Finite Group Databasebeta

← #15638587

Subgroups — #15638587

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082667C211yesmaximal, characteristic, complemented
2#41×D44C211yesmaximal, characteristic, complemented
3#13080557C211yesmaximal, characteristic, complemented
4#13080535C211yesmaximal, characteristic, complemented
5#13080500C212yesmaximal, complemented
6#13080483C211yesmaximal, characteristic, complemented
7#13080448C212yesmaximal, complemented
8#13080431C211yesmaximal, characteristic, complemented
9Q16×D44C211yesmaximal, characteristic, complemented
10#13080352C212yesmaximal, complemented
11#13080347C211yesmaximal, characteristic, complemented
12#13080337C211yesmaximal, characteristic, complemented
13#13080329C212yesmaximal, complemented
14SD16×D44C211yesmaximal, characteristic, complemented
15#13079588C211yesmaximal, characteristic, complemented
16#13079574C211yesmaximal, characteristic, complemented
17#13079407C212yesmaximal, complemented
18#13079401C212yesmaximal, complemented
19#13078687C211yesmaximal, characteristic, complemented
20#13077831C212yesmaximal, complemented
21D11×#452C212yesmaximal, complemented
22#13077639C211yesmaximal, characteristic, complemented
23C11×#3102C211yesmaximal, characteristic, complemented
24C2×#41×D11C2212yes—
25C11×#529C2211yescharacteristic, complemented
26C4×C11×#41C2211yescharacteristic
27C2×Q16×D11C2212yescomplemented
28C2×#66969C2212yescomplemented
29C2×SD16×D11C2212yescomplemented
30C2×#66965C2212yescomplemented
31#10623238—22no—
32#10623225C2212yescomplemented
33#10623208C2212yescomplemented
34#10623189—22no—
35D11×C22⋊Q8C2212yescomplemented
36#10623137C2212yescomplemented
37#10623115C2211yescharacteristic, complemented
38#10623108C2211yescharacteristic
39#10623107C2212yes—
40Q8×D44C2211yescharacteristic
41Q8×D44C2211yescharacteristic
42#10623086—21no—
43#10623086C2211yescharacteristic
44#10623086C2211yescharacteristic, complemented
45#10623085—22no—
46#10623085C2212yes—
47#10623082C2211yescharacteristic
48#10623081—21no—
49D4×D44—21no—
50D4×D44C2211yescharacteristic
51#10623074—21no—
52#10623065—21no—
53#10623055—22no—
54#10623055C2212yes—
55#10623054—21no—
56#10623008—21no—
57#10623008C2211yescharacteristic
58C2×C4×D44—21no—
59C2×C4×D44C2211yescharacteristic
60#10623001C2211yescharacteristic, complemented
61C11×#485C2211yescharacteristic, complemented
62C11×#482C2211yescharacteristic, complemented
63C11×#479C2211yescharacteristic, complemented
64C11×#478C2211yescharacteristic, complemented
65C11×#464C2211yescharacteristic, complemented
66C11×#463C2211yescharacteristic, complemented
67C11×#452C2211yescharacteristic
68C11×#449C2211yescharacteristic
69C4×C11×Q16C2211yescharacteristic, complemented
70C4×C11×SD16C2211yescharacteristic, complemented
71C4×C11×SD16C2211yescharacteristic, complemented
72C4×C11×D8C2211yescharacteristic, complemented
