Finite Group Databasebeta

← #15649510

Subgroups — #15649510

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082401C211yesmaximal, characteristic, complemented
2#13081515C212yesmaximal, complemented
3#13081330C212yesmaximal, complemented
4#13081205C212yesmaximal, complemented
5#13081056C214yesmaximal, complemented
6#13080921C212yesmaximal, complemented
7#13080577C214yesmaximal, complemented
8#13079978C212yesmaximal, complemented
9#13079928C211yesmaximal, characteristic, complemented
10#13079843C212yesmaximal, complemented
11#13079757C211yesmaximal, characteristic, complemented
12#13078767C212yesmaximal, complemented
13#13078616C211yesmaximal, characteristic, complemented
14#13078431C212yesmaximal, complemented
15C2×#10622620C211yesmaximal, characteristic, complemented
16#13077733C211yesmaximal, characteristic, complemented
17C11×#3475C211yesmaximal, characteristic, complemented
18C2×#67043—21no—
19C11×#556C2211yescharacteristic
20C11×#555C2211yescharacteristic
21C11×#554C2211yescharacteristic
22C11×#553—21no—
23C11×#552—21no—
24C11×#552C2212yes—
25C11×#551—22no—
26C11×#547C2211yescharacteristic
27C11×#546C2212yes—
28C11×#533C2211yescharacteristic
29C11×#529—22no—
30C11×#529C2212yes—
31C11×#525—21no—
32C4×C11×#41C2212yes—
33C4×C11×#41C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117—21no—
36Q8×D44—21no—
37Q8×D44C2212yescomplemented
38#10623086—21no—
39#10623086—22no—
40#10623086C2214yes—
41#10623086C2212yescomplemented
42#10623057—22no—
43#10623057—21no—
44#10623008C2211yescharacteristic
45#10623008C2212yescomplemented
46C2×#66922C2211yescharacteristic
47C2×#66922C2212yescomplemented
48#10622851C2214yes—
49#10622845C2214yes—
50#10622830C2212yes—
51C2×#66896C2212yes—
52#10622697C2212yescomplemented
53#10622696C2212yescomplemented
54#10622694C2212yescomplemented
55#10622692C2212yescomplemented
56#10622679C2214yescomplemented
57#10622678C2214yescomplemented
58#10622670C2214yes—
59#10622668C2214yes—
60#10622662C2214yescomplemented
61#10622661C2214yes—
62#10622657C2214yescomplemented
63#10622656C2214yes—
64#10622652C2214yes—
65#10622647C2214yes—
66#10622640C2212yescomplemented
67#10622639C2214yescomplemented
68#10622637C2212yescomplemented
69#10622634C2214yescomplemented
70#10622633C2212yescomplemented
71#10622633C2212yescomplemented
72#10622633C2212yescomplemented
73#10622628C2211yescharacteristic
74#10622628C2211yescharacteristic
75#10622627C2214yes—
76C4×#4323C2212yes—
77C4×#4323C2212yes—
78#10622625C2212yescomplemented
79#10622624C2214yes—
80#10622621C2214yes—
81#10622620C2211yescharacteristic
82#10622620C2212yes—
83#10622620C2211yescharacteristic
84#10622620C2212yes—
85#10622620C2212yes—
86#10622620C2212yes—
87#10622616C2214yescomplemented
88#10622608C2214yescomplemented
89#10622580C2212yes—
90C2×#66871C2212yes—
91#10622539C2212yescomplemented
92#10622538C2211yescharacteristic
93#10622537C2212yescomplemented
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C2×C11×#41D411yescharacteristic
96C2×C11×#41C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99#67043—48no—
