Finite Group Databasebeta

← #15622740

Subgroups — #15622740

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13078859C214yesmaximal, complemented
3#13078815C214yesmaximal, complemented
4#13078767C212yesmaximal, complemented
5#13078707C212yesmaximal, complemented
6#13078676C212yesmaximal, complemented
7#13078616C212yesmaximal, complemented
8#13078574C212yesmaximal, complemented
9#13078413C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078096C211yesmaximal, characteristic, complemented
12C2×#10622628C211yesmaximal, characteristic, complemented
13#13077884C212yesmaximal, complemented
14#13077466C212yesmaximal, complemented
15#13077444C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C4×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
18C2×C11×H(5,𝔽2)C2211yescharacteristic
19C11×#520—21no—
20C11×#520C2211yescharacteristic
21C11×#520C2211yescharacteristic
22C11×#520C2212yescomplemented
23C11×#518—22no—
24C11×#518—21no—
25C11×#518C2211yescharacteristic
26C11×#518C2212yescomplemented
27C4×C11×#41—21no—
28C4×C11×#41C2211yescharacteristic
29C4×C11×#41C2211yescharacteristic
30C4×C11×#41C2212yescomplemented
31C2×C4×D4×C11—21no—
32C2×C4×D4×C11—22no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2212yescomplemented
35#10623361C2212yes—
36C2×#67002C2212yes—
37C22×#4323C2212yes—
38#10623116—21no—
39#10623116—21no—
40#10623084—21no—
41#10623084—21no—
42#10623081—22no—
43#10623081—22no—
44#10623066C2214yescomplemented
45#10623052C2212yescomplemented
46#10623008C2212yescomplemented
47#10623008C2212yescomplemented
48C2×#66927C2211yescharacteristic, complemented
49#10623001C2211yescharacteristic, complemented
50#10622851C2214yescomplemented
51#10622851C2214yescomplemented
52#10622847C2212yes—
53#10622846C2212yes—
54#10622830C2214yescomplemented
55#10622830C2214yescomplemented
56#10622828C2212yes—
57#10622640C2212yescomplemented
58#10622640C2212yescomplemented
59#10622639C2214yescomplemented
60C4×#4325C2214yescomplemented
61#10622635C2212yescomplemented
62#10622634C2211yescharacteristic, complemented
63#10622633C2211yescharacteristic, complemented
64#10622628C2214yescomplemented
65#10622628C2212yescomplemented
66#10622628C2212yescomplemented
67#10622628C2212yescomplemented
68#10622628C2212yescomplemented
69#10622627C2214yescomplemented
70#10622627C2214yescomplemented
71#10622627C2214yescomplemented
72C4×#4323C2214yescomplemented
73C4×#4323C2214yescomplemented
74C4×#4323C2214yescomplemented
75#10622622C2214yescomplemented
76#10622622C2212yescomplemented
77#10622621C2211yescharacteristic, complemented
78#10622621C2212yescomplemented
79#10622620C2211yescharacteristic, complemented
80#10622620C2212yescomplemented
81#10622616C2214yescomplemented
82#10622616C2214yescomplemented
83#10622614C2212yescomplemented
84#10622613C2214yescomplemented
85#10622611C2212yescomplemented
86#10622610C2212yescomplemented
87#10622581C2214yescomplemented
88#10622580C2214yescomplemented
89C2×#66873C2212yescomplemented
90#10622577C2212yescomplemented
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic, complemented
