Finite Group Databasebeta

← #15622926

Subgroups — #15622926

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic, complemented
2#13078878C214yesmaximal, complemented
3#13078845C214yesmaximal, complemented
4#13078778C212yesmaximal, complemented
5#13078738C212yesmaximal, complemented
6#13078676C212yesmaximal, complemented
7#13078655C212yesmaximal, complemented
8#13078594C212yesmaximal, complemented
9#13078431C211yesmaximal, characteristic, complemented
10C2×#10622634C211yesmaximal, characteristic, complemented
11#13078088C211yesmaximal, characteristic, complemented
12#13078071C211yesmaximal, characteristic, complemented
13#13077931C212yesmaximal, complemented
14#13077489C212yesmaximal, complemented
15#13077459C212yesmaximal, complemented
16#13077282C211yesmaximal, characteristic, complemented
17C4×C11×2−1+4C211yesmaximal, characteristic, complemented
18C2×C11×2−1+4C2211yescharacteristic
19C11×#520—21no—
20C11×#520—22no—
21C11×#520C2212yes—
22C11×#520C2211yescharacteristic
23C11×#520C2211yescharacteristic
24C11×#519—21no—
25C11×#519C2212yes—
26C11×#519C2211yescharacteristic
27C4×C11×#41—21no—
28C4×C11×#41—22no—
29C4×C11×#41C2211yescharacteristic
30C4×C11×#41C2212yes—
31C4×C11×#41C2211yescharacteristic
32C2×C4×Q8×C11—21no—
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2212yes—
35#10623364C2212yes—
36C2×#67003C2212yes—
37C2×#66995C2212yes—
38#10623115—21no—
39#10623110—21no—
40#10623096—22no—
41#10623094—21no—
42#10623083—22no—
43#10623082—21no—
44#10623065C2214yes—
45#10623054C2212yes—
46#10623008C2211yescharacteristic
47#10623008C2212yes—
48#10623001C2212yes—
49C2×#66922C2211yescharacteristic
50#10622852C2214yes—
51#10622851C2214yes—
52#10622847C2212yes—
53#10622845C2212yes—
54#10622841C2214yes—
55#10622840C2214yes—
56C2×#66899C2212yes—
57#10622644C2211yescharacteristic
58#10622644C2212yes—
59#10622643C2214yes—
60C4×#4326C2214yes—
61C4×#4326C2214yes—
62#10622641C2212yes—
63#10622641C2214yes—
64#10622640C2211yescharacteristic
65#10622640C2212yes—
66#10622639C2214yes—
67#10622639C2214yes—
68C4×#4325C2214yes—
69#10622634C2214yes—
70#10622634C2212yes—
71#10622634C2212yes—
72#10622634C2212yes—
73#10622633C2212yes—
74#10622632C2211yescharacteristic
75#10622631C2214yes—
76#10622629C2212yes—
77#10622628C2211yescharacteristic
78C4×#4323C2214yes—
79#10622621C2212yes—
80#10622620C2212yes—
81#10622616C2214yes—
82#10622615C2212yes—
83#10622613C2214yes—
84#10622610C2212yes—
85#10622609C2214yes—
86#10622608C2212yes—
87#10622583C2214yes—
88#10622580C2214yes—
89#10622579C2212yes—
90C2×#66871C2212yes—
91#10622539C2212yes—
92#10622538C2212yes—
93#10622537C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C11×2−1+4—24no—
96C11×2−1+4—24no—
97C2×C11×#41—21no—
98C2×C11×#41—22no—
99C2×C11×#41C2312yes—
100C2×C11×#41C2311yescharacteristic
101C2×C11×#41C2311yescharacteristic
102C22×Q8×C11—21no—
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2311yescharacteristic
105C2×#4339—22no—
106C2×#4339C2312yes—
107C22×Dic22—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11—22no—
