Finite Group Databasebeta

← #15622797

Subgroups — #15622797

Order 2816.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13078907C214yesmaximal, complemented
3#13078815C214yesmaximal, complemented
4#13078767C212yesmaximal, complemented
5#13078738C212yesmaximal, complemented
6#13078676C212yesmaximal, complemented
7#13078647C212yesmaximal, complemented
8#13078574C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078404C211yesmaximal, characteristic, complemented
11#13078096C211yesmaximal, characteristic, complemented
12C2×#10622640C211yesmaximal, characteristic, complemented
13#13077902C212yesmaximal, complemented
14#13077475C212yesmaximal, complemented
15#13077444C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C4×C11×2−1+4C211yesmaximal, characteristic, complemented
18C2×C11×2−1+4C2211yescharacteristic
19C11×#520—22no—
20C11×#520—21no—
21C11×#520C2211yescharacteristic
22C11×#520C2211yescharacteristic
23C11×#520C2212yescomplemented
24C11×#519—21no—
25C11×#519C2211yescharacteristic
26C11×#519C2212yescomplemented
27C4×C11×#41—22no—
28C4×C11×#41—21no—
29C4×C11×#41C2211yescharacteristic
30C4×C11×#41C2211yescharacteristic
31C4×C11×#41C2212yescomplemented
32C2×C4×Q8×C11—21no—
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2212yescomplemented
35#10623361C2212yes—
36C2×#67002C2212yes—
37C22×#4325C2212yes—
38#10623116—21no—
39#10623116—21no—
40#10623084—21no—
41#10623084—21no—
42#10623081—22no—
43#10623081—22no—
44#10623066C2214yes—
45#10623052C2212yes—
46#10623008C2212yes—
47#10623008C2212yes—
48C2×#66927C2211yescharacteristic
49#10623001C2211yescharacteristic
50#10622851C2214yescomplemented
51#10622851C2214yescomplemented
52#10622847C2212yes—
53#10622846C2212yes—
54#10622840C2214yescomplemented
55#10622840C2214yescomplemented
56#10622838C2212yes—
57#10622640C2214yes—
58#10622640C2212yes—
59#10622640C2212yes—
60#10622640C2212yes—
61#10622640C2212yes—
62#10622639C2214yescomplemented
63#10622639C2214yescomplemented
64#10622639C2214yescomplemented
65C4×#4325C2214yescomplemented
66C4×#4325C2214yescomplemented
67C4×#4325C2214yescomplemented
68#10622635C2214yescomplemented
69#10622635C2212yescomplemented
70#10622634C2211yescharacteristic, complemented
71#10622634C2212yescomplemented
72#10622633C2211yescharacteristic, complemented
73#10622633C2212yescomplemented
74#10622628C2212yes—
75#10622628C2212yes—
76#10622627C2214yescomplemented
77C4×#4323C2214yescomplemented
78#10622622C2212yescomplemented
79#10622621C2211yescharacteristic, complemented
80#10622620C2211yescharacteristic, complemented
81#10622616C2214yescomplemented
82#10622616C2214yescomplemented
83#10622614C2212yes—
84#10622613C2214yescomplemented
85#10622611C2212yes—
86#10622610C2212yes—
87#10622581C2214yescomplemented
88#10622580C2214yescomplemented
89C2×#66873C2212yes—
90#10622577C2212yes—
91#10622539C2212yescomplemented
92#10622538C2212yescomplemented
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C11×2−1+4—24no—
96C11×2−1+4—24no—
97C2×C11×#41—22no—
98C2×C11×#41—21no—
99C2×C11×#41C2312yes—
100C2×C11×#41C2311yescharacteristic
101C2×C11×#41C2311yescharacteristic
102C22×Q8×C11—21no—