73C11×#431C2211yescharacteristic, complemented
74#10622852C2212yes—
75#10622800C2212yescomplemented
76#10622786C2212yescomplemented
77#10622783C2212yescomplemented
78#10622769C2212yescomplemented
79#10622681C2212yescomplemented
80#10622672C2212yescomplemented
81#10622660C2212yescomplemented
82#10622650C2212yescomplemented
83#10622644C2211yescharacteristic, complemented
84#10622644C2211yescharacteristic, complemented
85C4×#4326C2212yescomplemented
86#10622640C2211yescharacteristic, complemented
87#10622633C2211yescharacteristic, complemented
88#10622632C2211yescharacteristic, complemented
89#10622632C2211yescharacteristic, complemented
90C4×#4324C2212yescomplemented
91#10622628C2211yescharacteristic, complemented
92#10622620C2211yescharacteristic, complemented
93#10622609C2212yescomplemented
94#10622538C2211yescharacteristic, complemented
95#10622500C2212yescomplemented
96#10622500C2212yescomplemented
97#10622498C2212yescomplemented
98#10622495C2212yescomplemented
99#10622480C2212yescomplemented
100#10622477C2212yescomplemented
101#10622477C2212yescomplemented
102#10622475C2212yescomplemented
103#10622458C2212yescomplemented
104#10622458C2212yescomplemented
105#10622447C2212yescomplemented
106#10622447C2212yescomplemented
107#10622426C2212yescomplemented
108#10622423C2212yescomplemented
109#10622421C2212yescomplemented
110#10622421C2212yescomplemented
111#10622420C2212yescomplemented
112#10622419C2212yescomplemented
113#10622417C2212yescomplemented
114D11×#103C2212yescomplemented
115#10622396C2212yescomplemented
116#10622396C2212yescomplemented
117#10622394C2212yescomplemented
118#10622391C2212yescomplemented
119#10622389C2212yescomplemented
120#10622388C2212yescomplemented
121#10622385C2212yescomplemented
122D11×#102C2212yescomplemented
123#10622346C2212yescomplemented
124#10622346C2212yescomplemented
125D11×C22⋊C8C2212yescomplemented
126D11×C22⋊C8C2212yescomplemented
127#10622312C2211yescharacteristic, complemented
128#10622307C2211yescharacteristic, complemented
129#10622306C2211yescharacteristic, complemented
130C8×D44C2211yescharacteristic
131C8×D44C2211yescharacteristic
132C8×D44C2211yescharacteristic, complemented
133C8×D44C2211yescharacteristic, complemented
134#10622294C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136#41×D11—44no—
137#41×D11—44no—
138C2×#4343C2312yes—
139C2×Q8×D11C2312yes—
140C2×Q8×D11C2312yes—
141C2×#4341—22no—
142C2×#4341C2312yes—
143C2×#4341C2312yes—
144C2×D4×D11—22no—
145C2×D4×D11C2312yes—
146C2×#4339—21no—
147C2×#4339—22no—
148C2×#4339C2312yes—
149C22×D44—21no—
150C22×D44D411yescharacteristic
151C22×C4×D11—22no—
152C22×C4×D11C2312yes—
153C2×C11×Q16C2311yescharacteristic
154C2×C11×SD16C2311yescharacteristic
155C2×C11×SD16C2311yescharacteristic
156C2×C11×D8C2311yescharacteristic
157C11×#126—21no—
158C11×#125C2311yescharacteristic
159C11×#124C2311yescharacteristic
160C11×#123—21no—