113C4×Q8×C11—21no—
114C4×Q8×C11—22no—
115C4×Q8×C11—22no—
116C4×Q8×C11—21no—
117C4×Q8×C11D411yescharacteristic
118C4×Q8×C11D411yescharacteristic
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2311yescharacteristic
125C4×Q8×C11C2312yes—
126C4×D4×C11—21no—
127C4×D4×C11—22no—
128C4×D4×C11—21no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—21no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—22no—
135C4×D4×C11D411yescharacteristic
136C4×D4×C11D412yes—
137C4×D4×C11D411yescharacteristic
138C4×D4×C11D412yes—
139C4×D4×C11C2311yescharacteristic
140C4×D4×C11C2311yescharacteristic
141C4×D4×C11C2312yes—
142C11×#117—21no—
143C11×#117—22no—
144C11×#117—22no—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117—22no—
148C11×#117—21no—
149C11×#117C2311yescharacteristic
150C11×#117C2312yes—
151C11×#117C2311yescharacteristic
152C11×#117C2312yes—
153C2×C11×C4⋊C4—22no—
154C2×C11×C4⋊C4—21no—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4—22no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C42×C11—21no—
160C2×C42×C11—22no—
161C2×C42×C11—21no—
162C2×C42×C11—22no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165#67003—28no—
166#66999—22no—
167C2×#4326C2314yes—
168C2×#4326C2312yes—
169#66995—28no—
170C2×#4325C2314yes—
171C2×#4325C2312yes—
172#66992—24no—
173#66991—22no—
174C2×#4324C2312yes—
175C2×#4323C2312yes—
176#66983—21no—
177#66983—22no—
178#66983—21no—
179#66983C2314yes—
180#66979—22no—
181C2×C4⋊Dic11—21no—
182C2×C4⋊Dic11C2312yes—
183#66977—22no—
184#66977C2314yes—
185C2×#4318C2312yes—
186C22×C11⋊C8C2312yes—
187#66951—24no—
188#66949—24no—
189#66945—22no—
190C4⋊C4×D11—22no—
191#66938—24no—
192#66936—24no—
193(C22⋊D11)⋊C4—24no—
194#66928—22no—
195#66928C2312yes—
196#66927C2311yescharacteristic
197C4×D44—21no—
198C4×D44—21no—
199C4×D44—22no—
200C4×D44C2314yes—
201#66923—22no—
202#66922—21no—
203#66922—21no—
204#66922C2311yescharacteristic
205#66922C2312yes—
206#66922C2312yes—
207C4×Dic22—22no—
208C4×Dic22C2314yes—
209#66899C2314yes—
210#66899C2314yes—
211#66899C2314yes—
212#66896C2314yes—
213C22⋊(C11⋊C8)C2314yes—
214C22⋊(C11⋊C8)C2314yes—
215#66874C2314yes—
216#66874C2312yes—
217#66874C2312yes—
218#66873C2314yes—
219#66873C2312yes—
220#66873C2312yes—
221#66872C2314yes—
222#66871C2314yes—
223#66871C2314yes—
224#66871C2314yes—
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#60600—111nomaximal, Sylow
233C11×#41—216no—
234C11×#41—28no—
235C11×#41—24no—
236C11×#41—24no—
237C11×#41—22no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41#4114yescomplemented
241C2×Q8×C11—28no—
242C2×Q8×C11—24no—
243C2×Q8×C11—24no—
244C2×Q8×C11—22no—
245C2×Q8×C11—21no—
246C2×Q8×C11—22no—
247C2×Q8×C11C2×D411yescharacteristic
248C2×Q8×C11#4114yescomplemented
249C2×Q8×C11C2411yescharacteristic
250C2×Q8×C11C2412yes—
251C2×D4×C11—22no—
252C2×D4×C11—21no—
253C2×D4×C11C2×D411yescharacteristic
254C2×D4×C11C2×D412yes—
255C2×D4×C11C2411yescharacteristic
256C22×C4×C11—22no—
257C22×C4×C11—21no—
258C22×C4×C11—22no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—22no—