94C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
95C11×H(5,𝔽2)—24no—
96C11×H(5,𝔽2)—24no—
97C2×C11×#41—21no—
98C2×C11×#41C2312yes—
99C2×C11×#41C2311yescharacteristic
100C2×C11×#41C2311yescharacteristic
101C22×D4×C11—22no—
102C22×D4×C11—21no—
103C22×D4×C11C2312yes—
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11—21no—
106C23×C4×C11—22no—
107C2×#4339—22no—
108C2×#4339—22no—
109C22×D44—21no—
110C22×D44—21no—
111C22×D44C2312yes—
112C4×Q8×C11—21no—
113C4×Q8×C11D411yescharacteristic
114C4×Q8×C11D411yescharacteristic
115C4×Q8×C11C2311yescharacteristic
116C4×Q8×C11C2311yescharacteristic
117C4×Q8×C11C2312yes—
118C4×D4×C11—22no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—22no—
122C4×D4×C11—21no—
123C4×D4×C11—22no—
124C4×D4×C11—21no—
125C4×D4×C11—22no—
126C4×D4×C11—21no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—21no—
132C4×D4×C11—22no—
133C4×D4×C11—21no—
134C4×D4×C11—22no—
135C4×D4×C11D412yes—
136C4×D4×C11D412yes—
137C4×D4×C11D411yescharacteristic
138C4×D4×C11D411yescharacteristic
139C4×D4×C11C2312yes—
140C4×D4×C11C2312yes—
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2312yes—
143C4×D4×C11C2312yes—
144C4×D4×C11C2311yescharacteristic
145C4×D4×C11C2312yes—
146C11×#117—21no—
147C11×#117—22no—
148C11×#117—21no—
149C11×#117—22no—
150C11×#117C2311yescharacteristic
151C11×#117C2312yes—
152C11×#117C2311yescharacteristic
153C11×#117C2312yes—
154C2×C11×C4⋊C4—21no—
155C2×C11×C4⋊C4—22no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—22no—
160C2×C11×C22⋊C4—22no—
161C2×C11×C22⋊C4—22no—
162C2×C11×C22⋊C4—22no—
163C2×C42×C11—21no—
164C2×C42×C11—22no—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2312yes—
167#67002—28no—
168#67000—22no—
169C2×#4325C2314yes—
170#66993—22no—
171#66990—24no—
172C2×#4323—28no—
173C2×#4323C2314yes—
174C2×#4323C2314yes—
175C2×#4323C2314yes—
176#66983—22no—
177#66983—22no—
178#66983C2314yes—
179#66983C2314yes—
180#66979C2312yes—
181#66977—21no—
182#66977—21no—
183C2×#4318C2312yes—
184C22×C11⋊C8C2312yes—
185#66947—24no—
186#66947—24no—
187#66946—22no—
188#66946—22no—
189#66937—24no—
190#66937—24no—
191C22⋊C4×D11—24no—
192#66928—22no—
193#66928—22no—
194#66927—21no—
195#66927—21no—
196#66927C2312yes—
197#66927C2312yes—
198C4×D44—22no—
199C4×D44—22no—
200C4×D44C2314yes—
201C4×D44C2314yes—
202#66923C2312yes—
203#66922C2311yescharacteristic
204#66922C2311yescharacteristic
205C4×Dic22—21no—
206C4×Dic22—21no—
207#66899C2312yes—
208#66899C2312yes—
209#66896C2314yes—
210#66896C2314yes—
211#66896C2312yes—
212#66896C2312yes—
213C22⋊(C11⋊C8)C2314yes—
214C22⋊(C11⋊C8)C2314yes—
215#66873C2314yes—
216#66873C2314yes—
217#66873C2314yes—
218#66873C2314yes—
219#66872C2314yes—
220#66872C2312yes—
221#66872C2312yes—
222#66871C2314yes—
223#66871C2312yes—
224#66871C2312yes—
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2311yescharacteristic
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230#66867C2314yes—
231C4×C11⋊C8C2314yes—
232#60590—111nomaximal, Sylow
233C24×C11—22no—
234C24×C11—21no—
