Finite Group Databasebeta

← #15639269

Subgroups — #15639269

Order 2816.

2112 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082417C211yesmaximal, characteristic, complemented
2#41×D44C211yesmaximal, characteristic
3#13080956C211yesmaximal, characteristic, complemented
4#13080934C211yesmaximal, characteristic, complemented
5#13080724C212yesmaximal, complemented
6#13080694C212yesmaximal, complemented
7#13080494C211yesmaximal, characteristic, complemented
8#13080442C211yesmaximal, characteristic, complemented
9Q16×D44C211yesmaximal, characteristic, complemented
10SD16×D44C211yesmaximal, characteristic, complemented
11#13080283C211yesmaximal, characteristic, complemented
12#13080263C211yesmaximal, characteristic, complemented
13#13080192C212yesmaximal, complemented
14#13080132C212yesmaximal, complemented
15#13079623C211yesmaximal, characteristic, complemented
16#13079574C211yesmaximal, characteristic, complemented
17#13079450C212yesmaximal, complemented
18#13079401C212yesmaximal, complemented
19#13078778C211yesmaximal, characteristic, complemented
20#13077873C212yesmaximal, complemented
21D11×#452C212yesmaximal, complemented
22#13077650C211yesmaximal, characteristic, complemented
23C11×#3107C211yesmaximal, characteristic, complemented
24C2×#41×D11C2212yes—
25C11×#533C2211yescharacteristic, complemented
26C4×C11×#41C2211yescharacteristic
27C2×#66971C2212yescomplemented
28C2×Q16×D11C2212yescomplemented
29C2×#66968C2212yescomplemented
30C2×SD16×D11C2212yescomplemented
31#10623261C2212yescomplemented
32#10623258C2212yescomplemented
33#10623221—22no—
34#10623165—22no—
35D11×C22⋊Q8C2212yescomplemented
36D11×C22⋊Q8C2212yescomplemented
37#10623110—21no—
38#10623110—21no—
39#10623110C2211yescharacteristic
40#10623110C2211yescharacteristic, complemented
41#10623108C2211yescharacteristic
42#10623107C2212yes—
43Q8×D44C2211yescharacteristic
44Q8×D44C2211yescharacteristic
45Q8×D44C2211yescharacteristic, complemented
46#10623086—21no—
47#10623086C2211yescharacteristic
48#10623085—22no—
49#10623085C2212yes—
50D4×D44—21no—
51D4×D44C2211yescharacteristic
52#10623055—22no—
53#10623055C2212yes—
54#10623052—21no—
55#10623050—21no—
56#10623008—21no—
57#10623008C2211yescharacteristic
58C2×C4×D44—21no—
59C2×C4×D44C2211yescharacteristic
60#10623001C2211yescharacteristic, complemented
61C11×#485C2211yescharacteristic, complemented
62C11×#485C2211yescharacteristic, complemented
63C11×#475C2211yescharacteristic, complemented
64C11×#474C2211yescharacteristic, complemented
65C11×#462C2211yescharacteristic, complemented
66C11×#461C2211yescharacteristic, complemented
67C11×#452C2211yescharacteristic
68C11×#452C2211yescharacteristic
69C4×C11×Q16C2211yescharacteristic, complemented
70C4×C11×Q16C2211yescharacteristic, complemented
71C4×C11×SD16C2211yescharacteristic, complemented
72C4×C11×SD16C2211yescharacteristic, complemented
73C11×#431C2211yescharacteristic, complemented
74#10622852C2212yes—
75#10622800C2212yescomplemented
76#10622799C2212yescomplemented
77#10622786C2212yescomplemented
78#10622782C2212yescomplemented
79#10622702C2212yescomplemented
80#10622699C2212yescomplemented
81#10622660C2212yescomplemented
82#10622660C2212yescomplemented
83#10622644C2211yescharacteristic, complemented
84#10622644C2211yescharacteristic, complemented
85#10622644C2211yescharacteristic, complemented
86#10622643C2212yescomplemented
87#10622640C2211yescharacteristic, complemented
88#10622640C2211yescharacteristic, complemented
89#10622634C2211yescharacteristic, complemented
90#10622632C2211yescharacteristic, complemented
91#10622631C2212yescomplemented
92#10622621C2211yescharacteristic, complemented
