Finite Group Databasebeta

← #15634907

Subgroups — #15634907

Order 2816.

1922 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#13082478C211yesmaximal, characteristic, complemented
2#13082465C211yesmaximal, characteristic, complemented
3#13081688C214yesmaximal, complemented
4#13081663C212yesmaximal, complemented
5#13081652C212yesmaximal, complemented
6#13081617C212yesmaximal, complemented
7#13081609C214yesmaximal, complemented
8#13081594C212yesmaximal, complemented
9#13079093C212yesmaximal, complemented
10#13078164C212yesmaximal, complemented
11#13078153C212yesmaximal, complemented
12#13078084C211yesmaximal, characteristic, complemented
13#13078076C211yesmaximal, characteristic, complemented
14#13077550C211yesmaximal, characteristic, complemented
15#13077500C212yesmaximal, complemented
16C2×C4×#4314C211yesmaximal, characteristic, complemented
17C11×#3147C211yesmaximal, characteristic, complemented
18C2×C11×#135C2212yes—
19C2×C11×#135C2212yes—
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic
22#10623361C2212yes—
23#10623358C2212yes—
24#10623358C2212yes—
25#10623356C2212yes—
26C2×#67004C2212yes—
27C2×#67002C2212yes—
28C22×#4314C2211yescharacteristic
29#10623263C2212yes—
30#10623252C2212yescomplemented
31#10623249C2212yes—
32#10623244C2212yescomplemented
33#10623212C2214yes—
34#10623202C2214yescomplemented
35#10623148—22no—
36#10623137—22no—
37#10623133—22no—
38#10623131—22no—
39#10623096—22no—
40#10623094—21no—
41#10623086—21no—
42#10623074—21no—
43#10623073—21no—
44#10623072—22no—
45C2×C4×D44C2211yescharacteristic
46#10623001C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C11×#495C2212yescomplemented
49C11×#495C2212yescomplemented
50C11×#494C2211yescharacteristic, complemented
51C11×#493C2211yescharacteristic, complemented
52C11×#492C2211yescharacteristic, complemented
53C11×#492C2211yescharacteristic, complemented
54C2×C4×C8×C11C2211yescharacteristic
55#10622845C2212yes—
56#10622845C2212yes—
57#10622803C2214yes—
58#10622798C2214yes—
59#10622797C2214yescomplemented
60#10622795C2214yescomplemented
61#10622788C2214yes—
62#10622781C2214yes—
63#10622779C2214yescomplemented
64#10622778C2214yes—
65#10622776C2214yes—
66#10622775C2214yescomplemented
67SD16×Dic11C2214yescomplemented
68SD16×Dic11C2214yescomplemented
69#10622767C2214yes—
70#10622766C2214yescomplemented
71#10622765C2214yescomplemented
72#10622763C2214yes—
73C2×#66885C2211yescharacteristic
74C2×#66881C2211yescharacteristic
75C2×#66880C2211yescharacteristic
76#10622715C2212yes—
77#10622714C2212yes—
78#10622703C2212yescomplemented
79#10622696C2212yes—
80#10622688C2212yescomplemented
81#10622685C2212yes—
82#10622670C2214yes—
83#10622667C2214yescomplemented
84#10622537C2211yescharacteristic
85C4×#4314C2212yes—
86C4×#4314C2212yes—
87C4×#4314C2212yes—
88C4×#4314C2212yes—
89#10622292C2212yescomplemented
90#10622292C2212yescomplemented
91C8×Dic22C2212yescomplemented
92C8×Dic22C2212yescomplemented
93C2×C11×#41C2312yes—
94C2×C11×#41C2312yes—
95C2×#4341—22no—
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×Dic22C2311yescharacteristic
99C11×#135—28no—
100C11×#135—44no—
101C2×C11×Q16C2312yes—
102C2×C11×Q16C2312yes—
103C2×C11×SD16C2312yes—
104C2×C11×SD16C2312yes—
105C2×C11×SD16C2312yes—
106C2×C11×SD16C2312yes—
107C2×C11×D8C2312yes—
108C2×C11×D8C2312yes—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C11×C4⋊Q8C2311yescharacteristic
112C11×C4⋊Q8C2311yescharacteristic
113C11×#127C2311yescharacteristic
114C11×#127C2311yescharacteristic
115C11×#124C2312yes—
