q8—21no—
511C22×Q8—22no—
512C2×M16—112no—
513C22×C8—112no—
514C4⋊Q8—22no—
515C4⋊Q8—24no—
516C4⋊Q8—22no—
517C4⋊Q8—21no—
518C4⋊Q8—22no—
519C4⋊Q8—21no—
520C4⋊Q8—111no—
521C4⋊Q8C22×D1112yes—
522C4⋊Q8C22×D1111yescharacteristic
523C4⋊Q8C22×D1114yes—
524C4⋊Q8C22×D1112yes—
525C4⋊Q8C22×D1111yescharacteristic
526#127—111no—
527#126—222no—
528#126—222no—
529#126—222no—
530#126—222no—
531#125—22no—
532#125—24no—
533#125—112no—
534#125—112no—
535#125—222no—
536#125—222no—
537#125—221no—
538#125—221no—
539#125C22×D1114yes—
540#125C22×D1112yes—
541#124—111no—
542#124—111no—
543#123—222no—
544#123—222no—
545#123—222no—
546#123—222no—
547C22⋊Q8—21no—
548C22⋊Q8—22no—
549C22⋊Q8—21no—
550C22⋊Q8—22no—
551C22⋊Q8—24no—
552C22⋊Q8—24no—
553C22⋊Q8—24no—
554C22⋊Q8—112no—
555C22⋊Q8—112no—
556C22⋊Q8—221no—
557C22⋊Q8—221no—
558#121—112no—
559#121—112no—
560#121—221no—
561#121—221no—
562#121—222no—
563#121—222no—
564#121—221no—
565#121—221no—
566#121—222no—
567#121—222no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—21no—
571C4×Q8—22no—
572C4×Q8—21no—
573C4×Q8—112no—
574C4×Q8—112no—
575C4×Q8C22⋊D1111yescharacteristic
576C4×Q8C22⋊D1111yescharacteristic
577C4×D4—24no—
578C4×D4—22no—
579C4×D4—112no—
580C4×D4—112no—
581C4×D4—222no—
582C4×D4—222no—
583C4×D4—222no—
584C4×D4—222no—
585C4×D4—221no—
586C4×D4—221no—
587C4×D4C22⋊D1112yes—
588C4×D4C22⋊D1111yescharacteristic
589C4×D4C22⋊D1112yes—
590C4×D4C22⋊D1111yescharacteristic
591#117—221no—
592#117—221no—
593#117—222no—
594#117—222no—
595#117C22×D1112yes—
596#117C22×D1114yes—
597#117C22×D1111yescharacteristic
598#117C22×D1112yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4—221no—
607C2×C4⋊C4C22×D1112yes—
608C2×C4⋊C4C22×D1114yes—
609C2×C42C22×D1111yescharacteristic
610C2×C42C22×D1112yes—
611#107—114no—
612#107—114no—
613#107—114no—
614#107—114no—
615#106—114no—
616#106—114no—
617#106—114no—
618#106—114no—
619C4⋊C8—114no—
620C4⋊C8—114no—
621#103—112no—
622#103—112no—
623#103—112no—
624#103—112no—
625#103—114no—
626#103—114no—
627#102—112no—
628#102—112no—
629#102—112no—
630#102—112no—
631#102—114no—
632#102—114no—
633C22⋊C8—114no—
634C22⋊C8—114no—
635#97—111no—
636#97—111no—
637#97—112no—
638#97—112no—
639C4×C8—112no—
640C2×C11—22no—
641C2×C11—42no—
642C2×C11C2×#53611yescharacteristic
643C2×C11#358511yescharacteristic
644C2×C11#358611yescharacteristic
645D11—81no—
646D11—81no—
647#41—24no—
648#41—224no—
649#41—224no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—84no—
656C2×Q8—82no—
657C2×Q8—111no—
658C2×Q8—111no—
659C2×Q8C2×C22⋊D1111yescharacteristic
660C2×D4—111no—
661C2×D4—111no—
662C2×D4—221no—
663C2×D4—221no—
664C2×D4—222no—
665C2×D4—222no—
666C2×D4—221no—
667C2×D4—221no—
668C2×D4C2×C22⋊D1112yes—
669C2×D4C2×C22⋊D1111yescharacteristic
670C22×C4—24no—
671C22×C4—22no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1112yes—
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1112yes—
682C22×C4C23×D1112yes—
683C22×C4C23×D1111yescharacteristic
684M16—224no—
685C2×C8—114no—
686C2×C8—112no—
687C2×C8—112no—
688C2×C8—224no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—24no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—24no—
697C4⋊C4—22no—
698C4⋊C4—24no—
699C4⋊C4—22no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—222no—
705C4⋊C4—222no—
706C4⋊C4—222no—
707C4⋊C4—222no—
708C4⋊C4—222no—
709C4⋊C4—222no—
710C4⋊C4—222no—
711C4⋊C4—222no—