100C2×Q8×D11—22no—
101C2×#4341—24no—
102C2×#4341—22no—
103C2×#4339—21no—
104C2×#4339—22no—
105C22×Dic22—21no—
106C22×Dic22—22no—
107C11×C4⋊Q8C2311yescharacteristic
108C11×C4⋊Q8C2311yescharacteristic
109C11×#126—22no—
110C11×#126—22no—
111C11×#126—22no—
112C11×#125—22no—
113C11×#125—21no—
114C11×#125C2312yes—
115C11×#124—22no—
116C11×#124C2312yes—
117C11×#123—22no—
118C11×#123—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—22no—
130C11×#121C2312yes—
131C11×#120—22no—
132C4×Q8×C11—21no—
133C4×Q8×C11D411yescharacteristic
134C4×Q8×C11C2312yes—
135C4×Q8×C11C2312yes—
136C4×Q8×C11C2311yescharacteristic
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11D412yes—
143C4×D4×C11D411yescharacteristic
144C4×D4×C11C2311yescharacteristic
145C4×D4×C11C2311yescharacteristic
146C4×D4×C11C2311yescharacteristic
147C4×D4×C11C2311yescharacteristic
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2311yescharacteristic
151C11×#117—21no—
152C11×#117—21no—
153C11×#117—21no—
154C11×#117—22no—
155C11×#117—22no—
156C11×#117—22no—
157C11×#117D411yescharacteristic
158C11×#117D412yes—
159C11×#117C2312yes—
160C2×C11×C4⋊C4—21no—
161C2×C11×C4⋊C4—21no—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4—21no—
164C2×C11×C22⋊C4—22no—
165C2×C42×C11—22no—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×#4325C2314yes—
169C2×#4323C2312yes—
170C2×#4323C2312yes—
171#66983—21no—
172#66983—22no—
173#66983C2312yes—
174#66983C2314yes—
175C2×C4⋊Dic11—21no—
176C2×C4⋊Dic11—22no—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2314yes—
179C2×#4318C2314yes—
180C22×C11⋊C8C2312yes—
181#66950—22no—
182#66950—24no—
183#66950—24no—
184#66950—22no—
185#66939—24no—
186#66939—24no—
187#66939—24no—
188#66928—21no—
189#66928—22no—
190#66927C2311yescharacteristic
191C4×D44—21no—
192C4×D44—22no—
193C4×D44C2312yes—
194C4×D44C2314yes—
195#66922—21no—
196#66922—21no—
197#66922—22no—
198#66922—22no—
199#66922C2312yes—
200#66922C2312yes—
201#66922C2311yescharacteristic
202#66922C2314yes—
203#66899C2314yes—
204#66899C2314yes—
205#66899C2314yes—
206#66896C2314yes—
207#66896C2314yes—
208#66896C2312yes—
209#66896C2312yes—
210C22⋊(C11⋊C8)C2312yes—
211C22⋊(C11⋊C8)C2314yes—
212#66873C2312yes—
213#66873C2312yes—
214#66873C2314yes—
215#66872C2314yes—
216#66872C2314yes—
217#66872C2314yes—
218#66871C2314yes—
219#66871C2314yes—
220#66871C2312yes—
221#66871C2312yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2314yes—
226C4⋊(C11⋊C8)C2311yescharacteristic
227#66867C2314yes—
228C4×C11⋊C8C2312yes—
229#62107—111nomaximal, Sylow
230C24×C11—21no—
231C11×#41—24no—
232C11×#41—24no—
233C11×#41—42no—
234C2×Q8×C11—21no—
235C2×Q8×C11C2×D411yescharacteristic
236C2×Q8×C11C2412yes—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—21no—
241C2×D4×C11—41no—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D411yescharacteristic
244C2×D4×C11C2411yescharacteristic
245C2×D4×C11C2411yescharacteristic
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—22no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—22no—