116C11×#124C2312yes—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C2×C42×C11C2311yescharacteristic
126#67004—44no—
127#67002—44no—
128#67000C2314yes—
129Q8×Dic11C2314yes—
130Q8×Dic11C2314yes—
131#66997C2314yes—
132C2×#4326C2314yes—
133C2×#4325C2314yes—
134#66993C2314yes—
135#66992—24no—
136#66991—22no—
137#66990—24no—
138#66989—22no—
139#66989C2314yes—
140#66988—24no—
141#66988—24no—
142D4×Dic11—24no—
143D4×Dic11—24no—
144D4×Dic11—22no—
145D4×Dic11C2314yes—
146D4×Dic11C2314yes—
147C2×#4324C2314yes—
148C2×#4323C2314yes—
149#66983—22no—
150#66983—22no—
151C2×(C2×D11)⋊C4—21no—
152#66979—22no—
153#66979—22no—
154#66979C2312yes—
155C2×C4⋊Dic11—22no—
156C2×C4⋊Dic11—22no—
157C2×C4⋊Dic11C2311yescharacteristic
158C2×C4⋊Dic11C2311yescharacteristic
159#66977—22no—
160#66977—22no—
161#66977D412yes—
162#66977D412yes—
163C2×Dic11⋊C4—21no—
164C2×C4×Dic11—21no—
165C2×#4318C2312yes—
166C2×#4314—24no—
167C2×#4314C2312yes—
168C2×#4314C2312yes—
169#66951—24no—
170#66950—22no—
171#66945—22no—
172#66943—22no—
173#66942—24no—
174#66940—22no—
175#66939—24no—
176#66938—24no—
177#66936—24no—
178(C22⋊D11)⋊C4—24no—
179#66932—24no—
180#66932—24no—
181#66931—24no—
182#66930—24no—
183C4×D44—21no—
184C4×D44—21no—
185C4×D44C2312yes—
186C4×D44C2312yes—
187#66923D412yes—
188#66922D411yescharacteristic
189#66922D411yescharacteristic
190C4×Dic22—21no—
191C4×Dic22—21no—
192C4×Dic22C2312yes—
193C4×Dic22C2312yes—
194C4×Dic22C2312yes—
195C4×Dic22C2312yes—
196C4×C8×C11C2311yescharacteristic
197C4×C8×C11C2311yescharacteristic
198C4×C8×C11C2311yescharacteristic
199C4×C8×C11C2311yescharacteristic
200#66899C2314yes—
201#66899C2314yes—
202#66896C2314yes—
203#66896C2314yes—
204#66885C2312yes—
205#66885C2312yes—
206#66881C2312yes—
207#66881C2312yes—
208#66880C2312yes—
209#66880C2312yes—
210#66879C2314yes—
211Dic11⋊C8C2314yes—
212Dic11⋊C8C2314yes—
213C8×Dic11C2314yes—
214C4⋊(C11⋊C8)C2312yes—
215C4⋊(C11⋊C8)C2312yes—
216#61407—111nomaximal, Sylow
217C23×D11—21no—
218C11×#41—24no—
219C11×#41—24no—
220C11×#41—24no—
221C11×#41—24no—
222C2×Q8×C11C2412yes—
223C2×Q8×C11C2412yes—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11C2412yes—
231C2×D4×C11C2412yes—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C22×Dic11—24no—
240C22×Dic11—24no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244#4341—84no—
245C2×D44—21no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44C2412yes—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—82no—
252C2×Dic22—21no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22C2×D412yes—
256C2×Dic22C2×D412yes—
257C2×Dic22C2412yes—
258C11×Q16—24no—
259C11×Q16—42no—
260C11×SD16—24no—
261C11×SD16—24no—
262C11×SD16—42no—
263C11×SD16—42no—
264C11×D8—24no—
265C11×D8—42no—
266C2×C8×C11—22no—
267C2×C8×C11#4114yescomplemented
268C2×C8×C11C2411yescharacteristic
269C2×C8×C11C2411yescharacteristic
270C2×C8×C11C2411yescharacteristic
271C2×C8×C11C2411yescharacteristic
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2411yescharacteristic
283C42×C11C2411yescharacteristic
284C22⋊Dic11—24no—
285C22⋊Dic11—24no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288C22⋊Dic11C2×D414yes—
289#4326—44no—
290#4325—44no—
291#4324—44no—
292#4323—44no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—22no—
296(C2×D11)⋊C4—22no—
297C4⋊Dic11—24no—
298C4⋊Dic11—24no—
299C4⋊Dic11—21no—
300C4⋊Dic11—21no—
301C4⋊Dic11C2×D412yes—
302C4⋊Dic11C2×D412yes—
303C4⋊Dic11C2×D412yes—
304C4⋊Dic11C2×D412yes—
305C4⋊Dic11C2412yes—
306C4⋊Dic11C2412yes—
307Dic11⋊C4—24no—
308Dic11⋊C4—24no—
309Dic11⋊C4—22no—