264C22×C4×C11—21no—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2412yes—
270C22×C4×C11C2411yescharacteristic
271C2×C22⋊D11—22no—
272C2×C22⋊D11—24no—
273C22×Dic11—22no—
274#4339—24no—
275#4339—24no—
276#4339—84no—
277C2×D44—21no—
278C2×D44—21no—
279C2×D44C2412yes—
280C2×C4×D11—22no—
281C2×C4×D11—24no—
282C2×Dic22—22no—
283C2×Dic22—22no—
284C2×Dic22—82no—
285C2×Dic22C2412yes—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4C2×D411yescharacteristic
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2×D412yes—
299C11×C4⋊C4C2412yes—
300C11×C4⋊C4C2411yescharacteristic
301C11×C4⋊C4C2411yescharacteristic
302C11×C22⋊C4—22no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C11×C22⋊C4C2×D412yes—
310C42×C11—22no—
311C42×C11—21no—
312C42×C11—22no—
313C42×C11—21no—
314C42×C11—22no—
315C42×C11—22no—
316C42×C11—22no—
317C42×C11—22no—
318C42×C11—21no—
319C42×C11C2×D412yes—
320C42×C11C2×D411yescharacteristic
321C42×C11C2×D411yescharacteristic
322C42×C11C2×D412yes—
323C42×C11C2412yes—
324C42×C11C2411yescharacteristic
325C42×C11C2411yescharacteristic
326C22⋊Dic11—24no—
327#4326—28no—
328#4326—24no—
329#4325—28no—
330#4325—24no—
331#4324—24no—
332#4323—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—24no—
337C4⋊Dic11—21no—
338C4⋊Dic11—22no—
339C4⋊Dic11—22no—
340C4⋊Dic11—22no—
341C4⋊Dic11—21no—
342C4⋊Dic11C2414yes—
343Dic11⋊C4—24no—
344Dic11⋊C4—24no—
345C4×Dic11—24no—
346#4318—24no—
347C2×C11⋊C8—24no—
348C2×C11⋊C8C2412yes—
349C2×C11⋊C8C2414yes—
350C2×C11⋊C8C2412yes—
351#3511—111no—
352C4×2−1+4D1111yescharacteristic, complemented
353#3124—114no—
354#3121—114no—
355#3116—112no—
356#3112—112no—
357#3106—112no—
358#3104—112no—
359#3098—112no—
360#3079—111no—
361C2×#477—111no—
362#3037—111no—
363#3035—111no—
364#3013—112no—
365#2951—112no—
366#2947—112no—
367#2925—111no—
368C23×C11—21no—
369C23×C11C22×D412yes—
370C23×C11C22×D411yescharacteristic
371C22×D11—22no—
372Q8×C11—28no—
373Q8×C11—22no—
374Q8×C11—24no—
375Q8×C11—21no—
376Q8×C11—22no—
377Q8×C11C2×#4112yes—
378Q8×C11C2×#4114yes—
379D4×C11—28no—
380D4×C11—24no—
381D4×C11—24no—
382D4×C11—22no—
383D4×C11—21no—
384D4×C11C2×#4112yes—
385C2×C4×C11—28no—
386C2×C4×C11—28no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—21no—
390C2×C4×C11—24no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—22no—
398C2×C4×C11—41no—
399C2×C4×C11—42no—
400C2×C4×C11—42no—
401C2×C4×C11—81no—
402C2×C4×C11—82no—
403C2×C4×C11—81no—
404C2×C4×C11—82no—
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D412yes—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C2×#4112yes—
414C2×C4×C11C2×#4112yes—
415C2×C4×C11C2511yescharacteristic
416C22⋊D11—44no—
417C22⋊D11—84no—
418C2×Dic11—22no—
419C2×Dic11—24no—
420C2×Dic11—82no—
421D44—22no—
422D44—22no—
423D44—42no—
424D44—42no—
425C4×D11—44no—
426C4×D11—84no—
427Dic22—22no—
428Dic22—22no—
429Dic22—44no—
430Dic22—82no—
431C11⋊C8—22no—
432C11⋊C8—22no—
433C11⋊C8—24no—
434C2×2−1+4C2×D1111yescharacteristic
435C2×#137—112no—
436C2×#135—112no—
437#556—221no—
438#555—221no—