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2311yescharacteristic
105C2×#4339—22no—
106C2×#4339—22no—
107C22×D44—21no—
108C22×D44—21no—
109C22×D44C2312yes—
110C4×Q8×C11—21no—
111C4×Q8×C11—21no—
112C4×Q8×C11—22no—
113C4×Q8×C11—21no—
114C4×Q8×C11—22no—
115C4×Q8×C11—21no—
116C4×Q8×C11—22no—
117C4×Q8×C11—21no—
118C4×Q8×C11—22no—
119C4×Q8×C11D411yescharacteristic
120C4×Q8×C11D411yescharacteristic
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2311yescharacteristic
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2312yes—
126C4×Q8×C11C2311yescharacteristic
127C4×Q8×C11C2312yes—
128C4×D4×C11—22no—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11—22no—
132C4×D4×C11—21no—
133C4×D4×C11—22no—
134C4×D4×C11—22no—
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11D412yes—
138C4×D4×C11D412yes—
139C4×D4×C11D411yescharacteristic
140C4×D4×C11D411yescharacteristic
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2311yescharacteristic
143C4×D4×C11C2312yes—
144C11×#117—21no—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117—22no—
148C11×#117—22no—
149C11×#117—21no—
150C11×#117—22no—
151C11×#117C2311yescharacteristic
152C11×#117C2312yes—
153C11×#117C2311yescharacteristic
154C11×#117C2312yes—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4—22no—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4—22no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C42×C11—21no—
162C2×C42×C11—22no—
163C2×C42×C11—21no—
164C2×C42×C11—22no—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2312yes—
167#67002—28no—
168#67000—22no—
169C2×#4325—28no—
170C2×#4325C2314yes—
171C2×#4325C2314yes—
172C2×#4325C2314yes—
173#66993—22no—
174#66990—24no—
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#66899C2314yes—
208#66899C2314yes—
209#66899C2312yes—
210#66899C2312yes—
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#60593—111nomaximal, Sylow
233C23×D11—22no—
234C11×#41—216no—
235C11×#41—28no—
236C11×#41—24no—
237C11×#41—24no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41—22no—
241C11×#41#4114yescomplemented
242C2×Q8×C11—28no—
243C2×Q8×C11—24no—
244C2×Q8×C11—24no—
245C2×Q8×C11—22no—
246C2×Q8×C11—21no—
247C2×Q8×C11—22no—
248C2×Q8×C11C2×D411yescharacteristic
249C2×Q8×C11#4114yescomplemented
250C2×Q8×C11C2411yescharacteristic
251C2×Q8×C11C2412yes—
252C2×D4×C11—22no—
253C2×D4×C11—21no—
254C2×D4×C11C2×D412yes—
255C2×D4×C11C2×D411yescharacteristic
256C2×D4×C11C2411yescharacteristic
257C22×C4×C11—22no—
258C22×C4×C11—21no—
259C22×C4×C11—22no—
260C22×C4×C11—21no—
261C22×C4×C11—22no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—22no—
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2411yescharacteristic
272C2×C22⋊D11—24no—
273C2×C22⋊D11—24no—
274#4339—84no—
275#4339—84no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—24no—
282C2×D44—24no—
283C2×D44—82no—
284C2×D44—82no—
285C2×D44C2414yes—
286C2×C4×D11—24no—
287C2×C4×D11—24no—
288C2×Dic22—21no—
289C2×Dic22—21no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4C2×D411yescharacteristic
300C11×C4⋊C4C2×D411yescharacteristic
301C11×C4⋊C4C2×D412yes—
302C11×C4⋊C4C2×D412yes—
303C11×C4⋊C4C2412yes—