93#10622609C2212yescomplemented
94#10622539C2211yescharacteristic, complemented
95#10622500C2212yescomplemented
96#10622499C2212yescomplemented
97#10622497C2212yescomplemented
98#10622495C2212yescomplemented
99#10622481C2212yescomplemented
100#10622477C2212yescomplemented
101#10622476C2212yescomplemented
102#10622475C2212yescomplemented
103#10622458C2212yescomplemented
104#10622458C2212yescomplemented
105#10622449C2212yescomplemented
106#10622449C2212yescomplemented
107#10622429C2212yescomplemented
108#10622426C2212yescomplemented
109#10622425C2212yescomplemented
110#10622423C2212yescomplemented
111#10622421C2212yescomplemented
112#10622421C2212yescomplemented
113#10622421C2212yescomplemented
114#10622420C2212yescomplemented
115#10622419C2212yescomplemented
116#10622419C2212yescomplemented
117#10622416C2212yescomplemented
118D11×#103C2212yescomplemented
119#10622396C2212yescomplemented
120#10622389C2212yescomplemented
121#10622384C2212yescomplemented
122D11×#102C2212yescomplemented
123#10622346C2212yescomplemented
124#10622346C2212yescomplemented
125#10622339C2212yescomplemented
126D11×C22⋊C8C2212yescomplemented
127#10622312C2211yescharacteristic, complemented
128#10622307C2211yescharacteristic, complemented
129#10622306C2211yescharacteristic, complemented
130#10622301C2211yescharacteristic, complemented
131#10622301C2211yescharacteristic, complemented
132C8×D44C2211yescharacteristic
133C8×D44C2211yescharacteristic
134#10622294C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136#41×D11—44no—
137#41×D11—44no—
138C2×#4343C2312yes—
139C2×Q8×D11C2312yes—
140C2×Q8×D11C2312yes—
141C2×Q8×D11C2312yes—
142C2×#4341—22no—
143C2×#4341C2312yes—
144C2×D4×D11—22no—
145C2×D4×D11C2312yes—
146C2×#4339—22no—
147C2×#4339C2312yes—
148C22×D44—21no—
149C22×D44D411yescharacteristic
150C22×C4×D11—22no—
151C22×C4×D11C2312yes—
152C2×C11×Q16C2311yescharacteristic
153C2×C11×Q16C2311yescharacteristic
154C2×C11×SD16C2311yescharacteristic
155C2×C11×SD16C2311yescharacteristic
156C11×C4⋊Q8C2311yescharacteristic
157C11×C4⋊Q8C2311yescharacteristic
158C11×#125—21no—
159C11×C22⋊Q8—21no—
160C11×C22⋊Q8C2311yescharacteristic
161C11×C22⋊Q8C2311yescharacteristic
162C4×Q8×C11—21no—
163C4×Q8×C11C2311yescharacteristic
164C4×Q8×C11C2311yescharacteristic
165C4×Q8×C11C2311yescharacteristic
166C4×Q8×C11C2311yescharacteristic
167C4×D4×C11—21no—
168C4×D4×C11—21no—
169C4×D4×C11C2311yescharacteristic
170C4×D4×C11C2311yescharacteristic
171C11×#117—21no—
172C11×#117—21no—
173C11×#117C2311yescharacteristic
174C2×C42×C11—21no—
175C2×C42×C11C2311yescharacteristic
176#66999—22no—
177#66999—22no—
178#66999C2312yes—
179#66999C2312yes—
180C2×#4326C2312yes—
181C2×#4326C2312yes—
182C2×#4326C2312yes—
183C2×#4325C2312yes—
184C2×#4325C2312yes—
185C2×#4324C2312yes—
186#66983—21no—
187#66983—21no—
188#66983—21no—
189#66983—22no—
190#66983—21no—
191C2×(C2×D11)⋊C4—22no—
192C2×(C2×D11)⋊C4D412yes—
193#66979—21no—
194C2×C4⋊Dic11—21no—
195C2×C4⋊Dic11D411yescharacteristic
196#66977—21no—
197#66977C2312yes—
198#66971—44no—
199Q16×D11—44no—
200#66968—44no—
201SD16×D11—44no—
202C2×Dic44C2312yes—
203C2×Dic44C2312yes—
204C2×#4314C2312yes—
205C2×#4314C2312yes—
206C2×#4313C2312yes—
207C2×#4313C2312yes—
208C2×C8×D11C2312yes—
209C2×C8×D11C2312yes—
210#66950—22no—
211#66950—22no—
212#66950—22no—
213#66950—22no—
214#66950C2312yes—
215#66950C2312yes—
216#66950C2312yes—
217#66950C2312yes—
218#66949—22no—
219#66949—22no—
220#66949—22no—
221#66949—22no—
222#66949—22no—
223#66949—22no—
224#66948—22no—
225#66948—22no—
226#66948C2312yes—
227#66948C2312yes—
228#66946—22no—
229#66946—22no—
230C4⋊C4×D11—22no—
231C4⋊C4×D11—22no—