161C11×C22⋊Q8C2311yescharacteristic
162C11×#121C2311yescharacteristic
163C4×Q8×C11C2311yescharacteristic
164C4×Q8×C11C2311yescharacteristic
165C4×Q8×C11C2311yescharacteristic
166C4×D4×C11—21no—
167C4×D4×C11—21no—
168C4×D4×C11—21no—
169C4×D4×C11C2311yescharacteristic
170C4×D4×C11C2311yescharacteristic
171C4×D4×C11C2311yescharacteristic
172C11×#117—21no—
173C11×#117—21no—
174C11×#117C2311yescharacteristic
175C2×C42×C11—21no—
176C2×C42×C11C2311yescharacteristic
177#66999C2312yes—
178C2×#4326C2312yes—
179C2×#4326C2312yes—
180C2×#4325C2312yes—
181#66991C2312yes—
182#66990—22no—
183D4×Dic11—22no—
184C2×#4324C2312yes—
185C2×#4324C2312yes—
186C2×#4323C2312yes—
187#66983—21no—
188#66983—21no—
189#66983—21no—
190#66983—21no—
191#66983—22no—
192#66983—21no—
193C2×(C2×D11)⋊C4—22no—
194C2×(C2×D11)⋊C4D412yes—
195#66979—21no—
196C2×C4⋊Dic11—21no—
197C2×C4⋊Dic11—21no—
198C2×C4⋊Dic11D411yescharacteristic
199#66977—21no—
200#66977—21no—
201#66977C2312yes—
202Q16×D11—44no—
203#66969—44no—
204SD16×D11—44no—
205#66965—44no—
206C2×Dic44C2312yes—
207C2×Dic44C2312yes—
208C2×#4314C2312yes—
209C2×#4314C2312yes—
210C2×C8×D11C2312yes—
211C2×C8×D11C2312yes—
212C2×C8×D11C2312yes—
213C2×C8×D11C2312yes—
214#66951—22no—
215#66951—22no—
216#66950—22no—
217#66950—22no—
218#66950—22no—
219#66950C2312yes—
220#66950C2312yes—
221#66950C2312yes—
222#66950C2312yes—
223#66949—22no—
224#66948—22no—
225#66948—22no—
226#66948C2312yes—
227#66948C2312yes—
228#66947—22no—
229#66945—22no—
230#66945C2312yes—
231C4⋊C4×D11—22no—
232C4⋊C4×D11C2312yes—
233#66943—22no—
234#66939—22no—
235#66939—22no—
236#66939—22no—
237#66939—22no—
238#66938—22no—
239#66937—22no—
240#66936—22no—
241#66936—22no—
242#66935—22no—
243#66935—22no—
244#66935—22no—
245(C22⋊D11)⋊C4—22no—
246(C22⋊D11)⋊C4—22no—
247C22⋊C4×D11—22no—
248#66931—22no—
249#66931—22no—
250#66928—21no—
251#66928—22no—
252#66928C2312yes—
253#66927—21no—
254#66927C2311yescharacteristic
255C4×D44—21no—
256C4×D44—21no—
257C4×D44—22no—
258C4×D44—22no—
259C4×D44—21no—
260C4×D44—21no—
261C4×D44—22no—
262C4×D44—21no—
263C4×D44D412yes—
264C4×D44D411yescharacteristic
265C4×D44D411yescharacteristic
266C4×D44C2311yescharacteristic
267C4×D44C2311yescharacteristic
268C4×D44C2312yes—
269#66923—21no—
270#66922—21no—
271#66922—21no—
272#66922C2311yescharacteristic
273#66922C2311yescharacteristic
274#66922C2311yescharacteristic
275C4×Dic22—21no—
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×#102C2311yescharacteristic
289C11×#102C2311yescharacteristic
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
317C4×C11⋊C8C2312yes—
318#61568—111nomaximal, Sylow
319C23×D11—22no—
320C23×D11C2×D412yes—
321C11×#41—22no—
322C11×#41—22no—
323C2×Q8×C11C2411yescharacteristic
324C2×Q8×C11C2411yescharacteristic
325C2×D4×C11—21no—
326C2×D4×C11—21no—
327C2×D4×C11C2411yescharacteristic
328C2×D4×C11C2411yescharacteristic
329C22×C4×C11—21no—
330C22×C4×C11—21no—