253C22×C4×C11—44no—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2412yes—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—22no—
262C22×Dic11—24no—
263C22×Dic11—22no—
264Q8×D11—48no—
265#4341—416no—
266#4341—48no—
267#4339—48no—
268#4339—44no—
269C2×D44—21no—
270C2×D44—21no—
271C2×D44C2412yes—
272C2×C4×D11—24no—
273C2×C4×D11—22no—
274C2×Dic22—22no—
275C2×Dic22—21no—
276C2×Dic22—24no—
277C2×Dic22—22no—
278C2×Dic22—48no—
279C2×Dic22—44no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2411yescharacteristic
295C11×C4⋊C4C2411yescharacteristic
296C11×C4⋊C4C2412yes—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4C2×D412yes—
309C11×C22⋊C4C2×D412yes—
310C11×C22⋊C4C2×D412yes—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11C2×D412yes—
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D412yes—
317C42×C11C2×D411yescharacteristic
318C42×C11C2411yescharacteristic
319C42×C11C2412yes—
320C42×C11C2411yescharacteristic
321#4325—44no—
322#4323—24no—
323#4323—42no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—21no—
330C4⋊Dic11—24no—
331C4⋊Dic11—22no—
332C4⋊Dic11—24no—
333C4⋊Dic11—22no—
334C4⋊Dic11C2414yes—
335C4⋊Dic11C2412yes—
336#4318—44no—
337C2×C11⋊C8—42no—
338C2×C11⋊C8C2412yes—
339C2×C11⋊C8C2412yes—
340C2×C11⋊C8C2414yes—
341#3499—111no—
342#3475D1111yescharacteristic, complemented
343#3384—112no—
344#3367—112no—
345#3354—112no—
346#3343—114no—
347#3330—112no—
348#3306—114no—
349#3251—112no—
350#3246—111no—
351#3239—112no—
352#3229—111no—
353#3115—112no—
354#3100—111no—
355#3079—112no—
356C2×#474—111no—
357#2989—111no—
358C23×C11—21no—
359C23×C11—21no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—81no—
363C23×C11C22×D412yes—
364C23×C11C22×D411yescharacteristic
365C22×D11—22no—
366Q8×C11—22no—
367Q8×C11—22no—
368Q8×C11—22no—
369Q8×C11—81no—
370D4×C11—24no—
371D4×C11—22no—
372D4×C11—21no—
373D4×C11—21no—
374D4×C11—21no—
375D4×C11—42no—
376D4×C11—44no—
377D4×C11—82no—
378D4×C112−1+412yescomplemented
379C2×C4×C11—24no—
380C2×C4×C11—21no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—42no—
389C2×C4×C11—41no—
390C2×C4×C11—44no—
391C2×C4×C11—42no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—42no—
396C2×C4×C11—82no—
397C2×C4×C11AGL(1,ℤ/8)14yes—
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C2511yescharacteristic
407C22⋊D11—48no—
408C22⋊D11—44no—
409C2×Dic11—22no—
410C2×Dic11—24no—
411C2×Dic11—48no—
412C2×Dic11—44no—
413D44—22no—
414D44—22no—
415D44—42no—
416D44—42no—
417C4×D11—48no—
418C4×D11—44no—
419Dic22—48no—
420Dic22—42no—
421Dic22—44no—
422Dic22—44no—
423C11⋊C8—22no—
424C11⋊C8—24no—
425C11⋊C8—22no—
426C2×2−1+4—221no—
427#556C2×D1111yescharacteristic
428#555C2×D1111yescharacteristic
429#554C2×D1111yescharacteristic
430#553—21no—
431#552—21no—
432#552C2×D1112yes—
433#551—22no—
434D4×Q8—112no—
435D4×Q8—221no—
436#547—112no—
437#547—114no—
438#547—222no—
439#547—221no—
440#547C2×D1111yescharacteristic
441#546C2×D1112yes—
442#536—221no—
443#536—222no—
444#533C2×D1111yescharacteristic
445#532—111no—
446#532—112no—
447C2×C4⋊Q8—112no—