235C23×D11—22no—
236C11×#41—28no—
237C11×#41—24no—
238C11×#41—24no—
239C11×#41—22no—
240C11×#41—22no—
241C11×#41—22no—
242C11×#41#4114yescomplemented
243C2×Q8×C11C2×D411yescharacteristic
244C2×Q8×C11C2411yescharacteristic
245C2×D4×C11—216no—
246C2×D4×C11—28no—
247C2×D4×C11—22no—
248C2×D4×C11—21no—
249C2×D4×C11—24no—
250C2×D4×C11—24no—
251C2×D4×C11—22no—
252C2×D4×C11—21no—
253C2×D4×C11—22no—
254C2×D4×C11C2×D412yes—
255C2×D4×C11C2×D411yescharacteristic
256C2×D4×C11#4114yescomplemented
257C2×D4×C11C2411yescharacteristic
258C2×D4×C11C2412yes—
259C22×C4×C11—22no—
260C22×C4×C11—21no—
261C22×C4×C11—22no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—22no—
265C22×C4×C11—21no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—82no—
271C22×C4×C11—84no—
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2411yescharacteristic
278C2×C22⋊D11—24no—
279C2×C22⋊D11—24no—
280#4339—84no—
281#4339—84no—
282C2×D44—22no—
283C2×D44—22no—
284C2×D44—22no—
285C2×D44—22no—
286C2×D44—22no—
287C2×D44—24no—
288C2×D44—24no—
289C2×D44—82no—
290C2×D44—82no—
291C2×D44C2414yes—
292C2×C4×D11—24no—
293C2×C4×D11—24no—
294C2×Dic22—21no—
295C2×Dic22—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—21no—
300C11×C4⋊C4—21no—
301C11×C4⋊C4C2×D411yescharacteristic
302C11×C4⋊C4C2×D411yescharacteristic
303C11×C4⋊C4C2×D412yes—
304C11×C4⋊C4C2×D412yes—
305C11×C4⋊C4C2412yes—
306C11×C4⋊C4C2411yescharacteristic
307C11×C4⋊C4C2411yescharacteristic
308C11×C22⋊C4—22no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4C2×D412yes—
318C11×C22⋊C4C2×D412yes—
319C11×C22⋊C4C2×D412yes—
320C42×C11—21no—
321C42×C11—21no—
322C42×C11—22no—
323C42×C11—22no—
324C42×C11—21no—
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C42×C11C2×D412yes—
328C42×C11C2×D412yes—
329C42×C11C2412yes—
330C42×C11C2411yescharacteristic
331C42×C11C2411yescharacteristic
332C22⋊Dic11—22no—
333#4325—28no—
334#4323—28no—
335#4323—28no—
336#4323—28no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—24no—
339(C2×D11)⋊C4—24no—
340(C2×D11)⋊C4—24no—
341C4⋊Dic11—21no—
342C4⋊Dic11—21no—
343C4⋊Dic11C2412yes—
344C4⋊Dic11C2412yes—
345Dic11⋊C4—22no—
346Dic11⋊C4—22no—
347C4×Dic11—22no—
348#4318—24no—
349C2×C11⋊C8—24no—
350C2×C11⋊C8C2412yes—
351C2×C11⋊C8C2414yes—
352C2×C11⋊C8C2412yes—
353#3508—111no—
354C4×H(5,𝔽2)D1111yescharacteristic, complemented
355#3122—114no—
356#3119—114no—
357#3115—112no—
358#3109—112no—
359#3106—112no—
360#3100—112no—
361#3096—112no—
362#3077—111no—
363#3076—111no—
364#3038—111no—
365C2×#459—111no—
366#3008—112no—
367#2948—112no—
368#2946—112no—
369#2925—111no—
370C23×C11—28no—
371C23×C11—22no—
372C23×C11—21no—
373C23×C11—24no—
374C23×C11—81no—
375C23×C11—82no—
376C23×C11—81no—
377C23×C11—82no—
378C23×C11C22×D412yes—
379C23×C11C22×D411yescharacteristic
380C22×D11—24no—
381C22×D11—44no—
382C22×D11—82no—
383C22×D11—82no—
384Q8×C11—22no—
385Q8×C11—21no—
386Q8×C11C2×#4112yes—
387D4×C11—28no—
388D4×C11—28no—
389D4×C11—24no—
390D4×C11—24no—
391D4×C11—22no—
392D4×C11—24no—
393D4×C11—22no—
394D4×C11—21no—
395D4×C11C2×#4112yes—