331C22×C4×C11—21no—
332C22×C4×C11—21no—
333C22×C4×C11C2×D411yescharacteristic
334C22×C4×C11C2×D411yescharacteristic
335C22×C4×C11C2411yescharacteristic
336C2×C22⋊D11—22no—
337C2×C22⋊D11—22no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C22×Dic11—22no—
342C22×Dic11—22no—
343C22×Dic11C2×D412yes—
344#4343—24no—
345#4343—42no—
346Q8×D11—24no—
347Q8×D11—42no—
348Q8×D11—42no—
349Q8×D11—42no—
350#4341—24no—
351#4341—42no—
352#4341—42no—
353#4341—42no—
354#4341—48no—
355D4×D11—24no—
356D4×D11—42no—
357D4×D11—48no—
358#4339—42no—
359#4339—42no—
360#4339—48no—
361#4339—44no—
362C2×D44—24no—
363C2×D44—22no—
364C2×D44—22no—
365C2×D44—22no—
366C2×D44—21no—
367C2×D44—21no—
368C2×D44—44no—
369C2×D44C2×D411yescharacteristic
370C2×D44C2×D412yes—
371C2×D44C2×D411yescharacteristic
372C2×D44C2412yes—
373C2×C4×D11—22no—
374C2×C4×D11—22no—
375C2×C4×D11—22no—
376C2×C4×D11—22no—
377C2×C4×D11—22no—
378C2×C4×D11—42no—
379C2×C4×D11—42no—
380C2×C4×D11—48no—
381C2×C4×D11C2×D412yes—
382C2×C4×D11C2×D412yes—
383C2×C4×D11C2412yes—
384C2×C4×D11C2412yes—
385C2×Dic22—22no—
386C2×Dic22—22no—
387C2×Dic22—21no—
388C2×Dic22C2412yes—
389C2×Dic22C2412yes—
390C11×Q16—22no—
391C11×SD16—22no—
392C11×SD16—22no—
393C11×D8—22no—
394C2×C8×C11C2411yescharacteristic
395C2×C8×C11C2411yescharacteristic
396C2×C8×C11C2411yescharacteristic
397C2×C8×C11C2411yescharacteristic
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⋊C4C2411yescharacteristic
405C11×C4⋊C4C2411yescharacteristic
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C22⋊C4—21no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C42×C11—21no—
417C42×C11—21no—
418C42×C11—21no—
419C42×C11—21no—
420C42×C11C2×D411yescharacteristic
421C42×C11C2×D411yescharacteristic
422C42×C11C2411yescharacteristic
423C42×C11C2411yescharacteristic
424C22⋊Dic11—22no—
425C22⋊Dic11—22no—
426#4326—24no—
427#4326—42no—
428#4325—42no—
429#4324—24no—
430#4324—42no—
431#4323—42no—
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)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4C2×D412yes—
443(C2×D11)⋊C4C2×D412yes—
444(C2×D11)⋊C4C2×D412yes—
445(C2×D11)⋊C4C2×D412yes—
446C4⋊Dic11—22no—
447C4⋊Dic11—22no—
448C4⋊Dic11—22no—
449C4⋊Dic11—22no—
450C4⋊Dic11—21no—
451C4⋊Dic11—21no—
452C4⋊Dic11—21no—
453C4⋊Dic11—21no—
454C4⋊Dic11—21no—
455C4⋊Dic11C2×D411yescharacteristic
456C4⋊Dic11C2×D411yescharacteristic
457C4⋊Dic11C2×D412yes—
458C4⋊Dic11C2412yes—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463C4×Dic11—22no—
464C4×Dic11—22no—
465C2×C11⋊C8C2412yes—
466C2×C11⋊C8C2412yes—
467Dic44—42no—
468Dic44—42no—
469#4314—42no—
470#4314—42no—
471C8×D11—42no—
472C8×D11—42no—
473C8×D11—42no—
474C8×D11—42no—
475#3520—111no—
476D4×#41—111no—
477#3304—111no—
478#3302—111no—
479#3300—112no—
480#3298—111no—
481#3296—112no—
482#3294—111no—
483D4×Q16—111no—
484#3285—112no—
485#3284—111no—
486#3283—111no—
487#3282—112no—
488D4×SD16—111no—