232C4⋊C4×D11C2312yes—
233C4⋊C4×D11C2312yes—
234#66943—22no—
235#66941—22no—
236#66939—22no—
237#66939—22no—
238#66939—22no—
239#66935—22no—
240#66935—22no—
241#66935—22no—
242C22⋊C4×D11—22no—
243C22⋊C4×D11—22no—
244#66931—22no—
245#66931—22no—
246#66928—22no—
247#66928C2312yes—
248#66927—21no—
249#66927C2311yescharacteristic
250C4×D44—21no—
251C4×D44—21no—
252C4×D44—21no—
253C4×D44—21no—
254C4×D44—21no—
255C4×D44—22no—
256C4×D44—22no—
257C4×D44—21no—
258C4×D44—21no—
259C4×D44—22no—
260C4×D44—21no—
261C4×D44D411yescharacteristic
262C4×D44D411yescharacteristic
263C4×D44D412yes—
264C4×D44C2312yes—
265C4×D44C2311yescharacteristic
266C4×D44C2311yescharacteristic
267#66923—21no—
268#66923—21no—
269#66923—21no—
270#66922—21no—
271#66922—21no—
272#66922—21no—
273#66922C2311yescharacteristic
274#66922C2311yescharacteristic
275#66922C2311yescharacteristic
276C4×Dic22—21no—
277C4×Dic22C2312yes—
278C11×#107C2311yescharacteristic
279C11×#107C2311yescharacteristic
280C11×#106C2311yescharacteristic
281C11×#106C2311yescharacteristic
282C11×C4⋊C8C2311yescharacteristic
283C11×C4⋊C8C2311yescharacteristic
284C11×#103C2311yescharacteristic
285C11×#103C2311yescharacteristic
286C11×#103C2311yescharacteristic
287C11×#103C2311yescharacteristic
288C11×#103C2311yescharacteristic
289C11×#103C2311yescharacteristic
290C11×#102C2311yescharacteristic
291C11×#102C2311yescharacteristic
292C11×C22⋊C8C2311yescharacteristic
293C11×C22⋊C8C2311yescharacteristic
294C4×C8×C11C2311yescharacteristic
295C4×C8×C11C2311yescharacteristic
296#66899C2312yes—
297#66896C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299#66885C2312yes—
300#66885C2312yes—
301(C2×D11)⋊C8C2312yes—
302(C2×D11)⋊C8C2312yes—
303(C2×D11)⋊C8C2312yes—
304(C2×D11)⋊C8C2312yes—
305#66880C2312yes—
306#66880C2312yes—
307#66874C2312yes—
308#66874C2312yes—
309#66874C2312yes—
310#66874C2312yes—
311#66873C2312yes—
312#66873C2312yes—
313#66872C2312yes—
314#66871C2312yes—
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4⋊(C11⋊C8)C2311yescharacteristic
317#66867C2312yes—
318#61607—111nomaximal, Sylow
319C23×D11—22no—
320C23×D11C2×D412yes—
321C11×#41—22no—
322C11×#41—22no—
323C2×Q8×C11—21no—
324C2×Q8×C11C2411yescharacteristic
325C2×Q8×C11C2411yescharacteristic
326C2×Q8×C11C2411yescharacteristic
327C2×D4×C11—21no—
328C2×D4×C11C2411yescharacteristic
329C22×C4×C11—21no—
330C22×C4×C11—21no—
331C22×C4×C11—21no—
332C22×C4×C11C2×D411yescharacteristic
333C22×C4×C11C2×D411yescharacteristic
334C22×C4×C11C2411yescharacteristic
335C2×C22⋊D11—22no—
336C2×C22⋊D11—22no—
337C2×C22⋊D11—22no—
338C22×Dic11—22no—
339C22×Dic11C2×D412yes—
340#4343—24no—
341#4343—42no—
342Q8×D11—24no—
343Q8×D11—42no—
344Q8×D11—42no—
345Q8×D11—42no—
346Q8×D11—42no—
347Q8×D11—42no—
348#4341—24no—
349#4341—42no—
350#4341—48no—
351D4×D11—24no—
352D4×D11—42no—
353D4×D11—48no—
354#4339—42no—
355#4339—42no—
356#4339—48no—
357C2×D44—24no—
358C2×D44—22no—
359C2×D44—22no—
360C2×D44—22no—
361C2×D44—21no—
362C2×D44—21no—
363C2×D44—44no—
364C2×D44C2×D411yescharacteristic
365C2×D44C2×D412yes—
366C2×D44C2×D411yescharacteristic
367C2×D44C2412yes—
368C2×C4×D11—22no—
369C2×C4×D11—22no—
370C2×C4×D11—22no—
371C2×C4×D11—22no—
372C2×C4×D11—22no—
373C2×C4×D11—22no—
374C2×C4×D11—22no—
375C2×C4×D11—42no—
376C2×C4×D11—42no—
377C2×C4×D11—48no—
378C2×C4×D11C2×D412yes—
379C2×C4×D11C2×D412yes—
380C2×C4×D11C2412yes—
381C2×C4×D11C2412yes—
382C2×Dic22—22no—
383C2×Dic22—22no—
384C2×Dic22—22no—
385C2×Dic22—21no—
386C2×Dic22C2412yes—
387C2×Dic22C2412yes—
388C11×Q16—22no—
389C11×Q16—22no—
390C11×SD16—22no—
391C11×SD16—22no—
392C2×C8×C11C2411yescharacteristic
393C2×C8×C11C2411yescharacteristic