396D4×C11C2×#4114yes—
397C2×C4×C11—28no—
398C2×C4×C11—21no—
399C2×C4×C11—24no—
400C2×C4×C11—22no—
401C2×C4×C11—24no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—41no—
408C2×C4×C11—42no—
409C2×C4×C11—42no—
410C2×C4×C11—44no—
411C2×C4×C11—82no—
412C2×C4×C11—81no—
413C2×C4×C11—82no—
414C2×C4×C11—82no—
415C2×C4×C11—82no—
416C2×C4×C11—81no—
417C2×C4×C11—82no—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D412yes—
422C2×C4×C11C22×D412yes—
423C2×C4×C11C22×D412yes—
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C2×#4112yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2511yescharacteristic
429C22⋊D11—84no—
430C22⋊D11—84no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433D44—24no—
434D44—24no—
435D44—44no—
436D44—44no—
437D44—44no—
438D44—82no—
439D44—82no—
440C4×D11—84no—
441C4×D11—84no—
442Dic22—42no—
443Dic22—42no—
444C11⋊C8—22no—
445C11⋊C8—22no—
446C11⋊C8—24no—
447C2×H(5,𝔽2)C2×D1111yescharacteristic
448C2×AGL(1,ℤ/8)—112no—
449C22×D8—112no—
450#559—221no—
451#559—221no—
452#550—221no—
453#550—221no—
454#546—222no—
455#546—222no—
456#540—114no—
457#535—112no—
458#533—111no—
459#532—112no—
460#532—112no—
461C2×#127—111no—
462#520—21no—
463#520C2×D1111yescharacteristic
464#520C2×D1111yescharacteristic
465#520C2×D1112yescomplemented
466#518—22no—
467#518—21no—
468#518—112no—
469#518C2×D1111yescharacteristic
470#518C2×D1112yescomplemented
471C4×#41—21no—
472C4×#41C2×D1111yescharacteristic
473C4×#41C2×D1111yescharacteristic
474C4×#41C2×D1112yescomplemented
475C2×C4×D4—21no—
476C2×C4×D4—22no—
477C2×C4×D4C2×D1111yescharacteristic
478C2×C4×D4C2×D1112yescomplemented
479#482—114no—
480#482—114no—
481#481—114no—
482#480—114no—
483#479—112no—
484#478—112no—
485#478—114no—
486#477—111no—
487#476—111no—
488#476—112no—
489#475—111no—
490#474—111no—
491#474—112no—
492#460—112no—
493#460—112no—
494#459—112no—
495#459—112no—
496#459—112no—
497#459—114no—
498#459—112no—
499#449—114no—
500#449—114no—
501#447—114no—
502#447—114no—
503#442—114no—
504#442—114no—
505#442—114no—
506#440—114no—
507C4×SD16—114no—
508C4×D8—114no—
509C4×D8—114no—
510C4×D8—114no—
511#433—114no—
512#432—112no—
513#431—112no—
514#428—112no—
515#427—112no—
516#423—111no—
517C2×C4⋊C8—111no—
518#418—112no—
519#418—112no—
520#416—112no—
521C2×#102—112no—
522#408—112no—
523#405—112no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—22no—
527C22×C11—22no—
528C22×C11—24no—
529C22×C11—22no—
530C22×C11—22no—
531C22×C11—42no—
532C22×C11—41no—
533C22×C11—42no—
534C22×C11—41no—
535C22×C11—84no—
536C22×C11—88no—
537C22×C11#52512yes—
538C22×C11C23×D411yescharacteristic
539C2×D11—44no—
540C2×D11—44no—
541C2×D11—44no—
542C2×D11—164no—
543C4×C11—21no—
544C4×C11—22no—
545C4×C11—21no—
546C4×C11—22no—
547C4×C11—22no—
548C4×C11—22no—
549C4×C11—21no—
550C4×C11—41no—
551C4×C11—41no—
552C4×C11—42no—
553C4×C11#52512yes—
554C4×C11#57612yes—
555C4×C11C22×#4111yescharacteristic
556C4×C11C22×#4111yescharacteristic
557Dic11—42no—
558Dic11—42no—
559H(5,𝔽2)—24no—
560H(5,𝔽2)—24no—
561C2×#41—21no—
562C2×#41—222no—
563C2×#41—222no—