489#3212—111no—
490#3210—111no—
491#3191—112no—
492#3190—112no—
493#3107—111no—
494#3102D1111yescharacteristic, complemented
495#3002—112no—
496C2×#452—112no—
497#2972—111no—
498C23×C11—21no—
499C23×C11—21no—
500C23×C11C22×D411yescharacteristic
501C22×D11—24no—
502C22×D11—22no—
503C22×D11—42no—
504C22×D11—42no—
505C22×D11—44no—
506C22×D11—44no—
507C22×D11—82no—
508C22×D11C22×D412yes—
509C22×D11C22×D412yes—
510Q8×C11—21no—
511Q8×C11—21no—
512Q8×C11—21no—
513Q8×C11H(5,𝔽2)12yes—
514D4×C11—24no—
515D4×C11—21no—
516D4×C11—21no—
517D4×C11—21no—
518D4×C11—42no—
519D4×C11H(5,𝔽2)12yes—
520C2×C4×C11—24no—
521C2×C4×C11—21no—
522C2×C4×C11—22no—
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—21no—
530C2×C4×C11—41no—
531C2×C4×C11—42no—
532C2×C4×C11—42no—
533C2×C4×C11—81no—
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D411yescharacteristic
539C2×C4×C11C2511yescharacteristic
540C22⋊D11—44no—
541C22⋊D11—44no—
542C22⋊D11—44no—
543C22⋊D11—44no—
544C22⋊D11—82no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—42no—
549C2×Dic11—44no—
550C2×Dic11—82no—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553D44—24no—
554D44—22no—
555D44—22no—
556D44—22no—
557D44—44no—
558D44—44no—
559D44—42no—
560D44—81no—
561D44—82no—
562D44#13514yescomplemented
563C4×D11—22no—
564C4×D11—22no—
565C4×D11—22no—
566C4×D11—22no—
567C4×D11—42no—
568C4×D11—42no—
569C4×D11—44no—
570C4×D11—44no—
571C4×D11—44no—
572C4×D11—44no—
573C4×D11—82no—
574Dic22—22no—
575Dic22—22no—
576Dic22—22no—
577Dic22—22no—
578Dic22—44no—
579Dic22—42no—
580Dic22—82no—
581C8×C11—21no—
582C8×C11—21no—
583C8×C11—21no—
584C8×C11—21no—
585C11⋊C8—22no—
586C11⋊C8—22no—
587C22×#41—112no—
588C2×#135—112no—
589C2×#135—112no—
590C22×Q16—112no—
591C22×SD16—112no—
592#556—111no—
593#554—221no—
594#552—112no—
595#551—222no—
596#550—111no—
597D4×Q8—111no—
598D4×Q8—111no—
599#548—112no—
600#548—112no—
601#547—111no—
602#547—111no—
603#547—111no—
604#547—221no—
605#546—112no—
606#546—222no—
607#546—221no—
608D42—111no—
609D42—221no—
610#542—221no—
611#539—222no—
612#533—111no—
613#532—111no—
614#532—221no—
615#529C2×D1111yescharacteristic, complemented
616#525—112no—
617#525—112no—
618#525—222no—
619C2×C22⋊Q8—112no—
620#520—221no—
621C4×#41C2×D1111yescharacteristic
622C2×C4×D4—111no—
623C2×C4×D4—221no—
624#495—112no—
625#494—111no—
626#492—111no—
627#488—112no—
628#487—111no—
629#486—111no—
630#485—112no—
631#485—112no—
632#485C2×D1111yescharacteristic, complemented
633#483—112no—
634#482—112no—
635#482C2×D1111yescharacteristic, complemented
636#480—112no—
637#479C2×D1111yescharacteristic, complemented
638#478C2×D1111yescharacteristic, complemented
639#475—111no—
640#474—111no—
641#467—112no—
642#467—112no—
643#467—112no—
644#466—112no—
645#465—112no—
646#465—112no—
647#465—112no—
648#465—112no—
649#464—112no—
650#464—112no—
651#464C2×D1111yescharacteristic, complemented