304C11×C4⋊C4C2411yescharacteristic
305C11×C4⋊C4C2411yescharacteristic
306C11×C22⋊C4—22no—
307C11×C22⋊C4—21no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C42×C11—22no—
315C42×C11—21no—
316C42×C11—21no—
317C42×C11—22no—
318C42×C11—22no—
319C42×C11—22no—
320C42×C11—22no—
321C42×C11—22no—
322C42×C11—21no—
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D412yes—
326C42×C11C2×D412yes—
327C42×C11C2412yes—
328C42×C11C2411yescharacteristic
329C42×C11C2411yescharacteristic
330C22⋊Dic11—22no—
331#4325—28no—
332#4325—28no—
333#4325—28no—
334#4323—28no—
335(C2×D11)⋊C4—24no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—24no—
339C4⋊Dic11—21no—
340C4⋊Dic11—21no—
341C4⋊Dic11C2412yes—
342C4⋊Dic11C2412yes—
343Dic11⋊C4—22no—
344Dic11⋊C4—22no—
345C4×Dic11—22no—
346#4318—24no—
347C2×C11⋊C8—24no—
348C2×C11⋊C8C2412yes—
349C2×C11⋊C8C2414yes—
350C2×C11⋊C8C2412yes—
351#3508—111no—
352C4×2−1+4D1111yescharacteristic, complemented
353#3126—114no—
354#3119—114no—
355#3115—112no—
356#3112—112no—
357#3106—112no—
358#3103—112no—
359#3096—112no—
360#3078—111no—
361#3076—111no—
362#3038—111no—
363C2×#460—111no—
364#3010—112no—
365#2949—112no—
366#2946—112no—
367#2925—111no—
368C23×C11—21no—
369C23×C11C22×D412yes—
370C23×C11C22×D411yescharacteristic
371C22×D11—24no—
372C22×D11—44no—
373C22×D11—82no—
374C22×D11—82no—
375Q8×C11—28no—
376Q8×C11—22no—
377Q8×C11—24no—
378Q8×C11—21no—
379Q8×C11—22no—
380Q8×C11C2×#4112yes—
381Q8×C11C2×#4114yes—
382D4×C11—28no—
383D4×C11—24no—
384D4×C11—24no—
385D4×C11—22no—
386D4×C11—21no—
387D4×C11C2×#4112yes—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
390C2×C4×C11—24no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—24no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—41no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—82no—
405C2×C4×C11—81no—
406C2×C4×C11—81no—
407C2×C4×C11—82no—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D412yes—
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C2×#4112yes—
417C2×C4×C11C2×#4112yes—
418C2×C4×C11C2511yescharacteristic
419C22⋊D11—84no—
420C22⋊D11—84no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423D44—24no—
424D44—24no—
425D44—44no—
426D44—44no—
427D44—44no—
428D44—82no—
429D44—82no—
430C4×D11—84no—
431C4×D11—84no—
432Dic22—42no—
433Dic22—42no—
434C11⋊C8—22no—
435C11⋊C8—22no—
436C11⋊C8—24no—
437C2×2−1+4C2×D1111yescharacteristic
438C2×AGL(1,ℤ/8)—112no—
439C22×SD16—112no—
440#559—221no—
441#559—221no—
442#550—221no—
443#550—221no—
444#546—222no—
445#546—222no—
446#540—114no—
447#535—112no—
448#533—111no—
449#532—112no—
450#532—112no—
451C2×#127—111no—
452#520—22no—
453#520—21no—
454#520C2×D1111yescharacteristic
455#520C2×D1111yescharacteristic
456#520C2×D1112yescomplemented
457#519—21no—
458#519C2×D1111yescharacteristic
459#519C2×D1112yescomplemented
460#518—112no—
461C4×#41—22no—
462C4×#41—21no—
463C4×#41C2×D1111yescharacteristic
464C4×#41C2×D1111yescharacteristic
465C4×#41C2×D1112yescomplemented
466C2×C4×Q8—21no—
467C2×C4×Q8C2×D1111yescharacteristic
468C2×C4×Q8C2×D1112yescomplemented
469#482—114no—
470#482—114no—
471#481—114no—
472#480—114no—
473#479—112no—
474#479—114no—