439#554—221no—
440#553—222no—
441#548—222no—
442#547—221no—
443#542—114no—
444#537—112no—
445#533—112no—
446#532—112no—
447#532—111no—
448C2×C4⋊Q8—111no—
449#520—21no—
450#520—22no—
451#520—112no—
452#520C2×D1112yes—
453#520C2×D1111yescharacteristic
454#520C2×D1111yescharacteristic
455#519—21no—
456#519C2×D1112yes—
457#519C2×D1111yescharacteristic
458C4×#41—22no—
459C4×#41—21no—
460C4×#41C2×D1111yescharacteristic
461C4×#41C2×D1112yes—
462C4×#41C2×D1111yescharacteristic
463C2×C4×Q8—21no—
464C2×C4×Q8C2×D1111yescharacteristic
465C2×C4×Q8C2×D1112yes—
466#485—114no—
467#484—114no—
468#482—114no—
469#480—114no—
470#477—112no—
471#477—112no—
472#477—114no—
473#477—112no—
474#476—112no—
475#475—112no—
476#474—112no—
477#464—112no—
478#464—114no—
479#463—112no—
480#462—111no—
481#462—112no—
482#461—111no—
483#460—112no—
484#460—111no—
485#459—111no—
486#452—114no—
487#451—114no—
488#449—114no—
489#448—114no—
490#441—114no—
491#440—114no—
492#440—114no—
493#440—114no—
494C4×Q16—114no—
495C4×Q16—114no—
496C4×SD16—114no—
497C4×D8—114no—
498#433—114no—
499#432—112no—
500#431—112no—
501#428—112no—
502C2×#107—112no—
503#423—111no—
504C2×C4⋊C8—111no—
505#417—112no—
506#417—112no—
507#416—112no—
508C2×#103—112no—
509#408—112no—
510#405—112no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11#52512yes—
520C22×C11C23×D411yescharacteristic
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—22no—
527C4×C11—24no—
528C4×C11—22no—
529C4×C11—22no—
530C4×C11—22no—
531C4×C11—21no—
532C4×C11—41no—
533C4×C11—42no—
534C4×C11—41no—
535C4×C11#52512yes—
536C4×C11#57812yes—
537C4×C11C22×#4111yescharacteristic
538C4×C11C22×#4111yescharacteristic
539Dic11—44no—
540Dic11—42no—
5412−1+4—24no—
5422−1+4—24no—
543C2×#41—21no—
544C2×#41—22no—
545C2×#41—112no—
546C2×#41—222no—
547C2×#41C22×D1112yes—
548C2×#41C22×D1111yescharacteristic
549C2×#41C22×D1111yescharacteristic
550C22×Q8—21no—
551C22×Q8—221no—
552C22×Q8C22×D1112yes—
553C22×Q8C22×D1111yescharacteristic
554#137—228no—
555#135—228no—
556C2×Q16—112no—
557C2×Q16—114no—
558C2×SD16—112no—
559C2×SD16—114no—
560C2×SD16—112no—
561C2×D8—112no—
562C2×M16—112no—
563C22×C8—112no—
564C4⋊Q8—112no—
565C4⋊Q8—112no—
566C4⋊Q8—111no—
567C4⋊Q8—221no—
568C4⋊Q8—221no—
569#127—111no—
570#126—224no—
571#125—222no—
572#124—112no—
573#124—224no—
574#124—222no—
575#123—224no—
576C22⋊Q8—114no—
577C22⋊Q8—222no—
578C22⋊Q8—222no—
579C22⋊Q8—224no—
580#121—114no—
581#121—222no—
582#121—224no—
583#121—221no—
584#121—221no—
585#121—222no—
586C4×Q8—21no—
587C4×Q8—21no—
588C4×Q8—22no—
589C4×Q8—21no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—21no—
593C4×Q8—21no—
594C4×Q8—22no—
595C4×Q8—114no—
596C4×Q8—222no—
597C4×Q8C22⋊D1111yescharacteristic
598C4×Q8C22⋊D1111yescharacteristic
599C4×Q8C22×D1112yes—
600C4×Q8C22×D1111yescharacteristic
601C4×Q8C22×D1112yes—
602C4×Q8C22×D1112yes—
603C4×Q8C22×D1112yes—
604C4×Q8C22×D1112yes—
605C4×Q8C22×D1111yescharacteristic
606C4×D4—22no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—22no—