652#463C2×D1111yescharacteristic, complemented
653#462—111no—
654#462—111no—
655#461—111no—
656#461—111no—
657#460—111no—
658#459—111no—
659#452—112no—
660#452—112no—
661#452—112no—
662#452—112no—
663#452—112no—
664#452—112no—
665#452—112no—
666#452—112no—
667#452—112no—
668#452C2×D1111yescharacteristic
669#451—112no—
670#451—112no—
671#450—112no—
672#449—112no—
673#449—112no—
674#449C2×D1111yescharacteristic
675#448—112no—
676#448—112no—
677#447—112no—
678C4×Q16—112no—
679C4×Q16C2×D1111yescharacteristic, complemented
680C4×SD16—112no—
681C4×SD16C2×D1111yescharacteristic, complemented
682C4×SD16C2×D1111yescharacteristic, complemented
683C4×D8C2×D1111yescharacteristic, complemented
684C8×D4—112no—
685C8×D4—112no—
686C8×D4—111no—
687C8×D4—111no—
688C8×D4—111no—
689C8×D4—111no—
690#431—111no—
691#431C2×D1111yescharacteristic, complemented
692#416—112no—
693#416—112no—
694C2×#103—112no—
695C2×#102—112no—
696C2×C22⋊C8—112no—
697C2×C22⋊C8—112no—
698C22×C11—21no—
699C22×C11—21no—
700C22×C11—22no—
701C22×C11—21no—
702C22×C11—41no—
703C22×C11—41no—
704C22×C11—41no—
705C22×C11—41no—
706C22×C11—41no—
707C22×C11C23×D411yescharacteristic
708C2×D11—22no—
709C2×D11—22no—
710C2×D11—22no—
711C2×D11—22no—
712C2×D11—22no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—84no—
717C2×D11—88no—
718C2×D11C2×#13514yes—
719C4×C11—21no—
720C4×C11—21no—
721C4×C11—21no—
722C4×C11—22no—
723C4×C11—21no—
724C4×C11—41no—
725C4×C11—41no—
726C4×C11—41no—
727C4×C11—41no—
728C4×C11—41no—
729C4×C11C2×#13512yes—
730C4×C11C2×H(5,𝔽2)11yescharacteristic
731C4×C11C2×H(5,𝔽2)11yescharacteristic
732Dic11—22no—
733Dic11—22no—
734Dic11—42no—
735Dic11—42no—
736Dic11—42no—
737C2×#41—112no—
738C2×#41—112no—
739C2×#41—112no—
740C2×#41—112no—
741C2×#41—222no—
742C2×#41—221no—
743C2×#41—222no—
744C2×#41—444no—
745C2×#41—444no—
746C2×#41C22×D1111yescharacteristic
747C22×Q8—112no—
748C22×Q8—112no—
749C22×D4—112no—
750C22×D4—111no—
751C22×D4—221no—
752C22×D4—222no—
753C23×C4—112no—
754C23×C4—222no—
755#135—444no—
756#135—444no—
757C2×Q16—112no—
758C2×Q16—112no—
759C2×Q16—112no—
760C2×Q16—112no—
761C2×Q16—444no—
762C2×Q16C22×D1111yescharacteristic
763C2×SD16—112no—
764C2×SD16—112no—
765C2×SD16—112no—
766C2×SD16—112no—
767C2×SD16—112no—
768C2×SD16—444no—
769C2×SD16C22×D1111yescharacteristic
770C2×SD16C22×D1111yescharacteristic
771C2×D8—112no—
772C2×D8C22×D1111yescharacteristic
773C22×C8—112no—
774C22×C8—112no—
775C22×C8—112no—
776C22×C8—112no—
777C4⋊Q8—111no—
778C4⋊Q8—111no—
779C4⋊Q8—111no—
780C4⋊Q8—221no—
781C4⋊Q8—221no—
782#127—111no—
783#127—221no—
784#126—21no—
785#126—222no—
786#126—222no—
787#125—222no—
788#125—221no—
789#125C22×D1111yescharacteristic
790#124—112no—
791#124—222no—
792#124—221no—
793#124—222no—
794#124C22×D1111yescharacteristic
795#123—21no—
796#123—222no—
797#123—222no—
798#123—222no—
799#123—222no—
800#123—222no—
801#123—222no—
802#123—222no—
803C22⋊Q8—112no—