394C2×C8×C11C2411yescharacteristic
395C2×C8×C11C2411yescharacteristic
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4C2411yescharacteristic
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C42×C11—21no—
415C42×C11—21no—
416C42×C11—21no—
417C42×C11—21no—
418C42×C11—21no—
419C42×C11C2×D411yescharacteristic
420C42×C11C2×D411yescharacteristic
421C42×C11C2411yescharacteristic
422C42×C11C2411yescharacteristic
423C22⋊Dic11—22no—
424#4326—24no—
425#4326—42no—
426#4326—42no—
427#4325—42no—
428#4325—42no—
429#4324—24no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4C2×D412yes—
441(C2×D11)⋊C4C2×D412yes—
442(C2×D11)⋊C4C2×D412yes—
443(C2×D11)⋊C4C2×D412yes—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—22no—
447C4⋊Dic11—22no—
448C4⋊Dic11—21no—
449C4⋊Dic11—21no—
450C4⋊Dic11—21no—
451C4⋊Dic11—21no—
452C4⋊Dic11—21no—
453C4⋊Dic11C2×D411yescharacteristic
454C4⋊Dic11C2×D411yescharacteristic
455C4⋊Dic11C2×D412yes—
456C4⋊Dic11C2412yes—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463C4×Dic11—22no—
464C2×C11⋊C8C2412yes—
465C2×C11⋊C8C2412yes—
466Dic44—42no—
467Dic44—42no—
468#4314—42no—
469#4314—42no—
470#4313—42no—
471#4313—42no—
472C8×D11—42no—
473C8×D11—42no—
474#3501—111no—
475D4×#41—111no—
476#3333—111no—
477#3331—111no—
478#3316—112no—
479#3314—112no—
480#3299—111no—
481#3295—111no—
482D4×Q16—111no—
483D4×SD16—111no—
484#3278—111no—
485#3276—111no—
486#3270—112no—
487#3266—112no—
488#3216—111no—
489#3210—111no—
490#3196—112no—
491#3190—112no—
492#3116—111no—
493#3107D1111yescharacteristic, complemented
494#3007—112no—
495C2×#452—112no—
496#2974—111no—
497C23×C11—21no—
498C23×C11C22×D411yescharacteristic
499C22×D11—24no—
500C22×D11—22no—
501C22×D11—42no—
502C22×D11—42no—
503C22×D11—44no—
504C22×D11—44no—
505C22×D11—82no—
506C22×D11C22×D412yes—
507C22×D11C22×D412yes—
508Q8×C11—21no—
509Q8×C11—21no—
510Q8×C11—21no—
511Q8×C11—21no—
512Q8×C11—21no—
513Q8×C11—81no—
514Q8×C11H(5,𝔽2)12yes—
515D4×C11—24no—
516D4×C11—21no—
517D4×C11H(5,𝔽2)12yes—
518C2×C4×C11—24no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—21no—
529C2×C4×C11—41no—
530C2×C4×C11—42no—
531C2×C4×C11—81no—
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D411yescharacteristic
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C2511yescharacteristic
538C22⋊D11—44no—
539C22⋊D11—44no—
540C22⋊D11—44no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—42no—
545C2×Dic11—44no—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548D44—24no—
549D44—22no—
550D44—22no—
551D44—22no—
552D44—44no—
553D44—44no—
554D44—42no—
555D44—81no—
556D44—82no—
557D44#13714yescomplemented
558C4×D11—22no—
559C4×D11—22no—
560C4×D11—22no—
561C4×D11—22no—
562C4×D11—42no—
563C4×D11—42no—
564C4×D11—44no—
565C4×D11—44no—
566C4×D11—44no—
567C4×D11—82no—
568C4×D11—82no—
569C4×D11—82no—
570C4×D11—82no—
571Dic22—22no—
572Dic22—22no—
573Dic22—22no—
574Dic22—22no—
575Dic22—44no—
576Dic22—82no—
577Dic22—82no—
578Dic22—81no—
579C8×C11—21no—
580C8×C11—21no—
581C8×C11—21no—
582C8×C11—21no—
583C11⋊C8—22no—
584C11⋊C8—22no—
585C22×#41—112no—
586C2×#137—112no—
587C2×#137—112no—
588C22×Q16—112no—
589C22×SD16—112no—
590#554—112no—
591#554—111no—
592#554—111no—
593#554—221no—
594#554—221no—
595#554—222no—
596#550—111no—
597D4×Q8—112no—
598D4×Q8—111no—
599D4×Q8—111no—
600D4×Q8—111no—
601#548—112no—
602#547—111no—
603#547—221no—
604#546—112no—
605#546—222no—
606D42—111no—
607D42—221no—
608#544—221no—
609#543—222no—
610#533—111no—
611#533C2×D1111yescharacteristic, complemented
612#532—111no—
613#532—221no—
614#525—112no—
615#525—222no—
616C2×C22⋊Q8—112no—
617C2×C22⋊Q8—112no—
618#518—221no—
619C4×#41C2×D1111yescharacteristic
