Finite Group Databasebeta

← #15626910

Subgroups — #15626910

Order 2816.

1748 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082502C211yesmaximal, characteristic, complemented
2#13080066C214yesmaximal, complemented
3#13080042C214yesmaximal, complemented
4#13080007C212yesmaximal, complemented
5#13079989C212yesmaximal, complemented
6#13079958C212yesmaximal, complemented
7#13079953C212yesmaximal, complemented
8#13078452C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078309C212yesmaximal
12#13078268C212yesmaximal, complemented
13#13078142C212yesmaximal, complemented
14#13078103C211yesmaximal, characteristic, complemented
15C2×#10622644C211yesmaximal, characteristic, complemented
16#13077184C211yesmaximal, characteristic, complemented
17C11×#3461C211yesmaximal, characteristic
18C11×#544C2211yescharacteristic
19C11×#542—21no—
20C11×#542C2212yes—
21C11×#541—21no—
22C11×#541C2212yes—
23C11×#539—22no—
24C11×#537C2211yescharacteristic
25C11×#536C2211yescharacteristic
26C11×#536C2211yescharacteristic
27C11×#533—21no—
28C11×#533C2212yes—
29C11×#529—22no—
30C11×#529—21no—
31C11×#529C2212yes—
32C4×C11×#41C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35#10623356C2212yes—
36C2×#67004C2212yes—
37C2×#67001C2212yes—
38C22×#4326C2212yes—
39#10623098—21no—
40#10623098—21no—
41#10623073—21no—
42#10623073—21no—
43#10623072—22no—
44#10623072—22no—
45#10623049C2214yes—
46#10623047C2212yes—
47#10623001C2211yescharacteristic
48#10623001C2212yes—
49#10623001C2212yes—
50C2×#66922C2211yescharacteristic
51#10622846C2212yes—
52#10622838C2212yes—
53#10622707C2214yes—
54#10622704C2214yes—
55#10622703C2214yes—
56#10622703C2214yes—
57#10622676C2214yes—
58#10622676C2214yes—
59#10622667C2214yes—
60#10622667C2214yes—
61#10622665C2214yes—
62#10622665C2214yes—
63#10622665C2214yes—
64#10622664C2214yes—
65#10622664C2214yes—
66#10622664C2214yes—
67#10622655C2214yes—
68#10622654C2214yes—
69#10622644C2212yes—
70#10622644C2214yes—
71#10622644C2212yes—
72#10622644C2212yes—
73#10622644C2212yes—
74#10622635C2212yes—
75#10622635C2214yes—
76#10622634C2211yescharacteristic
77#10622634C2212yes—
78#10622633C2211yescharacteristic
79#10622633C2212yes—
80#10622632C2212yes—
81#10622632C2212yes—
82#10622622C2212yes—
83#10622621C2211yescharacteristic
84#10622620C2211yescharacteristic
85#10622617C2212yes—
86#10622612C2214yes—
87#10622612C2212yes—
88#10622611C2212yes—
89C2×#66874C2212yes—
90#10622577C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yes—
95C2×C11×#41C2311yescharacteristic
96C2×C11×#41C2311yescharacteristic
97C22×Q8×C11C2311yescharacteristic
98C22×Dic22C2312yes—
99C11×C4⋊Q8—21no—
100C11×C4⋊Q8—21no—
101C11×C4⋊Q8C2312yes—
102C11×C4⋊Q8C2312yes—
103C11×#126—22no—
104C11×#126—22no—
105C11×#126—22no—
106C11×#126—22no—
107C11×#125—22no—
108C11×#125—21no—
109C11×#125—22no—
110C11×#125—22no—
111C11×#125C2312yes—
112C11×#124—21no—
113C11×#124—22no—
114C11×#124C2312yes—
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×C22⋊Q8C2312yes—
128C11×#121—22no—
129C11×#121—21no—
130C11×#121C2312yes—
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11—22no—
134C4×Q8×C11D411yescharacteristic
135C4×Q8×C11D411yescharacteristic
136C4×Q8×C11C2312yes—
137C4×Q8×C11C2312yes—
138C4×Q8×C11C2311yescharacteristic