310Dic11⋊C4—22no—
311Dic11⋊C4C2×D414yes—
312Dic11⋊C4C2×D414yes—
313C4×Dic11—24no—
314C4×Dic11—24no—
315C4×Dic11—22no—
316C4×Dic11—22no—
317C4×Dic11C2414yes—
318#4318—24no—
319C2×C11⋊C8C2414yes—
320#4314—24no—
321#4314—24no—
322#3507—111no—
323#3506—111no—
324#3401—114no—
325#3399—112no—
326#3398—112no—
327#3394—114no—
328#3394—112no—
329#3392—112no—
330#3154—112no—
331#3147D1111yescharacteristic, complemented
332#3046—112no—
333#3045—112no—
334#3037—111no—
335#3036—111no—
336#2960—111no—
337#2952—112no—
338C2×C4×SD16—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343C22×D11—42no—
344C22×D11—81no—
345C22×D11—81no—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—44no—
355D4×C11—44no—
356D4×C11—42no—
357D4×C11—42no—
358D4×C11—81no—
359D4×C11—81no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—41no—
364C2×C4×C11—44no—
365C2×C4×C11—44no—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C2×#4112yes—
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—84no—
375C22⋊D11—84no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—42no—
380C2×Dic11—84no—
381C2×Dic11—84no—
382C2×Dic11—81no—
383C2×Dic11—81no—
384C2×Dic11C22×D414yes—
385C2×Dic11C22×D414yes—
386D44—22no—
387D44—22no—
388D44—42no—
389C4×D11—44no—
390C4×D11—82no—
391Dic22—24no—
392Dic22—22no—
393Dic22—22no—
394Dic22—42no—
395Dic22—42no—
396C8×C11—21no—
397C8×C11—21no—
398C8×C11C2×#4112yes—
399C8×C11C2×#4112yes—
400C11⋊C8—24no—
401C2×#137—112no—
402C2×AGL(1,ℤ/8)—112no—
403C2×#135C2×D1112yes—
404C2×#135C2×D1112yes—
405C22×SD16—111no—
406#559—112no—
407#559—114no—
408#557—112no—
409#556—112no—
410#556—114no—
411#556—221no—
412#555—221no—
413#554—221no—
414#553—222no—
415#552—222no—
416#550—112no—
417#547—221no—
418#539—222no—
419#538—222no—
420#536—112no—
421#535—112no—
422#533—111no—
423#532C2×D1111yescharacteristic
424#532C2×D1111yescharacteristic
425#529—222no—
426#525—222no—
427#520—112no—
428#520—112no—
429C2×C4×Q8—111no—
430C2×C4×D4—111no—
431#497—114no—
432#496—114no—
433#495—114no—
434#495C2×D1112yescomplemented
435#495C2×D1112yescomplemented
436#494C2×D1111yescharacteristic, complemented
437#493C2×D1111yescharacteristic, complemented
438#492—114no—
439#492C2×D1111yescharacteristic, complemented
440#492C2×D1111yescharacteristic, complemented
441#464—114no—
442#464—114no—
443#464—114no—
444#463—114no—
445#463—114no—
446#463—114no—
447#462—114no—
448#462—112no—
449#461—114no—
450#461—112no—
451#460—114no—
452#460—112no—
453#459—114no—
454#459—112no—
455#446—112no—
456#446—112no—
457C8×Q8—112no—
458C8×Q8—112no—
459#442—114no—
460#441—114no—
461C4×SD16—114no—
462C4×SD16—114no—
463C4×SD16—112no—
464C4×SD16—112no—
465C4×SD16—112no—
466C4×SD16—112no—
467C2×#106—111no—
468#424—112no—
469#423—111no—
470#417—112no—
471#417—112no—
472C2×#103—111no—
473C2×#102—111no—
474#405—112no—
475C2×C4×C8C2×D1111yescharacteristic
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11#55012yes—
485C22×C11C23×D411yescharacteristic
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—84no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—21no—
493C4×C11—42no—
494C4×C11—42no—
495C4×C11#55012yes—
496C4×C11#57712yes—
497C4×C11C22×#4111yescharacteristic
498C4×C11C2×H(5,𝔽2)11yescharacteristic
499Dic11—24no—
500Dic11—24no—
501Dic11—42no—
502Dic11—42no—
503Dic11—42no—
504C2×#41—222no—
505C2×#41C22×D1112yes—
506C2×#41C22×D1112yes—
507C22×Q8—111no—
508C22×D4—111no—
509C23×C4—221no—
510#137—444no—
511AGL(1,ℤ/8)—444no—
512#135—28no—
513#135—44no—
514C2×Q16—114no—
515C2×Q16C22×D1112yes—
516C2×Q16C22×D1112yes—