712C4⋊C4—221no—
713C4⋊C4—221no—
714C4⋊C4C2×C22⋊D1111yescharacteristic
715C4⋊C4C2×C22⋊D1111yescharacteristic
716C4⋊C4C2×C22⋊D1112yes—
717C4⋊C4C2×C22⋊D1112yes—
718C4⋊C4C23×D1112yes—
719C4⋊C4C23×D1114yes—
720C4⋊C4C23×D1112yes—
721C22⋊C4—24no—
722C22⋊C4—22no—
723C22⋊C4—222no—
724C22⋊C4—222no—
725C22⋊C4—221no—
726C22⋊C4—221no—
727C22⋊C4—222no—
728C22⋊C4—222no—
729C22⋊C4—222no—
730C22⋊C4—222no—
731C22⋊C4—221no—
732C22⋊C4—221no—
733C22⋊C4C2×C22⋊D1112yes—
734C22⋊C4C2×C22⋊D1112yes—
735C22⋊C4C2×C22⋊D1112yes—
736C42—24no—
737C42—22no—
738C42—222no—
739C42—222no—
740C42C2×C22⋊D1112yes—
741C42C2×C22⋊D1112yes—
742C42C2×C22⋊D1111yescharacteristic
743C42C2×C22⋊D1111yescharacteristic
744C42C23×D1111yescharacteristic
745C42C23×D1111yescharacteristic
746C42C23×D1112yes—
747C11#6088711yescharacteristic, complemented, Sylow
748C23—221no—
749C23—221no—
750C23C22×C22⋊D1112yes—
751C23C22×C22⋊D1111yescharacteristic
752Q8—22no—
753Q8—42no—
754Q8—44no—
755Q8—42no—
756Q8—84no—
757Q8—82no—
758Q8—222no—
759Q8—222no—
760D4—24no—
761D4—22no—
762D4—222no—
763D4—222no—
764D4—442no—
765D4—442no—
766D4—881no—
767D4—881no—
768D4—882no—
769D4—882no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—82no—
779C2×C4—84no—
780C2×C4—221no—
781C2×C4—221no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—442no—
785C2×C4—442no—
786C2×C4—882no—
787C2×C4—882no—
788C2×C4—881no—
789C2×C4—881no—
790C2×C4#6704014yes—
791C2×C4C22×C22⋊D1112yes—
792C2×C4C22×C22⋊D1112yes—
793C2×C4C22×C22⋊D1112yes—
794C2×C4C22×C22⋊D1111yescharacteristic
795C2×C4C22×C22⋊D1111yescharacteristic
796C2×C4C22×C22⋊D1111yescharacteristic
797C2×C4C22×C22⋊D1111yescharacteristic
798C2×C4C22×C22⋊D1111yescharacteristic
799C2×C4C24×D1111yescharacteristic
800C8—222no—
801C8—222no—
802C8—224no—
803C22—21no—
804C22—21no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—441no—
809C22—441no—
810C22—441no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22#1062334712yes—
815C22C23×C22⋊D1111yescharacteristic
816C4—21no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—22no—
821C4—21no—
822C4—22no—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—442no—
827C4—442no—
828C4—441no—
829C4—441no—
830C4#1062334712yes—
831C4C2×#6704012yes—
832C2—22no—
833C2—42no—
834C2—881no—
835C2—881no—
836C2C2×#1062334711yescharacteristic
837C2#1308339611yescharacteristic
838C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3503C2
socleC22×C11C23×D4
prime radical#13082538C2
hypercenter#3503D11
hypocenterC11#60887
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3503

Complements

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

NH ≅ G/Ntype
2. #13079884C2semidirect
3. #13079869C2semidirect
4. #13079856C2semidirect
5. #13079856C2semidirect
6. #13079846C2semidirect
7. #13079837C2semidirect
8. #13079169C2semidirect
9. C2×#10622693C2semidirect
10. #13079012C2semidirect
11. #13078964C2semidirect
12. #13078605C2semidirect
13. #13078594C2semidirect
14. #13078474C2semidirect
15. #13078463C2semidirect
16. #13077267C2semidirect
17. C11×#3503C2semidirect
330. #3503D11semidirect
747. C11#60887semidirect

Maximal subgroups

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

subgroupindex
#130825382
#130798842
#130798692
#130798562
#130798462
#130798372
#130791692
C2×#106226932
#130790122
#130789642
#130786052
#130785942
#130784742
#130784632
#130772672
C11×#35032
#6088711