448C2×C4⋊Q8—111no—
449#529—22no—
450#529C2×D1112yes—
451#525—21no—
452C4×#41C2×D1112yes—
453C4×#41C2×D1111yescharacteristic
454C2×C4×D4C2×D1111yescharacteristic
455C2×#117—21no—
456#501—114no—
457#498—112no—
458#489—114no—
459#487—112no—
460#484—114no—
461#483—114no—
462#482—114no—
463#481—114no—
464#480—112no—
465#478—114no—
466#477—114no—
467#476—112no—
468#476—114no—
469#475—112no—
470#475—112no—
471#475—112no—
472#474—112no—
473#474—111no—
474#474—112no—
475#474—112no—
476#474—111no—
477#474—112no—
478#469—114no—
479#468—114no—
480#465—114no—
481#463—114no—
482#461—112no—
483#460—112no—
484#459—111no—
485#459—111no—
486#449—114no—
487#447—112no—
488#446—112no—
489#442—114no—
490#440—114no—
491C4×D8—112no—
492C4×D8—112no—
493#436—112no—
494#435—114no—
495#432—112no—
496#431—111no—
497#428—114no—
498C2×#107—112no—
499#423—112no—
500C2×C4⋊C8—111no—
501#417—114no—
502C2×#102—112no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11—84no—
515C22×C11C2×AGL(1,ℤ/8)12yes—
516C22×C11C23×D411yescharacteristic
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C4×C11—21no—
521C4×C11—22no—
522C4×C11—21no—
523C4×C11—22no—
524C4×C11—21no—
525C4×C11—22no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—41no—
529C4×C11—41no—
530C4×C11C2×AGL(1,ℤ/8)12yes—
531C4×C11C2×AGL(1,ℤ/8)12yes—
532C4×C11C2×2−1+411yescharacteristic
533C4×C11#58511yescharacteristic
534Dic11—42no—
535Dic11—44no—
5362−1+4—448no—
537C2×#41—224no—
538C2×#41—222no—
539C2×#41—222no—
540C2×#41—221no—
541C2×#41C22⋊D1111yescharacteristic
542C2×#41C22×D1112yes—
543C22×Q8—222no—
544C22×Q8—222no—
545C22×Q8—221no—
546C22×D4C22×D1111yescharacteristic
547C23×C4—21no—
548C2×SD16—114no—
549C2×D8—112no—
550C2×D8—112no—
551C2×M16—114no—
552C22×C8—112no—
553C4⋊Q8—111no—
554C4⋊Q8—112no—
555C4⋊Q8—112no—
556C4⋊Q8—114no—
557C4⋊Q8—222no—
558C4⋊Q8—221no—
559C4⋊Q8—222no—
560C4⋊Q8—221no—
561C4⋊Q8C22×D1111yescharacteristic
562C4⋊Q8C22×D1111yescharacteristic
563#127—111no—
564#126—22no—
565#126—22no—
566#126—22no—
567#125—22no—
568#125—21no—
569#125C22×D1112yes—
570#124—22no—
571#124—222no—
572#124—221no—
573#124C22×D1112yes—
574#123—22no—
575#123—22no—
576#123—22no—
577#123—22no—
578#123—224no—
579#123—224no—
580#123—224no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—22no—
585C22⋊Q8—222no—
586C22⋊Q8—224no—
587C22⋊Q8—222no—
588C22⋊Q8—224no—
589C22⋊Q8C22×D1112yes—
590C22⋊Q8C22×D1112yes—
591#121—21no—
592#121—21no—
593#121—22no—
594#121—112no—
595#121—114no—
596#121—221no—
597#121—222no—
598#121C22×D1112yes—
599#120—22no—
600C4×Q8—21no—
601C4×Q8C22⋊D1111yescharacteristic
602C4×Q8C22×D1112yes—
603C4×Q8C22×D1112yes—
604C4×Q8C22×D1111yescharacteristic
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—112no—
611C4×D4—114no—
612C4×D4—222no—
613C4×D4—221no—
614C4×D4C22⋊D1112yes—
615C4×D4C22⋊D1111yescharacteristic
616C4×D4C22×D1111yescharacteristic
617C4×D4C22×D1111yescharacteristic
618C4×D4C22×D1111yescharacteristic
619C4×D4C22×D1111yescharacteristic
620C4×D4C22×D1112yes—
621C4×D4C22×D1112yes—
622C4×D4C22×D1111yescharacteristic