139C4×Q8×C11C2311yescharacteristic
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—22no—
143C4×D4×C11D412yes—
144C4×D4×C11D412yes—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D411yescharacteristic
147C4×D4×C11C2311yescharacteristic
148C4×D4×C11C2311yescharacteristic
149C11×#117—22no—
150C11×#117—21no—
151C11×#117—22no—
152C11×#117C2311yescharacteristic
153C11×#117C2311yescharacteristic
154C11×#117C2312yes—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2312yes—
161#67004—44no—
162#67001—44no—
163#66997—22no—
164C2×#4326—44no—
165C2×#4326C2314yes—
166C2×#4326C2314yes—
167C2×#4326C2314yes—
168#66989—22no—
169#66988—24no—
170C2×#4324C2314yes—
171#66979—22no—
172#66979—22no—
173#66979C2312yes—
174C2×C4⋊Dic11—21no—
175C2×C4⋊Dic11—21no—
176#66977—21no—
177#66977—21no—
178#66977—22no—
179#66977—22no—
180#66977C2314yes—
181#66977C2314yes—
182C2×#4318C2312yes—
183C2×#4318C2314yes—
184C22×C11⋊C8C2312yes—
185C22×C11⋊C8C2314yes—
186#66942—24no—
187#66942—24no—
188#66940—22no—
189#66940—22no—
190#66932—24no—
191#66932—24no—
192#66930—24no—
193#66923—22no—
194#66923—22no—
195#66923C2312yes—
196#66922—21no—
197#66922—21no—
198#66922C2312yes—
199#66922C2312yes—
200#66922C2311yescharacteristic
201#66922C2311yescharacteristic
202C4×Dic22—22no—
203C4×Dic22—22no—
204C4×Dic22—21no—
205C4×Dic22—21no—
206C4×Dic22C2314yes—
207C4×Dic22C2314yes—
208#66899C2314yes—
209#66899C2314yes—
210#66899C2312yes—
211#66899C2312yes—
212#66896C2312yes—
213#66896C2312yes—
214#66874C2314yes—
215#66874C2314yes—
216#66874C2314yes—
217#66874C2314yes—
218#66872C2314yes—
219#66872C2312yes—
220#66872C2312yes—
221#66871C2314yes—
222#66871C2312yes—
223#66871C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2314yes—
231#60925—111nomaximal, Sylow
232C11×#41—22no—
233C11×#41—22no—
234C11×#41—22no—
235C11×#41—22no—
236C2×Q8×C11—21no—
237C2×Q8×C11—22no—
238C2×Q8×C11—22no—
239C2×Q8×C11—22no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2412yes—
242C2×Q8×C11C2411yescharacteristic
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11C2×D412yes—
246C2×D4×C11C2×D411yescharacteristic
247C2×D4×C11C2411yescharacteristic
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×Dic11—22no—
260C2×Dic22—21no—
261C2×Dic22—21no—
262C2×Dic22—22no—
263C2×Dic22—24no—
264C2×Dic22—24no—
265C2×Dic22C2414yes—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4C2×D411yescharacteristic
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2412yes—
284C11×C4⋊C4C2411yescharacteristic
285C11×C4⋊C4C2411yescharacteristic
286C11×C22⋊C4—22no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4C2×D412yes—
296C11×C22⋊C4C2×D412yes—
297C11×C22⋊C4C2×D412yes—
298C42×C11—22no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—21no—
302C42×C11—22no—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D412yes—
306C42×C11C2×D412yes—
307C42×C11C2412yes—
308C42×C11C2411yescharacteristic
309C42×C11C2411yescharacteristic
310C22⋊Dic11—22no—
311C22⋊Dic11—24no—
312C22⋊Dic11—24no—
313#4326—44no—
314#4326—44no—
315#4326—44no—
316#4324—44no—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11—22no—
322C4⋊Dic11—22no—
323C4⋊Dic11C2412yes—
324C4⋊Dic11C2412yes—
325Dic11⋊C4—24no—
326Dic11⋊C4—24no—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331C4×Dic11—22no—