610C4×D4—21no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—114no—
616C4×D4—224no—
617C4×D4—221no—
618C4×D4—222no—
619C4×D4—221no—
620C4×D4C22⋊D1112yes—
621C4×D4C22⋊D1111yescharacteristic
622C4×D4C22⋊D1111yescharacteristic
623C4×D4C22⋊D1112yes—
624C4×D4C22×D1111yescharacteristic
625C4×D4C22×D1112yes—
626C4×D4C22×D1111yescharacteristic
627#117—21no—
628#117—22no—
629#117—22no—
630#117—22no—
631#117—22no—
632#117—21no—
633#117—22no—
634#117—222no—
635#117—222no—
636#117C22×D1111yescharacteristic
637#117C22×D1112yes—
638#117C22×D1111yescharacteristic
639#117C22×D1112yes—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—221no—
646C2×C4⋊C4—222no—
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1112yes—
649C2×C42—21no—
650C2×C42—22no—
651C2×C42—22no—
652C2×C42—21no—
653C2×C42C22×D1111yescharacteristic
654C2×C42C22×D1112yes—
655#107—114no—
656#107—114no—
657#107—114no—
658#106—114no—
659C4⋊C8—111no—
660C4⋊C8—111no—
661C4⋊C8—112no—
662C4⋊C8—112no—
663C4⋊C8—112no—
664#103—114no—
665#103—114no—
666#103—114no—
667#103—112no—
668#103—112no—
669#103—114no—
670#102—114no—
671#102—112no—
672#102—112no—
673#102—114no—
674C22⋊C8—114no—
675C22⋊C8—114no—
676#97—114no—
677C4×C8—114no—
678C2×C11—22no—
679C2×C11—42no—
680C2×C11—42no—
681C2×C11C2×#52511yescharacteristic
682C2×C11C2×#57811yescharacteristic
683C2×C11#358511yescharacteristic
684D11—82no—
685#41—216no—
686#41—28no—
687#41—24no—
688#41—24no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—224no—
693#41—224no—
694#41—884no—
695#41#433914yescomplemented
696C2×Q8—28no—
697C2×Q8—24no—
698C2×Q8—24no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—112no—
703C2×Q8—222no—
704C2×Q8—222no—
705C2×Q8—882no—
706C2×Q8#433914yescomplemented
707C2×Q8C2×C22⋊D1111yescharacteristic
708C2×Q8C23×D1111yescharacteristic
709C2×Q8C23×D1112yes—
710C2×D4—22no—
711C2×D4—21no—
712C2×D4—112no—
713C2×D4—222no—
714C2×D4—224no—
715C2×D4—221no—
716C2×D4—221no—
717C2×D4C2×C22⋊D1112yes—
718C2×D4C2×C22⋊D1111yescharacteristic
719C2×D4C23×D1111yescharacteristic
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—224no—
732C22×C4C2×C22⋊D1111yescharacteristic
733C22×C4C2×C22⋊D1112yes—
734C22×C4C2×C22⋊D1111yescharacteristic
735C22×C4C2×C22⋊D1112yes—
736C22×C4C23×D1112yes—
737C22×C4C23×D1111yescharacteristic
738Q16—224no—
739Q16—228no—
740SD16—224no—
741SD16—228no—
742SD16—224no—
743D8—224no—
744M16—224no—
745C2×C8—112no—
746C2×C8—114no—
747C2×C8—112no—
748C2×C8—224no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4—21no—
754C4⋊C4—22no—
755C4⋊C4—21no—
756C4⋊C4—22no—
757C4⋊C4—21no—
758C4⋊C4—114no—
759C4⋊C4—222no—
760C4⋊C4—222no—
761C4⋊C4—224no—
762C4⋊C4—222no—
763C4⋊C4—221no—
764C4⋊C4—221no—
765C4⋊C4—224no—
766C4⋊C4C2×C22⋊D1111yescharacteristic
767C4⋊C4C2×C22⋊D1112yes—
768C4⋊C4C2×C22⋊D1111yescharacteristic
769C4⋊C4C2×C22⋊D1112yes—
770C4⋊C4C23×D1111yescharacteristic
771C4⋊C4C23×D1111yescharacteristic
772C4⋊C4C23×D1112yes—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—22no—
777C22⋊C4—21no—
778C22⋊C4—224no—
779C22⋊C4—224no—