623#117—21no—
624#117—21no—
625#117—21no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117C22⋊D1111yescharacteristic
630#117C22⋊D1112yes—
631#117C22×D1112yes—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4C22×D1111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—22no—
641C2×C42—22no—
642C2×C42C22×D1111yescharacteristic
643C2×C42C22×D1112yes—
644#107—114no—
645#107—114no—
646#107—112no—
647#107—112no—
648#106—114no—
649#106—114no—
650#106—114no—
651C4⋊C8—112no—
652C4⋊C8—112no—
653C4⋊C8—111no—
654C4⋊C8—114no—
655C4⋊C8—111no—
656#103—114no—
657#103—114no—
658#103—114no—
659#102—114no—
660#102—114no—
661#102—112no—
662#102—112no—
663#102—112no—
664#102—112no—
665#102—114no—
666C22⋊C8—112no—
667C22⋊C8—114no—
668#97—114no—
669C4×C8—112no—
670C2×C11—22no—
671C2×C11—42no—
672C2×C11—42no—
673C2×C11—81no—
674C2×C11#348911yescharacteristic
675C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
676C2×C11#358611yescharacteristic
677D11—82no—
678C24—21no—
679#41—24no—
680#41—24no—
681#41—42no—
682#41—448no—
683#41—4416no—
684#41—448no—
685#41—444no—
686C2×Q8—21no—
687C2×Q8—224no—
688C2×Q8—222no—
689C2×Q8—221no—
690C2×Q8—222no—
691C2×Q8—448no—
692C2×Q8—448no—
693C2×Q8—444no—
694C2×Q8C2×C22⋊D1111yescharacteristic
695C2×Q8C23×D1112yes—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—41no—
701C2×D4—112no—
702C2×D4—224no—
703C2×D4—222no—
704C2×D4—221no—
705C2×D4—221no—
706C2×D4C2×C22⋊D1112yes—
707C2×D4C2×C22⋊D1111yescharacteristic
708C2×D4C23×D1111yescharacteristic
709C2×D4C23×D1111yescharacteristic
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—44no—
718C22×C4—224no—
719C22×C4—222no—
720C22×C4—224no—
721C22×C4—222no—
722C22×C4C2×C22⋊D1112yes—
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1112yes—
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1112yes—
728SD16—444no—
729D8—224no—
730D8—442no—
731M16—444no—
732C2×C8—112no—
733C2×C8—112no—
734C2×C8—114no—
735C2×C8—442no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—21no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—114no—
747C4⋊C4—112no—
748C4⋊C4—224no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—221no—
752C4⋊C4—224no—
753C4⋊C4—222no—
754C4⋊C4C2×C22⋊D1111yescharacteristic
755C4⋊C4C2×C22⋊D1111yescharacteristic
756C4⋊C4C2×C22⋊D1112yes—
757C4⋊C4C2×C22⋊D1112yes—
758C4⋊C4C23×D1112yes—
759C4⋊C4C23×D1111yescharacteristic
760C4⋊C4C23×D1111yescharacteristic
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—21no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—224no—
773C22⋊C4—222no—
774C22⋊C4—224no—
775C22⋊C4—222no—
776C22⋊C4C2×C22⋊D1112yes—
777C22⋊C4C2×C22⋊D1112yes—
778C22⋊C4C2×C22⋊D1112yes—
779C42—22no—
780C42—22no—
781C42—22no—
782C42C2×C22⋊D1112yes—
783C42C2×C22⋊D1112yes—
784C42C2×C22⋊D1111yescharacteristic
785C42C2×C22⋊D1111yescharacteristic
786C42C23×D1111yescharacteristic
787C42C23×D1112yes—
788C42C23×D1111yescharacteristic
789C11#6210711yescharacteristic, complemented, Sylow
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—81no—
795C23—222no—
796C23C22×C22⋊D1112yes—