564C2×#41C22×D1112yes—
565C2×#41C22×D1111yescharacteristic
566C2×#41C22×D1111yescharacteristic
567C22×D4—22no—
568C22×D4—21no—
569C22×D4—112no—
570C22×D4—221no—
571C22×D4—221no—
572C22×D4C22×D1112yes—
573C22×D4C22×D1111yescharacteristic
574C23×C4—21no—
575C23×C4—22no—
576AGL(1,ℤ/8)—228no—
577C2×SD16—114no—
578C2×D8—114no—
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—228no—
582C2×M16—112no—
583C22×C8—112no—
584C4⋊Q8—111no—
585C4⋊Q8—111no—
586#127—112no—
587#127—112no—
588#127—222no—
589#127—221no—
590#127—221no—
591#125—112no—
592#124—222no—
593#124—222no—
594#124—222no—
595#123—224no—
596#123—224no—
597C22⋊Q8—221no—
598C22⋊Q8—221no—
599#121—114no—
600#121—114no—
601#121—222no—
602#121—222no—
603#121—224no—
604#121—224no—
605#120—224no—
606C4×Q8—21no—
607C4×Q8—221no—
608C4×Q8—221no—
609C4×Q8C22⋊D1111yescharacteristic
610C4×Q8C22⋊D1111yescharacteristic
611C4×Q8C22×D1111yescharacteristic
612C4×Q8C22×D1111yescharacteristic
613C4×Q8C22×D1112yes—
614C4×D4—22no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—22no—
618C4×D4—21no—
619C4×D4—22no—
620C4×D4—21no—
621C4×D4—22no—
622C4×D4—21no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—21no—
628C4×D4—22no—
629C4×D4—21no—
630C4×D4—22no—
631C4×D4—114no—
632C4×D4—114no—
633C4×D4—222no—
634C4×D4—222no—
635C4×D4—222no—
636C4×D4—222no—
637C4×D4C22⋊D1112yes—
638C4×D4C22⋊D1111yescharacteristic
639C4×D4C22⋊D1112yes—
640C4×D4C22⋊D1111yescharacteristic
641C4×D4C22×D1112yes—
642C4×D4C22×D1112yes—
643C4×D4C22×D1111yescharacteristic
644C4×D4C22×D1112yes—
645C4×D4C22×D1112yes—
646C4×D4C22×D1111yescharacteristic
647C4×D4C22×D1112yes—
648#117—21no—
649#117—22no—
650#117—21no—
651#117—22no—
652#117—112no—
653#117C22×D1111yescharacteristic
654#117C22×D1112yes—
655#117C22×D1111yescharacteristic
656#117C22×D1112yes—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C4⋊C4C22×D1112yes—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—224no—
667C2×C42—21no—
668C2×C42—22no—
669C2×C42C22×D1111yescharacteristic
670C2×C42C22×D1112yes—
671#107—112no—
672#107—112no—
673#107—114no—
674#106—112no—
675#106—112no—
676#106—114no—
677C4⋊C8—111no—
678C4⋊C8—111no—
679C4⋊C8—112no—
680C4⋊C8—112no—
681C4⋊C8—112no—
682#103—112no—
683#103—112no—
684#102—112no—
685#102—112no—
686#102—114no—
687#102—114no—
688#102—114no—
689#102—114no—
690#102—114no—
691#102—114no—
692C22⋊C8—114no—
693C22⋊C8—114no—
694#97—114no—
695C4×C8—114no—
696C2×C11—22no—
697C2×C11—42no—
698C2×C11—44no—
699C2×C11—42no—
700C2×C11C2×#52511yescharacteristic
701C2×C11C2×#57611yescharacteristic
702C2×C11#358511yescharacteristic
703D11—84no—
704C24—22no—
705C24—21no—
706C24—222no—
707#41—28no—
708#41—24no—
709#41—24no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—884no—
714#41—884no—
715#41#433914yescomplemented
716C2×Q8—221no—
717C2×Q8—221no—
718C2×Q8C2×C22⋊D1111yescharacteristic
719C2×Q8C23×D1111yescharacteristic
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—114no—
730C2×D4—224no—
731C2×D4—224no—
732C2×D4—224no—
733C2×D4—224no—
734C2×D4—222no—
735C2×D4—222no—