620C2×C4×D4—111no—
621C2×C4×D4—221no—
622#497—112no—
623#494—111no—
624#492—111no—
625#489—112no—
626#487—111no—
627#486—111no—
628#485—112no—
629#485C2×D1111yescharacteristic, complemented
630#485C2×D1111yescharacteristic, complemented
631#484—112no—
632#483—112no—
633#481—112no—
634#480—112no—
635#477—111no—
636#476—111no—
637#475C2×D1111yescharacteristic, complemented
638#474C2×D1111yescharacteristic, complemented
639#470—112no—
640#470—112no—
641#468—112no—
642#468—112no—
643#467—112no—
644#467—112no—
645#465—112no—
646#465—112no—
647#464—112no—
648#464—112no—
649#462—111no—
650#462—111no—
651#462—111no—
652#462C2×D1111yescharacteristic, complemented
653#461—111no—
654#461C2×D1111yescharacteristic, complemented
655#460—111no—
656#460—111no—
657#452—112no—
658#452—112no—
659#452—112no—
660#452—112no—
661#452—112no—
662#452—112no—
663#452—112no—
664#452—112no—
665#452—112no—
666#452C2×D1111yescharacteristic
667#452C2×D1111yescharacteristic
668#451—112no—
669#451—112no—
670#451—112no—
671#451—112no—
672#450—112no—
673#450—112no—
674#448—112no—
675#448—112no—
676#441—112no—
677#440—112no—
678C4×Q16C2×D1111yescharacteristic, complemented
679C4×Q16C2×D1111yescharacteristic, complemented
680C4×SD16C2×D1111yescharacteristic, complemented
681C4×SD16C2×D1111yescharacteristic, complemented
682#436—111no—
683#436—111no—
684#435—112no—
685#435—112no—
686C8×D4—111no—
687C8×D4—111no—
688#432—111no—
689#431C2×D1111yescharacteristic, complemented
690#417—112no—
691#417—112no—
692C2×#103—112no—
693C2×#102—112no—
694#407—112no—
695C2×C22⋊C8—112no—
696C22×C11—21no—
697C22×C11—21no—
698C22×C11—22no—
699C22×C11—21no—
700C22×C11—41no—
701C22×C11—41no—
702C22×C11C23×D411yescharacteristic
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—22no—
706C2×D11—22no—
707C2×D11—22no—
708C2×D11—42no—
709C2×D11—42no—
710C2×D11—42no—
711C2×D11—84no—
712C2×D11—88no—
713C2×D11C2×#13714yes—
714C4×C11—21no—
715C4×C11—21no—
716C4×C11—21no—
717C4×C11—22no—
718C4×C11—21no—
719C4×C11—41no—
720C4×C11—41no—
721C4×C11—41no—
722C4×C11—41no—
723C4×C11—41no—
724C4×C11—41no—
725C4×C11C2×#13712yes—
726C4×C11C2×H(5,𝔽2)11yescharacteristic
727C4×C11C2×H(5,𝔽2)11yescharacteristic
728Dic11—22no—
729Dic11—22no—
730Dic11—42no—
731Dic11—42no—
732Dic11—42no—
733C2×#41—112no—
734C2×#41—112no—
735C2×#41—112no—
736C2×#41—222no—
737C2×#41—222no—
738C2×#41—444no—
739C2×#41—444no—
740C2×#41C22×D1111yescharacteristic
741C22×Q8—112no—
742C22×Q8—112no—
743C22×Q8—112no—
744C22×D4—112no—
745C22×D4—111no—
746C22×D4—221no—
747C22×D4—222no—
748C23×C4—112no—
749C23×C4—222no—
750#137—444no—
751#137—444no—
752C2×Q16—112no—
753C2×Q16—112no—
754C2×Q16—112no—
755C2×Q16—112no—
756C2×Q16—112no—
757C2×Q16—444no—
758C2×Q16C22×D1111yescharacteristic
759C2×Q16C22×D1111yescharacteristic
760C2×SD16—112no—
761C2×SD16—112no—
762C2×SD16—112no—
763C2×SD16—112no—
764C2×SD16—112no—
765C2×SD16—444no—
766C2×SD16C22×D1111yescharacteristic
767C2×SD16C22×D1111yescharacteristic
768C2×M16—112no—
769C2×M16—112no—
770C22×C8—112no—
771C22×C8—112no—
772C4⋊Q8—111no—
773C4⋊Q8—111no—
774C4⋊Q8—111no—
775C4⋊Q8—221no—
776C4⋊Q8—221no—
777C4⋊Q8—221no—
778C4⋊Q8—222no—
779C4⋊Q8C22×D1111yescharacteristic
780C4⋊Q8C22×D1111yescharacteristic
781#127—111no—
782#127—221no—
783#125—21no—
784#125—221no—
785#125—221no—
786#125—222no—
787#125—221no—
788#124—112no—
789#124—222no—
790#123—222no—
791#123—222no—
792#123—222no—
793C22⋊Q8—21no—
794C22⋊Q8—112no—
795C22⋊Q8—112no—
796C22⋊Q8—112no—
797C22⋊Q8—112no—
798C22⋊Q8—112no—
799C22⋊Q8—112no—
800C22⋊Q8—112no—
801C22⋊Q8—222no—
802C22⋊Q8—222no—
803C22⋊Q8—222no—
804C22⋊Q8—222no—
805C22⋊Q8—222no—
806C22⋊Q8—222no—