797C23C22×C22⋊D1111yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—81no—
802Q8—448no—
803Q8—442no—
804Q8—444no—
805Q8—444no—
806D4—24no—
807D4—22no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—42no—
812D4—44no—
813D4—82no—
814D4—222no—
815D4—222no—
816D4—442no—
817D4—448no—
818D4—444no—
819D4—442no—
820D4#6704312yescomplemented
821C2×C4—24no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—82no—
839C2×C4—224no—
840C2×C4—222no—
841C2×C4—448no—
842C2×C4—448no—
843C2×C4—444no—
844C2×C4—444no—
845C2×C4#6700214yes—
846C2×C4C22×C22⋊D1112yes—
847C2×C4C22×C22⋊D1112yes—
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1112yes—
852C2×C4C22×C22⋊D1111yescharacteristic
853C2×C4C22×C22⋊D1111yescharacteristic
854C2×C4C24×D1111yescharacteristic
855C8—222no—
856C8—224no—
857C8—222no—
858C22—21no—
859C22—21no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—84no—
870C22—442no—
871C22—442no—
872C22—442no—
873C22C2×#6700212yes—
874C22C23×C22⋊D1111yescharacteristic
875C4—21no—
876C4—22no—
877C4—21no—
878C4—22no—
879C4—21no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—41no—
884C4—41no—
885C4—444no—
886C4—442no—
887C4C2×#6700212yes—
888C4C2×#6700212yes—
889C4C2×#6704311yescharacteristic
890C4#1062345311yescharacteristic
891C2—22no—
892C2—42no—
893C2—42no—
894C2—81no—
895C2—882no—
896C2#1308229611yescharacteristic
897C2C22×#6700211yescharacteristic
898C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3475C2
socleC22×C11C23×D4
hypercenter#3475D11
hypocenterC11#62107
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13082401C2semidirect
2. #13081515C2semidirect
3. #13081330C2semidirect
4. #13081205C2semidirect
5. #13081056C2semidirect
6. #13080921C2semidirect
7. #13080577C2semidirect
8. #13079978C2semidirect
9. #13079928C2semidirect
10. #13079843C2semidirect
11. #13079757C2semidirect
12. #13078767C2semidirect
13. #13078616C2semidirect
14. #13078431C2semidirect
15. C2×#10622620C2semidirect
16. #13077733C2semidirect
17. C11×#3475C2semidirect
37. Q8×D44C22semidirect
41. #10623086C22semidirect
45. #10623008C22semidirect
47. C2×#66922C22semidirect
52. #10622697C22semidirect
53. #10622696C22semidirect
54. #10622694C22semidirect
55. #10622692C22semidirect
56. #10622679C22semidirect
57. #10622678C22semidirect
60. #10622662C22semidirect
62. #10622657C22semidirect
66. #10622640C22semidirect
67. #10622639C22semidirect
68. #10622637C22semidirect
69. #10622634C22semidirect
70. #10622633C22semidirect
71. #10622633C22semidirect
72. #10622633C22semidirect
78. #10622625C22semidirect
87. #10622616C22semidirect
88. #10622608C22semidirect
91. #10622539C22semidirect
93. #10622537C22semidirect
342. #3475D11semidirect
378. D4×C112−1+4semidirect
789. C11#62107semidirect
820. D4#67043semidirect

Maximal subgroups

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

subgroupindex
#130824012
#130815152
#130813302
#130812052
#130810562
#130809212
#130805772
#130799782
#130799282
#130798432
#130797572
#130787672
#130786162
#130784312
C2×#106226202
#130777332
C11×#34752
#6210711