804C22⋊Q8—112no—
805C22⋊Q8—112no—
806C22⋊Q8—112no—
807C22⋊Q8—112no—
808C22⋊Q8—112no—
809C22⋊Q8—222no—
810C22⋊Q8—222no—
811C22⋊Q8—222no—
812C22⋊Q8—222no—
813C22⋊Q8—222no—
814C22⋊Q8—222no—
815C22⋊Q8—221no—
816C22⋊Q8—221no—
817C22⋊Q8C22×D1111yescharacteristic
818#121—112no—
819#121—112no—
820#121—112no—
821#121—222no—
822#121—222no—
823#121—222no—
824#121—222no—
825#121—221no—
826#121—221no—
827#121—221no—
828#121—221no—
829#121—221no—
830#121C22×D1111yescharacteristic
831#120—222no—
832#120—222no—
833#120—222no—
834#120—222no—
835C4×Q8—112no—
836C4×Q8—221no—
837C4×Q8—221no—
838C4×Q8C22×D1111yescharacteristic
839C4×Q8C22×D1111yescharacteristic
840C4×Q8C22×D1111yescharacteristic
841C4×D4—21no—
842C4×D4—21no—
843C4×D4—21no—
844C4×D4—111no—
845C4×D4—112no—
846C4×D4—111no—
847C4×D4—111no—
848C4×D4—112no—
849C4×D4—111no—
850C4×D4—222no—
851C4×D4—221no—
852C4×D4—222no—
853C4×D4—222no—
854C4×D4—221no—
855C4×D4—221no—
856C4×D4—222no—
857C4×D4—222no—
858C4×D4—222no—
859C4×D4—221no—
860C4×D4—221no—
861C4×D4C22×D1111yescharacteristic
862C4×D4C22×D1111yescharacteristic
863C4×D4C22×D1111yescharacteristic
864#117—21no—
865#117—21no—
866#117—112no—
867#117—222no—
868#117—221no—
869#117C22×D1111yescharacteristic
870C2×C4⋊C4—111no—
871C2×C4⋊C4—112no—
872C2×C4⋊C4—222no—
873C2×C4⋊C4—221no—
874C2×C4⋊C4—221no—
875C2×C22⋊C4—112no—
876C2×C22⋊C4—222no—
877C2×C22⋊C4—222no—
878C2×C42—21no—
879C2×C42C22×D1111yescharacteristic
880#107—112no—
881#107C22×D1111yescharacteristic
882#107C22×D1111yescharacteristic
883#106—112no—
884#106C22×D1111yescharacteristic
885#106C22×D1111yescharacteristic
886C4⋊C8—111no—
887C4⋊C8—111no—
888C4⋊C8C22×D1111yescharacteristic
889C4⋊C8C22×D1111yescharacteristic
890#103—112no—
891#103—112no—
892#103—112no—
893#103—112no—
894#103—112no—
895#103—112no—
896#103—112no—
897#103C22×D1111yescharacteristic
898#103C22×D1111yescharacteristic
899#103C22×D1111yescharacteristic
900#103C22×D1111yescharacteristic
901#102—112no—
902#102—112no—
903#102—112no—
904#102—112no—
905#102—112no—
906#102C22×D1111yescharacteristic
907#102C22×D1111yescharacteristic
908#102C22×D1111yescharacteristic
909#102C22×D1111yescharacteristic
910C22⋊C8—112no—
911C22⋊C8—112no—
912C22⋊C8—112no—
913C22⋊C8—112no—
914C22⋊C8—112no—
915C22⋊C8C22×D1111yescharacteristic
916C22⋊C8C22×D1111yescharacteristic
917C4×C8—112no—
918C4×C8C22×D1111yescharacteristic
919C4×C8C22×D1111yescharacteristic
920C2×C11—41no—
921C2×C11—42no—
922C2×C11—81no—
923C2×C11#348411yescharacteristic
924C2×C11C22×#13511yescharacteristic
925C2×C11#358611yescharacteristic
926D11—24no—
927D11—42no—
928D11—82no—
929C24—112no—
930C24—222no—
931#41—22no—
932#41—22no—
933#41—224no—
934#41—224no—
935#41—442no—
936#41—442no—
937#41—448no—
938#41—444no—
939#41—442no—
940#41—442no—
941#41—442no—
942#41—442no—
943#41—448no—
944C2×Q8—112no—
945C2×Q8—112no—
946C2×Q8—222no—
947C2×Q8—222no—
948C2×Q8—221no—