332C4×Dic11—24no—
333C4×Dic11—24no—
334#4318—24no—
335#4318—44no—
336C2×C11⋊C8—24no—
337C2×C11⋊C8—44no—
338C2×C11⋊C8C2412yes—
339C2×C11⋊C8C2414yes—
340C2×C11⋊C8C2412yes—
341#3509—111no—
342#3461D1111yescharacteristic
343#3261—114no—
344#3258—114no—
345#3255—112no—
346#3252—112no—
347#3249—112no—
348#3248—112no—
349#3082—112no—
350#3078—111no—
351#3076—111no—
352#3063—112no—
353#3059—112no—
354#3044—112no—
355#3039—111no—
356C2×#462—111no—
357#2906—111no—
358C23×C11—21no—
359C23×C11C22×D412yes—
360C23×C11C22×D411yescharacteristic
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—21no—
364Q8×C11—22no—
365Q8×C11—21no—
366Q8×C11—42no—
367Q8×C11—82no—
368D4×C11—24no—
369D4×C11—22no—
370D4×C11—21no—
371D4×C11—21no—
372D4×C11—42no—
373D4×C11—82no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—21no—
379C2×C4×C11—22no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—81no—
389C2×C4×C11—81no—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11H(5,𝔽2)12yes—
399C2×C4×C112−1+412yes—
400C2×C4×C11C2511yescharacteristic
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—24no—
404C2×Dic11—44no—
405Dic22—24no—
406Dic22—24no—
407Dic22—42no—
408Dic22—44no—
409Dic22—42no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C11⋊C8—24no—
413C2×#137—112no—
414C22×Q16—112no—
415C2×#131—112no—
416#557—221no—
417#557—221no—
418#556—221no—
419#556—221no—
420#552—222no—
421#552—222no—
422#544C2×D1111yescharacteristic
423#542—21no—
424#542C2×D1112yes—
425#541—21no—
426#541—114no—
427#541C2×D1112yes—
428#539—22no—
429#537C2×D1111yescharacteristic
430#536—112no—
431#536C2×D1111yescharacteristic
432#536C2×D1111yescharacteristic
433#533—21no—
434#533—111no—
435#533—112no—
436#533—112no—
437#533C2×D1112yes—
438C2×C4⋊Q8—111no—
439#529—22no—
440#529—21no—
441#529C2×D1112yes—
442#519—112no—
443C4×#41C2×D1111yescharacteristic
444C4×#41C2×D1111yescharacteristic
445C2×C4×Q8C2×D1111yescharacteristic
446#479—114no—
447#479—114no—
448#479—112no—
449#479—114no—
450#478—112no—
451#477—114no—
452#477—111no—
453#477—112no—
454#476—111no—
455#475—114no—
456#475—111no—
457#475—112no—
458#474—111no—
459#470—114no—
460#470—114no—
461#470—114no—
462#468—114no—
463#467—114no—
464#467—114no—
465#467—114no—
466#465—114no—
467#464—114no—
468#464—114no—
469#462—114no—
470#462—114no—
471#462—112no—
472#462—112no—
473#462—112no—
474#462—114no—
475#462—112no—
476#461—112no—
477#461—112no—
478#428—112no—
479#427—112no—
480#424—112no—
481#424—114no—
482#423—111no—
483#423—112no—
484C2×C4⋊C8—111no—
485C2×C4⋊C8—112no—
486#419—112no—
487#419—112no—
488#416—112no—
489C2×#103—112no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11#53712yes—
499C22×C11C23×D411yescharacteristic
500C4×C11—21no—
501C4×C11—21no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—22no—
505C4×C11—21no—
506C4×C11—42no—
507C4×C11—41no—
508C4×C11—41no—
509C4×C11—42no—
510C4×C11—41no—
511C4×C11#53712yes—
512C4×C11#57812yes—
513C4×C11C2×H(5,𝔽2)11yescharacteristic
514C4×C11C2×2−1+411yescharacteristic
515Dic11—42no—
516Dic11—44no—
517Dic11—42no—
518C2×#41C22×D1111yescharacteristic
519C2×#41C22×D1111yescharacteristic
520C22×Q8—112no—
521C22×Q8C22×D1111yescharacteristic
522#137—444no—
523C2×Q16—114no—
524C2×Q16—114no—
525C2×Q16—114no—
526C2×Q16—444no—