475#478—112no—
476#477—111no—
477#477—112no—
478#476—111no—
479#475—111no—
480#475—112no—
481#474—111no—
482#460—112no—
483#460—112no—
484#460—112no—
485#460—114no—
486#460—112no—
487#459—112no—
488#459—112no—
489#449—114no—
490#449—114no—
491#448—114no—
492#448—114no—
493#442—114no—
494#440—114no—
495#440—114no—
496#440—114no—
497C4×SD16—114no—
498C4×SD16—114no—
499C4×SD16—114no—
500C4×D8—114no—
501#433—114no—
502#432—112no—
503#431—112no—
504#428—112no—
505#427—112no—
506#423—111no—
507C2×C4⋊C8—111no—
508#419—112no—
509#418—112no—
510#416—112no—
511C2×#102—112no—
512#408—112no—
513#405—112no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—22no—
519C22×C11—22no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11#52512yes—
523C22×C11C23×D411yescharacteristic
524C2×D11—44no—
525C2×D11—44no—
526C2×D11—44no—
527C2×D11—164no—
528C4×C11—21no—
529C4×C11—22no—
530C4×C11—21no—
531C4×C11—24no—
532C4×C11—22no—
533C4×C11—22no—
534C4×C11—22no—
535C4×C11—21no—
536C4×C11—42no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11#52512yes—
540C4×C11#57712yes—
541C4×C11C22×#4111yescharacteristic
542C4×C11C22×#4111yescharacteristic
543Dic11—42no—
544Dic11—42no—
5452−1+4—24no—
5462−1+4—24no—
547C2×#41—22no—
548C2×#41—21no—
549C2×#41—222no—
550C2×#41—222no—
551C2×#41C22×D1112yes—
552C2×#41C22×D1111yescharacteristic
553C2×#41C22×D1111yescharacteristic
554C22×Q8—21no—
555C22×Q8C22×D1112yes—
556C22×Q8C22×D1111yescharacteristic
557C22×D4—112no—
558C22×D4—221no—
559C22×D4—221no—
560AGL(1,ℤ/8)—228no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—114no—
564C2×SD16—228no—
565C2×D8—114no—
566C2×M16—112no—
567C22×C8—112no—
568C4⋊Q8—111no—
569C4⋊Q8—111no—
570#127—112no—
571#127—112no—
572#127—222no—
573#127—221no—
574#127—221no—
575#125—112no—
576#124—222no—
577#124—222no—
578#124—222no—
579#123—224no—
580#123—224no—
581C22⋊Q8—221no—
582C22⋊Q8—221no—
583#121—114no—
584#121—114no—
585#121—222no—
586#121—222no—
587#121—224no—
588#121—224no—
589#120—224no—
590C4×Q8—21no—
591C4×Q8—21no—
592C4×Q8—22no—
593C4×Q8—21no—
594C4×Q8—22no—
595C4×Q8—21no—
596C4×Q8—22no—
597C4×Q8—21no—
598C4×Q8—22no—
599C4×Q8—221no—
600C4×Q8—221no—
601C4×Q8C22⋊D1111yescharacteristic
602C4×Q8C22⋊D1111yescharacteristic
603C4×Q8C22×D1112yes—
604C4×Q8C22×D1112yes—
605C4×Q8C22×D1111yescharacteristic
606C4×Q8C22×D1112yes—
607C4×Q8C22×D1112yes—
608C4×Q8C22×D1111yescharacteristic
609C4×Q8C22×D1112yes—
610C4×D4—22no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—114no—
620C4×D4—114no—
621C4×D4—222no—
622C4×D4—222no—
623C4×D4—222no—
624C4×D4—222no—
625C4×D4C22⋊D1112yes—
626C4×D4C22⋊D1111yescharacteristic
627C4×D4C22⋊D1112yes—
628C4×D4C22⋊D1111yescharacteristic
629C4×D4C22×D1111yescharacteristic
630C4×D4C22×D1111yescharacteristic
631C4×D4C22×D1112yes—
632#117—21no—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—21no—
638#117—22no—
639#117—112no—
640#117C22×D1111yescharacteristic
641#117C22×D1112yes—
642#117C22×D1111yescharacteristic
643#117C22×D1112yes—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1112yes—
650C2×C22⋊C4—224no—
651C2×C42—21no—
652C2×C42—22no—
653C2×C42—21no—
654C2×C42—22no—