517C2×SD16—114no—
518C2×SD16—114no—
519C2×SD16—112no—
520C2×SD16—112no—
521C2×SD16—224no—
522C2×SD16C22×D1112yes—
523C2×SD16C22×D1112yes—
524C2×SD16C22×D1112yes—
525C2×SD16C22×D1112yes—
526C2×D8—114no—
527C2×D8C22×D1112yes—
528C2×D8C22×D1112yes—
529C2×M16—112no—
530C22×C8C22×D1111yescharacteristic
531C22×C8C22×D1111yescharacteristic
532C4⋊Q8—114no—
533C4⋊Q8—111no—
534C4⋊Q8—111no—
535C4⋊Q8C22×D1111yescharacteristic
536C4⋊Q8C22×D1111yescharacteristic
537#127—114no—
538#127C22×D1111yescharacteristic
539#127C22×D1111yescharacteristic
540#126—224no—
541#126—224no—
542#126—224no—
543#125—112no—
544#125—222no—
545#125—224no—
546#124—114no—
547#124—114no—
548#124—224no—
549#124—222no—
550#124C22×D1112yes—
551#124C22×D1112yes—
552#123—224no—
553#123—224no—
554#123—224no—
555#123—224no—
556C22⋊Q8—112no—
557C22⋊Q8—112no—
558C22⋊Q8—224no—
559C22⋊Q8—222no—
560C22⋊Q8—222no—
561C22⋊Q8—222no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—222no—
567#121—222no—
568#121—222no—
569#121—224no—
570#120—224no—
571C4×Q8—112no—
572C4×Q8—112no—
573C4×Q8—114no—
574C4×Q8—114no—
575C4×Q8—112no—
576C4×Q8—112no—
577C4×Q8—222no—
578C4×Q8—221no—
579C4×Q8—221no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—114no—
585C4×D4—114no—
586C4×D4—112no—
587C4×D4—112no—
588C4×D4—224no—
589C4×D4—224no—
590C4×D4—224no—
591C4×D4—222no—
592C4×D4—221no—
593C4×D4—221no—
594#117—112no—
595#117—224no—
596#117—222no—
597#117—222no—
598#117—222no—
599C2×C4⋊C4—111no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C42—221no—
606C2×C42C22×D1111yescharacteristic
607#106—112no—
608#106—112no—
609C4⋊C8—114no—
610C4⋊C8—114no—
611C4⋊C8—112no—
612C4⋊C8—112no—
613#103—114no—
614#103—114no—
615#103—112no—
616#103—112no—
617#102—114no—
618#102—114no—
619#102—112no—
620#102—112no—
621#97—114no—
622C4×C8—114no—
623C4×C8C22×D1111yescharacteristic
624C4×C8C22×D1111yescharacteristic
625C4×C8C22×D1111yescharacteristic
626C4×C8C22×D1111yescharacteristic
627C2×C11—22no—
628C2×C11—82no—
629C2×C11—82no—
630C2×C11C2×#55011yescharacteristic
631C2×C11C2×#57711yescharacteristic
632C2×C11#358411yescharacteristic
633D11—82no—
634C24—221no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—24no—
639#41—884no—
640C2×Q8—112no—
641C2×Q8—112no—
642C2×Q8—112no—
643C2×Q8—221no—
644C2×Q8—222no—
645C2×Q8—222no—
646C2×Q8C23×D1112yes—
647C2×Q8C23×D1112yes—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—112no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—221no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4C23×D1112yes—
661C2×D4C23×D1112yes—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—882no—
672C22×C4D4×D1111yescharacteristic
673C22×C4D4×D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675Q16—24no—
676Q16—42no—
677Q16—444no—
678SD16—24no—
679SD16—24no—
680SD16—42no—
681SD16—42no—
682SD16—224no—
683SD16—224no—
684SD16—444no—
685SD16—444no—
686D8—24no—
687D8—42no—
688D8—444no—
689M16—224no—
690C2×C8—22no—
691C2×C8—114no—
692C2×C8#434114yescomplemented
693C2×C8C23×D1111yescharacteristic
694C2×C8C23×D1111yescharacteristic
695C2×C8C23×D1111yescharacteristic
696C2×C8C23×D1111yescharacteristic
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—112no—
702C4⋊C4—112no—
703C4⋊C4—112no—
704C4⋊C4—114no—
705C4⋊C4—114no—
706C4⋊C4—112no—
707C4⋊C4—112no—
708C4⋊C4—112no—
709C4⋊C4—224no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—222no—
716C4⋊C4—222no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—114no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C22⋊C4—224no—
728C22⋊C4—222no—