807C22⋊Q8—222no—
808C22⋊Q8—222no—
809C22⋊Q8—222no—
810C22⋊Q8—222no—
811C22⋊Q8—222no—
812C22⋊Q8—222no—
813C22⋊Q8—222no—
814C22⋊Q8—222no—
815C22⋊Q8—221no—
816C22⋊Q8C22×D1111yescharacteristic
817C22⋊Q8C22×D1111yescharacteristic
818#121—112no—
819#121—112no—
820#121—222no—
821#121—222no—
822#121—222no—
823#121—221no—
824#121—221no—
825#121—221no—
826#121—221no—
827#120—222no—
828#120—222no—
829#120—222no—
830C4×Q8—21no—
831C4×Q8—112no—
832C4×Q8—221no—
833C4×Q8C22×D1111yescharacteristic
834C4×Q8C22×D1111yescharacteristic
835C4×Q8C22×D1111yescharacteristic
836C4×Q8C22×D1111yescharacteristic
837C4×D4—21no—
838C4×D4—21no—
839C4×D4—111no—
840C4×D4—112no—
841C4×D4—111no—
842C4×D4—111no—
843C4×D4—112no—
844C4×D4—111no—
845C4×D4—222no—
846C4×D4—221no—
847C4×D4—222no—
848C4×D4—222no—
849C4×D4—221no—
850C4×D4—221no—
851C4×D4—221no—
852C4×D4—221no—
853C4×D4—221no—
854C4×D4—222no—
855C4×D4—222no—
856C4×D4—221no—
857C4×D4—221no—
858C4×D4C22×D1111yescharacteristic
859C4×D4C22×D1111yescharacteristic
860#117—21no—
861#117—21no—
862#117—221no—
863#117C22×D1111yescharacteristic
864C2×C4⋊C4—111no—
865C2×C4⋊C4—112no—
866C2×C4⋊C4—112no—
867C2×C4⋊C4—222no—
868C2×C4⋊C4—222no—
869C2×C4⋊C4—221no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—222no—
872C2×C22⋊C4—222no—
873C2×C22⋊C4—222no—
874C2×C42—21no—
875C2×C42C22×D1111yescharacteristic
876#107—112no—
877#107C22×D1111yescharacteristic
878#107C22×D1111yescharacteristic
879#106—112no—
880#106C22×D1111yescharacteristic
881#106C22×D1111yescharacteristic
882C4⋊C8—111no—
883C4⋊C8—111no—
884C4⋊C8C22×D1111yescharacteristic
885C4⋊C8C22×D1111yescharacteristic
886#103—112no—
887#103—112no—
888#103—112no—
889#103—112no—
890#103—112no—
891#103—112no—
892#103—112no—
893#103C22×D1111yescharacteristic
894#103C22×D1111yescharacteristic
895#103C22×D1111yescharacteristic
896#103C22×D1111yescharacteristic
897#103C22×D1111yescharacteristic
898#103C22×D1111yescharacteristic
899#102—112no—
900#102—112no—
901#102—112no—
902#102—112no—
903#102—112no—
904#102C22×D1111yescharacteristic
905#102C22×D1111yescharacteristic
906C22⋊C8—112no—
907C22⋊C8—112no—
908C22⋊C8—112no—
909C22⋊C8—112no—
910C22⋊C8—112no—
911C22⋊C8C22×D1111yescharacteristic
912C22⋊C8C22×D1111yescharacteristic
913#97—112no—
914C4×C8C22×D1111yescharacteristic
915C4×C8C22×D1111yescharacteristic
916C2×C11—41no—
917C2×C11—42no—
918C2×C11#348411yescharacteristic
919C2×C11C22×#13711yescharacteristic
920C2×C11#358411yescharacteristic
921D11—24no—
922D11—42no—
923D11—82no—
924C24—112no—
925C24—222no—
926#41—22no—
927#41—22no—
928#41—224no—
929#41—224no—
930#41—442no—
931#41—442no—
932#41—448no—
933#41—442no—
934#41—442no—
935#41—448no—
936C2×Q8—21no—
937C2×Q8—112no—
938C2×Q8—112no—
939C2×Q8—222no—
940C2×Q8—222no—
941C2×Q8—222no—
942C2×Q8—221no—
943C2×Q8—224no—
944C2×Q8—442no—
945C2×Q8—442no—
946C2×Q8—442no—
947C2×Q8—442no—
948C2×Q8—442no—
949C2×Q8C23×D1111yescharacteristic
950C2×Q8C23×D1111yescharacteristic
951C2×Q8C23×D1111yescharacteristic
952C2×D4—21no—
953C2×D4—111no—
954C2×D4—112no—
955C2×D4—111no—
956C2×D4—112no—
957C2×D4—224no—
958C2×D4—222no—
959C2×D4—222no—
960C2×D4—222no—
961C2×D4—222no—
962C2×D4—224no—
963C2×D4—222no—
964C2×D4—222no—
965C2×D4—221no—
966C2×D4—221no—
967C2×D4—444no—
968C2×D4—442no—
969C2×D4—448no—
970C2×D4C23×D1111yescharacteristic
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—112no—
975C22×C4—112no—
976C22×C4—112no—
977C22×C4—112no—
978C22×C4—112no—
979C22×C4—222no—
980C22×C4—222no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—222no—
984C22×C4—222no—
985C22×C4—222no—
986C22×C4—222no—
987C22×C4—442no—
988C22×C4—442no—
989C22×C4—448no—
990C22×C4D4×D1111yescharacteristic