736C2×D4—222no—
737C2×D4—222no—
738C2×D4—222no—
739C2×D4—882no—
740C2×D4—882no—
741C2×D4#433914yescomplemented
742C2×D4C2×C22⋊D1112yes—
743C2×D4C2×C22⋊D1111yescharacteristic
744C2×D4C23×D1111yescharacteristic
745C2×D4C23×D1112yes—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—82no—
758C22×C4—84no—
759C22×C4—224no—
760C22×C4—224no—
761C22×C4C2×C22⋊D1112yes—
762C22×C4C2×C22⋊D1111yescharacteristic
763C22×C4C2×C22⋊D1112yes—
764C22×C4C2×C22⋊D1111yescharacteristic
765C22×C4C23×D1112yes—
766C22×C4C23×D1111yescharacteristic
767SD16—228no—
768D8—228no—
769D8—228no—
770D8—228no—
771M16—224no—
772C2×C8—112no—
773C2×C8—114no—
774C2×C8—112no—
775C2×C8—224no—
776C4⋊C4—22no—
777C4⋊C4—21no—
778C4⋊C4—22no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—112no—
782C4⋊C4—112no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4—222no—
786C4⋊C4—222no—
787C4⋊C4C2×C22⋊D1111yescharacteristic
788C4⋊C4C2×C22⋊D1112yes—
789C4⋊C4C2×C22⋊D1111yescharacteristic
790C4⋊C4C2×C22⋊D1112yes—
791C4⋊C4C23×D1112yes—
792C4⋊C4C23×D1111yescharacteristic
793C4⋊C4C23×D1111yescharacteristic
794C22⋊C4—22no—
795C22⋊C4—21no—
796C22⋊C4—22no—
797C22⋊C4—21no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—21no—
803C22⋊C4—222no—
804C22⋊C4—224no—
805C22⋊C4—224no—
806C22⋊C4—224no—
807C22⋊C4—224no—
808C22⋊C4C2×C22⋊D1112yes—
809C22⋊C4C2×C22⋊D1112yes—
810C22⋊C4C2×C22⋊D1112yes—
811C42—21no—
812C42—22no—
813C42—21no—
814C42—22no—
815C42—21no—
816C42—222no—
817C42C2×C22⋊D1112yes—
818C42C2×C22⋊D1111yescharacteristic
819C42C2×C22⋊D1112yes—
820C42C2×C22⋊D1111yescharacteristic
821C42C23×D1112yes—
822C42C23×D1111yescharacteristic
823C42C23×D1111yescharacteristic
824C11#6059011yescharacteristic, complemented, Sylow
825C23—28no—
826C23—22no—
827C23—21no—
828C23—24no—
829C23—81no—
830C23—82no—
831C23—81no—
832C23—82no—
833C23—224no—
834C23—444no—
835C23—882no—
836C23—882no—
837C23C22×C22⋊D1112yes—
838C23C22×C22⋊D1111yescharacteristic
839Q8—22no—
840Q8—21no—
841Q8—442no—
842Q8—442no—
843Q8C2×#433912yes—
844D4—28no—
845D4—28no—
846D4—24no—
847D4—24no—
848D4—24no—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—224no—
853D4—224no—
854D4—444no—
855D4—444no—
856D4—444no—
857D4—882no—
858D4—882no—
859D4—884no—
860D4—884no—
861D4C2×#433912yes—
862D4C2×#433914yes—
863C2×C4—28no—
864C2×C4—21no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—44no—
877C2×C4—82no—
878C2×C4—81no—
879C2×C4—82no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—82no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—884no—
887C2×C4—884no—
888C2×C4C2×#433912yes—
889C2×C4C2×#433912yes—
890C2×C4C22×C22⋊D1112yes—
891C2×C4C22×C22⋊D1112yes—
892C2×C4C22×C22⋊D1111yescharacteristic
893C2×C4C22×C22⋊D1111yescharacteristic
894C2×C4C22×C22⋊D1112yes—
895C2×C4C22×C22⋊D1111yescharacteristic
896C2×C4C22×C22⋊D1111yescharacteristic
897C2×C4C22×C22⋊D1111yescharacteristic
898C2×C4C24×D1111yescharacteristic
899C8—222no—
900C8—222no—
901C8—224no—
902C22—21no—
903C22—21no—
904C22—22no—
905C22—24no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—84no—