655C2×C42C22×D1111yescharacteristic
656C2×C42C22×D1112yes—
657#107—112no—
658#107—112no—
659#107—114no—
660#106—112no—
661#106—112no—
662#106—114no—
663C4⋊C8—111no—
664C4⋊C8—111no—
665C4⋊C8—112no—
666C4⋊C8—112no—
667C4⋊C8—112no—
668#103—112no—
669#103—112no—
670#103—114no—
671#103—114no—
672#102—112no—
673#102—112no—
674#102—114no—
675#102—114no—
676#102—114no—
677#102—114no—
678C22⋊C8—114no—
679C22⋊C8—114no—
680#97—114no—
681C4×C8—114no—
682C2×C11—22no—
683C2×C11—42no—
684C2×C11—42no—
685C2×C11C2×#52511yescharacteristic
686C2×C11C2×#57711yescharacteristic
687C2×C11#358511yescharacteristic
688D11—84no—
689C24—222no—
690#41—216no—
691#41—28no—
692#41—24no—
693#41—24no—
694#41—22no—
695#41—22no—
696#41—22no—
697#41—884no—
698#41—884no—
699#41#433914yescomplemented
700C2×Q8—28no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—221no—
707C2×Q8—221no—
708C2×Q8#433914yescomplemented
709C2×Q8C2×C22⋊D1111yescharacteristic
710C2×Q8C23×D1111yescharacteristic
711C2×Q8C23×D1112yes—
712C2×D4—22no—
713C2×D4—21no—
714C2×D4—114no—
715C2×D4—224no—
716C2×D4—224no—
717C2×D4—224no—
718C2×D4—224no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—882no—
725C2×D4—882no—
726C2×D4C2×C22⋊D1112yes—
727C2×D4C2×C22⋊D1111yescharacteristic
728C2×D4C23×D1111yescharacteristic
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—224no—
739C22×C4—224no—
740C22×C4C2×C22⋊D1112yes—
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1112yes—
743C22×C4C2×C22⋊D1111yescharacteristic
744C22×C4C23×D1112yes—
745C22×C4C23×D1111yescharacteristic
746SD16—228no—
747SD16—228no—
748SD16—228no—
749D8—228no—
750M16—224no—
751C2×C8—112no—
752C2×C8—114no—
753C2×C8—112no—
754C2×C8—224no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—22no—
761C4⋊C4—21no—
762C4⋊C4—22no—
763C4⋊C4—21no—
764C4⋊C4—112no—
765C4⋊C4—112no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4C2×C22⋊D1111yescharacteristic
771C4⋊C4C2×C22⋊D1112yes—
772C4⋊C4C2×C22⋊D1111yescharacteristic
773C4⋊C4C2×C22⋊D1112yes—
774C4⋊C4C23×D1112yes—
775C4⋊C4C23×D1111yescharacteristic
776C4⋊C4C23×D1111yescharacteristic
777C22⋊C4—22no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—22no—
781C22⋊C4—21no—
782C22⋊C4—222no—
783C22⋊C4—224no—
784C22⋊C4—224no—
785C22⋊C4—224no—
786C22⋊C4—224no—
787C22⋊C4C2×C22⋊D1112yes—
788C22⋊C4C2×C22⋊D1112yes—
789C22⋊C4C2×C22⋊D1112yes—
790C42—22no—
791C42—21no—
792C42—22no—
793C42—21no—
794C42—22no—
795C42—22no—
796C42—22no—
797C42—22no—
798C42—21no—
799C42—222no—
800C42C2×C22⋊D1112yes—
801C42C2×C22⋊D1111yescharacteristic
802C42C2×C22⋊D1112yes—
803C42C2×C22⋊D1111yescharacteristic
804C42C23×D1112yes—
805C42C23×D1111yescharacteristic
806C42C23×D1111yescharacteristic
807C11#6059311yescharacteristic, complemented, Sylow
808C23—21no—
809C23—224no—
810C23—444no—
811C23—882no—
812C23—882no—
813C23C22×C22⋊D1112yes—
814C23C22×C22⋊D1111yescharacteristic
815Q8—28no—
816Q8—24no—
817Q8—22no—
818Q8—21no—
819Q8—22no—
820Q8—442no—
821Q8—442no—
822Q8C2×#433912yes—
823Q8C2×#433914yes—
824D4—28no—
825D4—24no—
826D4—24no—
827D4—22no—
828D4—21no—
829D4—224no—
830D4—224no—
831D4—444no—
832D4—444no—
833D4—444no—
834D4—882no—
835D4—882no—
836D4—884no—