991C22×C4D4×D1111yescharacteristic
992C22×C4C23×D1111yescharacteristic
993Q16—22no—
994Q16—22no—
995Q16—224no—
996Q16—442no—
997Q16—442no—
998Q16—442no—
999Q16—442no—
1000SD16—22no—
1001SD16—22no—
1002SD16—224no—
1003SD16—442no—
1004SD16—442no—
1005SD16—442no—
1006SD16—442no—
1007M16—442no—
1008M16—442no—
1009C2×C8—112no—
1010C2×C8—112no—
1011C2×C8—442no—
1012C2×C8—442no—
1013C2×C8C23×D1111yescharacteristic
1014C2×C8C23×D1111yescharacteristic
1015C2×C8C23×D1111yescharacteristic
1016C2×C8C23×D1111yescharacteristic
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—111no—
1027C4⋊C4—111no—
1028C4⋊C4—112no—
1029C4⋊C4—112no—
1030C4⋊C4—222no—
1031C4⋊C4—222no—
1032C4⋊C4—222no—
1033C4⋊C4—222no—
1034C4⋊C4—222no—
1035C4⋊C4—222no—
1036C4⋊C4—222no—
1037C4⋊C4—222no—
1038C4⋊C4—222no—
1039C4⋊C4—221no—
1040C4⋊C4—221no—
1041C4⋊C4—221no—
1042C4⋊C4—221no—
1043C4⋊C4—222no—
1044C4⋊C4—221no—
1045C4⋊C4C23×D1111yescharacteristic
1046C4⋊C4C23×D1111yescharacteristic
1047C4⋊C4C23×D1111yescharacteristic
1048C4⋊C4C23×D1111yescharacteristic
1049C22⋊C4—21no—
1050C22⋊C4—21no—
1051C22⋊C4—21no—
1052C22⋊C4—21no—
1053C22⋊C4—21no—
1054C22⋊C4—112no—
1055C22⋊C4—112no—
1056C22⋊C4—112no—
1057C22⋊C4—112no—
1058C22⋊C4—222no—
1059C22⋊C4—222no—
1060C22⋊C4—222no—
1061C22⋊C4—222no—
1062C22⋊C4—222no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—222no—
1075C42D4×D1111yescharacteristic
1076C42D4×D1111yescharacteristic
1077C42C23×D1111yescharacteristic
1078C42C23×D1111yescharacteristic
1079C11#6160711yescharacteristic, complemented, Sylow
1080C23—21no—
1081C23—112no—
1082C23—112no—
1083C23—224no—
1084C23—222no—
1085C23—442no—
1086C23—442no—
1087C23—444no—
1088C23—444no—
1089C23—882no—
1090C23C2×D4×D1111yescharacteristic
1091Q8—21no—
1092Q8—21no—
1093Q8—21no—
1094Q8—21no—
1095Q8—21no—
1096Q8—81no—
1097Q8—222no—
1098Q8—222no—
1099Q8—222no—
1100Q8—222no—
1101Q8—444no—
1102Q8—881no—
1103Q8—882no—
1104Q8—882no—
1105Q8#6704212yes—
1106D4—24no—
1107D4—21no—
1108D4—114no—
1109D4—224no—
1110D4—222no—
1111D4—222no—
1112D4—222no—
1113D4—444no—
1114D4—444no—
1115D4—444no—
1116D4—444no—
1117D4—444no—
1118D4—442no—
1119D4—881no—
1120D4—882no—
1121D4#6704212yes—
1122C2×C4—24no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—81no—
1136C2×C4—112no—
1137C2×C4—112no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—442no—
1146C2×C4—442no—
1147C2×C4—444no—
1148C2×C4—444no—
1149C2×C4—444no—
1150C2×C4—442no—
1151C2×C4—444no—
1152C2×C4—882no—
1153C2×C4—882no—
1154C2×C4—882no—
1155C2×C4—882no—
1156C2×C4C2×D4×D1111yescharacteristic
1157C2×C4C2×D4×D1111yescharacteristic
1158C2×C4C2×D4×D1111yescharacteristic
1159C2×C4C2×D4×D1111yescharacteristic
1160C2×C4C2×D4×D1111yescharacteristic
1161C2×C4C24×D1111yescharacteristic
1162C8—21no—
1163C8—21no—
1164C8—21no—
1165C8—21no—
1166C8—222no—
1167C8—222no—
1168C22—21no—
1169C22—22no—
1170C22—21no—
1171C22—21no—
1172C22—41no—
1173C22—41no—
1174C22—114no—
1175C22—222no—
1176C22—222no—
1177C22—222no—
1178C22—222no—
1179C22—222no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—884no—
1184C22—888no—
1185C22C22×D4×D1111yescharacteristic
1186C4—21no—
1187C4—22no—
1188C4—21no—
1189C4—21no—
1190C4—21no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—222no—
1198C4—222no—
1199C4—442no—
1200C4—442no—
1201C4—442no—
1202C4D11×#13712yes—
1203C4C2×#6704211yescharacteristic
1204C4C2×#6704211yescharacteristic
1205C2—41no—
1206C2—42no—
1207C2—224no—
1208C2—442no—
1209C2—882no—
1210C2#1308224911yescharacteristic
1211C2C2×D11×#13711yescharacteristic
1212C2#1308338511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3107C2
socleC22×C11C23×D4
prime radical#41×D44C2