729C22⋊C4—222no—
730C42—114no—
731C42—224no—
732C42—224no—
733C42—222no—
734C42—222no—
735C42D4×D1111yescharacteristic
736C42D4×D1111yescharacteristic
737C42C23×D1111yescharacteristic
738C42C23×D1111yescharacteristic
739C11#6140711yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—222no—
743C23—442no—
744C23—881no—
745C23—881no—
746C23C2×D4×D1111yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—224no—
752Q8—222no—
753Q8—222no—
754Q8—442no—
755Q8—442no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—42no—
763D4—42no—
764D4—81no—
765D4—81no—
766D4—222no—
767D4—222no—
768D4—442no—
769D4—884no—
770D4—884no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—114no—
778C2×C4—114no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—442no—
783C2×C4—444no—
784C2×C4—882no—
785C2×C4—884no—
786C2×C4—884no—
787C2×C4—881no—
788C2×C4—881no—
789C2×C4C2×D4×D1111yescharacteristic
790C2×C4C2×D4×D1111yescharacteristic
791C2×C4C2×D4×D1111yescharacteristic
792C2×C4C2×D4×D1111yescharacteristic
793C2×C4C2×D4×D1111yescharacteristic
794C2×C4C2×#434112yes—
795C2×C4#6703712yes—
796C2×C4C24×D1111yescharacteristic
797C8—21no—
798C8—21no—
799C8—224no—
800C8C2×#434112yes—
801C8C2×#434112yes—
802C22—21no—
803C22—21no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—884no—
814C22#1062324912yes—
815C22C22×D4×D1111yescharacteristic
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—224no—
822C4—224no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4#1062324912yes—
827C4#1062330112yes—
828C4C22×#434111yescharacteristic
829C4C2×#6703711yescharacteristic
830C2—22no—
831C2—82no—
832C2—82no—
833C2—882no—
834C2C2×#1062324911yescharacteristic
835C2C2×#1062330111yescharacteristic
836C2#1308338511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3147C2
socleC22×C11C23×D4
hypercenter#3147D11
hypocenterC11#61407
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13082478C2semidirect
2. #13082465C2semidirect
3. #13081688C2semidirect
4. #13081663C2semidirect
5. #13081652C2semidirect
6. #13081617C2semidirect
7. #13081609C2semidirect
8. #13081594C2semidirect
9. #13079093C2semidirect
10. #13078164C2semidirect
11. #13078153C2semidirect
12. #13078084C2semidirect
13. #13078076C2semidirect
14. #13077550C2semidirect
15. #13077500C2semidirect
16. C2×C4×#4314C2semidirect
17. C11×#3147C2semidirect
30. #10623252C22semidirect
32. #10623244C22semidirect
34. #10623202C22semidirect
48. C11×#495C22semidirect
49. C11×#495C22semidirect
50. C11×#494C22semidirect
51. C11×#493C22semidirect
52. C11×#492C22semidirect
53. C11×#492C22semidirect
59. #10622797C22semidirect
60. #10622795C22semidirect
63. #10622779C22semidirect
66. #10622775C22semidirect
67. SD16×Dic11C22semidirect
68. SD16×Dic11C22semidirect
70. #10622766C22semidirect
71. #10622765C22semidirect
78. #10622703C22semidirect
80. #10622688C22semidirect
83. #10622667C22semidirect
89. #10622292C22semidirect
90. #10622292C22semidirect
91. C8×Dic22C22semidirect
92. C8×Dic22C22semidirect
267. C2×C8×C11#41semidirect
331. #3147D11semidirect
434. #495C2×D11semidirect
435. #495C2×D11semidirect
436. #494C2×D11semidirect
437. #493C2×D11semidirect
439. #492C2×D11semidirect
440. #492C2×D11semidirect
692. C2×C8#4341semidirect
739. C11#61407semidirect

Maximal subgroups

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

subgroupindex
#130824782
#130824652
#130816882
#130816632
#130816522
#130816172
#130816092
#130815942
#130790932
#130781642
#130781532
#130780842
#130780762
#130775502
#130775002
C2×C4×#43142
C11×#31472
#6140711