527C2×SD16—114no—
528#131—444no—
529C2×M16—112no—
530C2×M16—114no—
531C22×C8—112no—
532C22×C8—114no—
533C4⋊Q8—21no—
534C4⋊Q8—21no—
535C4⋊Q8—111no—
536C4⋊Q8—111no—
537C4⋊Q8—112no—
538C4⋊Q8—112no—
539C4⋊Q8—222no—
540C4⋊Q8—221no—
541C4⋊Q8—221no—
542C4⋊Q8C22×D1112yes—
543C4⋊Q8C22×D1112yes—
544#126—22no—
545#126—22no—
546#126—22no—
547#126—22no—
548#126—224no—
549#126—224no—
550#125—22no—
551#125—21no—
552#125—22no—
553#125—22no—
554#125—112no—
555#125—224no—
556#125—224no—
557#125—222no—
558#125—222no—
559#125C22×D1112yes—
560#124—21no—
561#124—22no—
562#124—222no—
563#124C22×D1112yes—
564#123—22no—
565#123—22no—
566#123—22no—
567#123—22no—
568#123—224no—
569C22⋊Q8—21no—
570C22⋊Q8—22no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—114no—
576C22⋊Q8—114no—
577C22⋊Q8—221no—
578C22⋊Q8—221no—
579C22⋊Q8—222no—
580C22⋊Q8—222no—
581C22⋊Q8C22×D1112yes—
582C22⋊Q8C22×D1112yes—
583C22⋊Q8C22×D1112yes—
584#121—22no—
585#121—21no—
586#121C22×D1112yes—
587C4×Q8—21no—
588C4×Q8—21no—
589C4×Q8—22no—
590C4×Q8—114no—
591C4×Q8—114no—
592C4×Q8—222no—
593C4×Q8—222no—
594C4×Q8—222no—
595C4×Q8—222no—
596C4×Q8—221no—
597C4×Q8—221no—
598C4×Q8C22⋊D1111yescharacteristic
599C4×Q8C22⋊D1111yescharacteristic
600C4×Q8C22×D1112yes—
601C4×Q8C22×D1112yes—
602C4×Q8C22×D1111yescharacteristic
603C4×Q8C22×D1111yescharacteristic
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—22no—
607C4×D4C22⋊D1112yes—
608C4×D4C22⋊D1111yescharacteristic
609C4×D4C22⋊D1112yes—
610C4×D4C22⋊D1111yescharacteristic
611C4×D4C22×D1111yescharacteristic
612C4×D4C22×D1111yescharacteristic
613#117—22no—
614#117—21no—
615#117—22no—
616#117—112no—
617#117—222no—
618#117—222no—
619#117—224no—
620#117C22×D1111yescharacteristic
621#117C22×D1111yescharacteristic
622#117C22×D1112yes—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—221no—
625C2×C4⋊C4—221no—
626C2×C4⋊C4C22×D1111yescharacteristic
627C2×C42—21no—
628C2×C42—21no—
629C2×C42C22×D1111yescharacteristic
630C2×C42C22×D1112yes—
631#107—112no—
632#107—112no—
633#107—114no—
634#106—112no—
635#106—112no—
636#106—114no—
637C4⋊C8—111no—
638C4⋊C8—112no—
639C4⋊C8—111no—
640C4⋊C8—112no—
641C4⋊C8—114no—
642C4⋊C8—112no—
643C4⋊C8—114no—
644#103—112no—
645#103—112no—
646#103—114no—
647#103—114no—
648#103—114no—
649#103—114no—
650#103—114no—
651#103—114no—
652#102—112no—
653#102—112no—
654C2×C11—22no—
655C2×C11—42no—
656C2×C11—81no—
657C2×C11C2×#53711yescharacteristic
658C2×C11C2×#57811yescharacteristic
659C2×C11#358611yescharacteristic
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664C2×Q8—21no—
665C2×Q8—22no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—114no—
669C2×Q8—221no—
670C2×Q8—221no—
671C2×Q8—222no—
672C2×Q8—224no—
673C2×Q8—224no—
674C2×Q8C2×C22⋊D1111yescharacteristic
675C2×Q8C23×D1112yes—
676C2×Q8C23×D1111yescharacteristic
677C2×D4—21no—
678C2×D4—22no—
679C2×D4C2×C22⋊D1112yes—
680C2×D4C2×C22⋊D1111yescharacteristic
681C2×D4C23×D1111yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—222no—
688C22×C4C2×C22⋊D1111yescharacteristic
689C22×C4C2×C22⋊D1112yes—
690C22×C4C2×C22⋊D1111yescharacteristic
691C22×C4C2×C22⋊D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1111yescharacteristic
694Q16—444no—
695Q16—444no—
696Q16—444no—
697SD16—444no—
698M16—224no—
699M16—444no—