780C22⋊C4—224no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4C2×C22⋊D1112yes—
784C22⋊C4C2×C22⋊D1112yes—
785C22⋊C4C2×C22⋊D1112yes—
786C42—22no—
787C42—21no—
788C42—21no—
789C42—22no—
790C42—22no—
791C42—22no—
792C42—22no—
793C42—22no—
794C42—21no—
795C42—224no—
796C42C2×C22⋊D1112yes—
797C42C2×C22⋊D1111yescharacteristic
798C42C2×C22⋊D1111yescharacteristic
799C42C2×C22⋊D1112yes—
800C42C23×D1112yes—
801C42C23×D1111yescharacteristic
802C42C23×D1111yescharacteristic
803C11#6060011yescharacteristic, complemented, Sylow
804C23—21no—
805C23—222no—
806C23C22×C22⋊D1112yes—
807C23C22×C22⋊D1111yescharacteristic
808Q8—28no—
809Q8—24no—
810Q8—22no—
811Q8—21no—
812Q8—22no—
813Q8—222no—
814Q8—222no—
815Q8—444no—
816Q8—882no—
817Q8C2×#433912yes—
818Q8C2×#433914yes—
819D4—28no—
820D4—24no—
821D4—24no—
822D4—22no—
823D4—21no—
824D4—222no—
825D4—222no—
826D4—442no—
827D4—444no—
828D4—442no—
829D4—884no—
830D4C2×#433912yes—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—82no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—82no—
851C2×C4—222no—
852C2×C4—224no—
853C2×C4—444no—
854C2×C4—884no—
855C2×C4—882no—
856C2×C4C2×#433912yes—
857C2×C4C2×#433912yes—
858C2×C4C22×C22⋊D1112yes—
859C2×C4C22×C22⋊D1111yescharacteristic
860C2×C4C22×C22⋊D1112yes—
861C2×C4C22×C22⋊D1111yescharacteristic
862C2×C4C22×C22⋊D1112yes—
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C22×C22⋊D1111yescharacteristic
865C2×C4C22×C22⋊D1111yescharacteristic
866C2×C4C24×D1111yescharacteristic
867C8—222no—
868C8—222no—
869C8—224no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—41no—
877C22—41no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22#1062332212yes—
882C22C23×C22⋊D1111yescharacteristic
883C4—24no—
884C4—22no—
885C4—22no—
886C4—21no—
887C4—22no—
888C4—21no—
889C4—22no—
890C4—21no—
891C4—42no—
892C4—41no—
893C4—41no—
894C4—442no—
895C4—444no—
896C4#1062332212yes—
897C4#1062336912yes—
898C4C22×#433911yescharacteristic
899C4C22×#433911yescharacteristic
900C2—22no—
901C2—42no—
902C2—42no—
903C2—882no—
904C2C2×#1062332211yescharacteristic
905C2C2×#1062336911yescharacteristic
906C2#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#60600
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. #13082527C2semidirect
2. #13078878C2semidirect
3. #13078845C2semidirect
4. #13078778C2semidirect
5. #13078738C2semidirect
6. #13078676C2semidirect
7. #13078655C2semidirect
8. #13078594C2semidirect
9. #13078431C2semidirect
10. C2×#10622634C2semidirect
11. #13078088C2semidirect
12. #13078071C2semidirect
13. #13077931C2semidirect
14. #13077489C2semidirect
15. #13077459C2semidirect
16. #13077282C2semidirect
17. C4×C11×2−1+4C2semidirect
240. C11×#41#41semidirect
248. C2×Q8×C11#41semidirect
352. C4×2−1+4D11semidirect
695. #41#4339semidirect
706. C2×Q8#4339semidirect
803. C11#60600semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130788782
#130788452
#130787782
#130787382
#130786762
#130786552
#130785942
#130784312
C2×#106226342
#130780882
#130780712
#130779312
#130774892
#130774592
#130772822
C4×C11×2−1+42
#6060011