837D4—884no—
838D4C2×#433912yes—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—82no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—82no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—884no—
862C2×C4—884no—
863C2×C4C2×#433912yes—
864C2×C4C2×#433912yes—
865C2×C4C22×C22⋊D1112yes—
866C2×C4C22×C22⋊D1111yescharacteristic
867C2×C4C22×C22⋊D1112yes—
868C2×C4C22×C22⋊D1112yes—
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C22×C22⋊D1111yescharacteristic
872C2×C4C22×C22⋊D1111yescharacteristic
873C2×C4C24×D1111yescharacteristic
874C8—222no—
875C8—222no—
876C8—224no—
877C22—21no—
878C22—21no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—444no—
886C22—444no—
887C22—444no—
888C22—1764no—
889C22#1062332212yes—
890C22C23×C22⋊D1111yescharacteristic
891C4—24no—
892C4—22no—
893C4—22no—
894C4—21no—
895C4—22no—
896C4—21no—
897C4—22no—
898C4—21no—
899C4—42no—
900C4—41no—
901C4—41no—
902C4—442no—
903C4—442no—
904C4#1062332212yes—
905C4#1062336812yes—
906C4C22×#433911yescharacteristic
907C4C22×#433911yescharacteristic
908C2—22no—
909C2—42no—
910C2—42no—
911C2—884no—
912C2C2×#1062332211yescharacteristic
913C2C2×#1062336811yescharacteristic
914C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×2−1+4C2
socleC22×C11C23×D4
hypercenterC4×2−1+4D11
hypocenterC11#60593
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13078907C2semidirect
3. #13078815C2semidirect
4. #13078767C2semidirect
5. #13078738C2semidirect
6. #13078676C2semidirect
7. #13078647C2semidirect
8. #13078574C2semidirect
9. #13078421C2semidirect
10. #13078404C2semidirect
11. #13078096C2semidirect
12. C2×#10622640C2semidirect
13. #13077902C2semidirect
14. #13077475C2semidirect
15. #13077444C2semidirect
16. #13077282C2semidirect
17. C4×C11×2−1+4C2semidirect
23. C11×#520C22semidirect
26. C11×#519C22semidirect
31. C4×C11×#41C22semidirect
34. C2×C4×Q8×C11C22semidirect
50. #10622851C22semidirect
51. #10622851C22semidirect
54. #10622840C22semidirect
55. #10622840C22semidirect
62. #10622639C22semidirect
63. #10622639C22semidirect
64. #10622639C22semidirect
65. C4×#4325C22semidirect
66. C4×#4325C22semidirect
67. C4×#4325C22semidirect
68. #10622635C22semidirect
69. #10622635C22semidirect
70. #10622634C22semidirect
71. #10622634C22semidirect
72. #10622633C22semidirect
73. #10622633C22semidirect
76. #10622627C22semidirect
77. C4×#4323C22semidirect
78. #10622622C22semidirect
79. #10622621C22semidirect
80. #10622620C22semidirect
81. #10622616C22semidirect
82. #10622616C22semidirect
84. #10622613C22semidirect
87. #10622581C22semidirect
88. #10622580C22semidirect
91. #10622539C22semidirect
92. #10622538C22semidirect
241. C11×#41#41semidirect
249. C2×Q8×C11#41semidirect
352. C4×2−1+4D11semidirect
456. #520C2×D11semidirect
459. #519C2×D11semidirect
465. C4×#41C2×D11semidirect
468. C2×C4×Q8C2×D11semidirect
699. #41#4339semidirect
708. C2×Q8#4339semidirect
807. C11#60593semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130789072
#130788152
#130787672
#130787382
#130786762
#130786472
#130785742
#130784212
#130784042
#130780962
C2×#106226402
#130779022
#130774752
#130774442
#130772822
C4×C11×2−1+42
#6059311