700C2×C8—112no—
701C2×C8—112no—
702C2×C8—114no—
703C2×C8—224no—
704C2×C8—444no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—112no—
719C4⋊C4—112no—
720C4⋊C4—222no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4—224no—
727C4⋊C4—224no—
728C4⋊C4—224no—
729C4⋊C4—224no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4C2×C22⋊D1111yescharacteristic
733C4⋊C4C2×C22⋊D1111yescharacteristic
734C4⋊C4C2×C22⋊D1112yes—
735C4⋊C4C2×C22⋊D1112yes—
736C4⋊C4C23×D1112yes—
737C4⋊C4C23×D1111yescharacteristic
738C4⋊C4C23×D1111yescharacteristic
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—21no—
742C22⋊C4—22no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—222no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4C2×C22⋊D1112yes—
752C22⋊C4C2×C22⋊D1112yes—
753C22⋊C4C2×C22⋊D1112yes—
754C42—22no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—22no—
759C42—222no—
760C42—224no—
761C42—224no—
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1112yes—
764C42C2×C22⋊D1111yescharacteristic
765C42C2×C22⋊D1112yes—
766C42C23×D1111yescharacteristic
767C42C23×D1111yescharacteristic
768C42C23×D1112yes—
769C11#6092511yescharacteristic, complemented, Sylow
770C23—21no—
771C23C22×C22⋊D1112yes—
772C23C22×C22⋊D1111yescharacteristic
773Q8—22no—
774Q8—22no—
775Q8—21no—
776Q8—22no—
777Q8—21no—
778Q8—42no—
779Q8—82no—
780Q8—224no—
781Q8—224no—
782Q8—442no—
783Q8—444no—
784Q8—442no—
785D4—24no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—42no—
790D4—82no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—224no—
810C2×C4—444no—
811C2×C4#6704212yes—
812C2×C4#6704312yes—
813C2×C4C22×C22⋊D1111yescharacteristic
814C2×C4C22×C22⋊D1111yescharacteristic
815C2×C4C22×C22⋊D1112yes—
816C2×C4C22×C22⋊D1112yes—
817C2×C4C22×C22⋊D1111yescharacteristic
818C2×C4C22×C22⋊D1112yes—
819C2×C4C22×C22⋊D1111yescharacteristic
820C2×C4C22×C22⋊D1111yescharacteristic
821C2×C4C24×D1111yescharacteristic
822C8—222no—
823C8—222no—
824C8—224no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22#1062336412yes—
834C22C23×C22⋊D1111yescharacteristic
835C4—21no—
836C4—21no—
837C4—22no—
838C4—22no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—42no—
845C4—41no—
846C4—442no—
847C4—444no—
848C4—442no—
849C4#1062336412yes—
850C4#1062336912yes—
851C4C2×#6704211yescharacteristic
852C4C2×#6704311yescharacteristic
853C2—22no—
854C2—42no—
855C2—81no—
856C2C2×#1062336411yescharacteristic
857C2C2×#1062336911yescharacteristic
858C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3461C2
socleC22×C11C23×D4
prime radicalC11×#537C22
hypercenter#3461D11
hypocenterC11#60925
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13080066C2semidirect
3. #13080042C2semidirect
4. #13080007C2semidirect
5. #13079989C2semidirect
6. #13079958C2semidirect
7. #13079953C2semidirect
8. #13078452C2semidirect
9. #13078421C2semidirect
10. #13078404C2semidirect
12. #13078268C2semidirect
13. #13078142C2semidirect
14. #13078103C2semidirect
15. C2×#10622644C2semidirect
16. #13077184C2semidirect
769. C11#60925semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130800662
#130800422
#130800072
#130799892
#130799582
#130799532
#130784522
#130784212
#130784042
#130783092
#130782682
#130781422
#130781032
C2×#106226442
#130771842
C11×#34612
#6092511