hypercenter#3107D11
hypocenterC11#61607
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #13082417C2semidirect
3. #13080956C2semidirect
4. #13080934C2semidirect
5. #13080724C2semidirect
6. #13080694C2semidirect
7. #13080494C2semidirect
8. #13080442C2semidirect
9. Q16×D44C2semidirect
10. SD16×D44C2semidirect
11. #13080283C2semidirect
12. #13080263C2semidirect
13. #13080192C2semidirect
14. #13080132C2semidirect
15. #13079623C2semidirect
16. #13079574C2semidirect
17. #13079450C2semidirect
18. #13079401C2semidirect
19. #13078778C2semidirect
20. #13077873C2semidirect
21. D11×#452C2semidirect
22. #13077650C2semidirect
23. C11×#3107C2semidirect
25. C11×#533C22semidirect
27. C2×#66971C22semidirect
28. C2×Q16×D11C22semidirect
29. C2×#66968C22semidirect
30. C2×SD16×D11C22semidirect
31. #10623261C22semidirect
32. #10623258C22semidirect
35. D11×C22⋊Q8C22semidirect
36. D11×C22⋊Q8C22semidirect
40. #10623110C22semidirect
45. Q8×D44C22semidirect
60. #10623001C22semidirect
61. C11×#485C22semidirect
62. C11×#485C22semidirect
63. C11×#475C22semidirect
64. C11×#474C22semidirect
65. C11×#462C22semidirect
66. C11×#461C22semidirect
69. C4×C11×Q16C22semidirect
70. C4×C11×Q16C22semidirect
71. C4×C11×SD16C22semidirect
72. C4×C11×SD16C22semidirect
73. C11×#431C22semidirect
75. #10622800C22semidirect
76. #10622799C22semidirect
77. #10622786C22semidirect
78. #10622782C22semidirect
79. #10622702C22semidirect
80. #10622699C22semidirect
81. #10622660C22semidirect
82. #10622660C22semidirect
83. #10622644C22semidirect
84. #10622644C22semidirect
85. #10622644C22semidirect
86. #10622643C22semidirect
87. #10622640C22semidirect
88. #10622640C22semidirect
89. #10622634C22semidirect
90. #10622632C22semidirect
91. #10622631C22semidirect
92. #10622621C22semidirect
93. #10622609C22semidirect
94. #10622539C22semidirect
95. #10622500C22semidirect
96. #10622499C22semidirect
97. #10622497C22semidirect
98. #10622495C22semidirect
99. #10622481C22semidirect
100. #10622477C22semidirect
101. #10622476C22semidirect
102. #10622475C22semidirect
103. #10622458C22semidirect
104. #10622458C22semidirect
105. #10622449C22semidirect
106. #10622449C22semidirect
107. #10622429C22semidirect
108. #10622426C22semidirect
109. #10622425C22semidirect
110. #10622423C22semidirect
111. #10622421C22semidirect
112. #10622421C22semidirect
113. #10622421C22semidirect
114. #10622420C22semidirect
115. #10622419C22semidirect
116. #10622419C22semidirect
117. #10622416C22semidirect
118. D11×#103C22semidirect
119. #10622396C22semidirect
120. #10622389C22semidirect
121. #10622384C22semidirect
122. D11×#102C22semidirect
123. #10622346C22semidirect
124. #10622346C22semidirect
125. #10622339C22semidirect
126. D11×C22⋊C8C22semidirect
127. #10622312C22semidirect
128. #10622307C22semidirect
129. #10622306C22semidirect
130. #10622301C22semidirect
131. #10622301C22semidirect
134. #10622294C22semidirect
493. #3107D11semidirect
557. D44#137semidirect
611. #533C2×D11semidirect
629. #485C2×D11semidirect
630. #485C2×D11semidirect
637. #475C2×D11semidirect
638. #474C2×D11semidirect
652. #462C2×D11semidirect
654. #461C2×D11semidirect
678. C4×Q16C2×D11semidirect
679. C4×Q16C2×D11semidirect
680. C4×SD16C2×D11semidirect
681. C4×SD16C2×D11semidirect
689. #431C2×D11semidirect
1079. C11#61607semidirect

Maximal subgroups

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

subgroupindex
#130824172
#41×D442
#130809562
#130809342
#130807242
#130806942
#130804942
#130804422
Q16×D442
SD16×D442
#130802832
#130802632
#130801922
#130801322
#130796232
#130795742
#130794502
#130794012
#130787782
#130778732
D11×#4522
#130776502
C11×#31072
#6160711