914C22—88no—
915C22—444no—
916C22—444no—
917C22—444no—
918C22—1764no—
919C22#1062332212yes—
920C22C23×C22⋊D1111yescharacteristic
921C4—22no—
922C4—22no—
923C4—21no—
924C4—22no—
925C4—21no—
926C4—22no—
927C4—21no—
928C4—41no—
929C4—41no—
930C4—42no—
931C4—442no—
932C4—442no—
933C4#1062332212yes—
934C4#1062336612yes—
935C4C22×#433911yescharacteristic
936C4C22×#433911yescharacteristic
937C2—22no—
938C2—42no—
939C2—44no—
940C2—42no—
941C2—884no—
942C2C2×#1062332211yescharacteristic
943C2C2×#1062336611yescharacteristic
944C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×H(5,𝔽2)C2
socleC22×C11C23×D4
hypercenterC4×H(5,𝔽2)D11
hypocenterC11#60590
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13078859C2semidirect
3. #13078815C2semidirect
4. #13078767C2semidirect
5. #13078707C2semidirect
6. #13078676C2semidirect
7. #13078616C2semidirect
8. #13078574C2semidirect
9. #13078413C2semidirect
10. #13078404C2semidirect
11. #13078096C2semidirect
12. C2×#10622628C2semidirect
13. #13077884C2semidirect
14. #13077466C2semidirect
15. #13077444C2semidirect
16. #13077282C2semidirect
17. C4×C11×H(5,𝔽2)C2semidirect
22. C11×#520C22semidirect
26. C11×#518C22semidirect
30. C4×C11×#41C22semidirect
34. C2×C4×D4×C11C22semidirect
44. #10623066C22semidirect
45. #10623052C22semidirect
46. #10623008C22semidirect
47. #10623008C22semidirect
48. C2×#66927C22semidirect
49. #10623001C22semidirect
50. #10622851C22semidirect
51. #10622851C22semidirect
54. #10622830C22semidirect
55. #10622830C22semidirect
57. #10622640C22semidirect
58. #10622640C22semidirect
59. #10622639C22semidirect
60. C4×#4325C22semidirect
61. #10622635C22semidirect
62. #10622634C22semidirect
63. #10622633C22semidirect
64. #10622628C22semidirect
65. #10622628C22semidirect
66. #10622628C22semidirect
67. #10622628C22semidirect
68. #10622628C22semidirect
69. #10622627C22semidirect
70. #10622627C22semidirect
71. #10622627C22semidirect
72. C4×#4323C22semidirect
73. C4×#4323C22semidirect
74. C4×#4323C22semidirect
75. #10622622C22semidirect
76. #10622622C22semidirect
77. #10622621C22semidirect
78. #10622621C22semidirect
79. #10622620C22semidirect
80. #10622620C22semidirect
81. #10622616C22semidirect
82. #10622616C22semidirect
83. #10622614C22semidirect
84. #10622613C22semidirect
85. #10622611C22semidirect
86. #10622610C22semidirect
87. #10622581C22semidirect
88. #10622580C22semidirect
89. C2×#66873C22semidirect
90. #10622577C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
93. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
242. C11×#41#41semidirect
256. C2×D4×C11#41semidirect
354. C4×H(5,𝔽2)D11semidirect
465. #520C2×D11semidirect
470. #518C2×D11semidirect
474. C4×#41C2×D11semidirect
478. C2×C4×D4C2×D11semidirect
715. #41#4339semidirect
741. C2×D4#4339semidirect
824. C11#60590semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130788592
#130788152
#130787672
#130787072
#130786762
#130786162
#130785742
#130784132
#130784042
#130780962
C2×#106226282
#130778842
#130774662
#130774442
#130772822
C4×C11×H(5,𝔽2)2
#6059011