949C2×Q8—224no—
950C2×Q8—442no—
951C2×Q8—442no—
952C2×Q8—442no—
953C2×Q8C23×D1111yescharacteristic
954C2×Q8C23×D1111yescharacteristic
955C2×D4—21no—
956C2×D4—21no—
957C2×D4—111no—
958C2×D4—112no—
959C2×D4—111no—
960C2×D4—112no—
961C2×D4—224no—
962C2×D4—222no—
963C2×D4—222no—
964C2×D4—222no—
965C2×D4—222no—
966C2×D4—224no—
967C2×D4—222no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—222no—
971C2×D4—221no—
972C2×D4—221no—
973C2×D4—444no—
974C2×D4—442no—
975C2×D4—448no—
976C2×D4C23×D1111yescharacteristic
977C2×D4C23×D1111yescharacteristic
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—112no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—222no—
988C22×C4—222no—
989C22×C4—222no—
990C22×C4—222no—
991C22×C4—222no—
992C22×C4—222no—
993C22×C4—222no—
994C22×C4—442no—
995C22×C4—442no—
996C22×C4—448no—
997C22×C4D4×D1111yescharacteristic
998C22×C4D4×D1111yescharacteristic
999C22×C4C23×D1111yescharacteristic
1000Q16—22no—
1001Q16—224no—
1002Q16—442no—
1003Q16—442no—
1004Q16—442no—
1005SD16—22no—
1006SD16—22no—
1007SD16—224no—
1008SD16—442no—
1009SD16—442no—
1010SD16—442no—
1011SD16—442no—
1012D8—22no—
1013D8—442no—
1014C2×C8—112no—
1015C2×C8—112no—
1016C2×C8—442no—
1017C2×C8—442no—
1018C2×C8—442no—
1019C2×C8—442no—
1020C2×C8C23×D1111yescharacteristic
1021C2×C8C23×D1111yescharacteristic
1022C2×C8C23×D1111yescharacteristic
1023C2×C8C23×D1111yescharacteristic
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—111no—
1031C4⋊C4—111no—
1032C4⋊C4—112no—
1033C4⋊C4—112no—
1034C4⋊C4—222no—
1035C4⋊C4—222no—
1036C4⋊C4—222no—
1037C4⋊C4—222no—
1038C4⋊C4—222no—
1039C4⋊C4—222no—
1040C4⋊C4—221no—
1041C4⋊C4—221no—
1042C4⋊C4—222no—
1043C4⋊C4—221no—
1044C4⋊C4—221no—
1045C4⋊C4—221no—
1046C4⋊C4—222no—
1047C4⋊C4C23×D1111yescharacteristic
1048C4⋊C4C23×D1111yescharacteristic
1049C4⋊C4C23×D1111yescharacteristic
1050C4⋊C4C23×D1111yescharacteristic
1051C22⋊C4—21no—
1052C22⋊C4—21no—
1053C22⋊C4—21no—
1054C22⋊C4—21no—
1055C22⋊C4—21no—
1056C22⋊C4—21no—
1057C22⋊C4—21no—
1058C22⋊C4—21no—
1059C22⋊C4—112no—
1060C22⋊C4—112no—
1061C22⋊C4—112no—
1062C22⋊C4—112no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—222no—
1080C42—222no—
1081C42D4×D1111yescharacteristic
1082C42D4×D1111yescharacteristic
1083C42C23×D1111yescharacteristic
1084C42C23×D1111yescharacteristic
1085C11#6156811yescharacteristic, complemented, Sylow
1086C23—21no—
1087C23—21no—
1088C23—112no—
1089C23—112no—
1090C23—224no—
1091C23—222no—
1092C23—442no—
1093C23—442no—
1094C23—444no—
1095C23—444no—
1096C23—882no—
1097C23C2×D4×D1111yescharacteristic
1098Q8—21no—
1099Q8—21no—
1100Q8—21no—
1101Q8—222no—
1102Q8—222no—
1103Q8—222no—
1104Q8—222no—
1105Q8—444no—
1106Q8—442no—
1107Q8—882no—
1108Q8#6704212yes—
1109D4—24no—
1110D4—21no—
1111D4—21no—
1112D4—21no—
1113D4—42no—
1114D4—114no—
1115D4—224no—
1116D4—222no—
1117D4—222no—
1118D4—222no—
1119D4—444no—
1120D4—444no—
1121D4—444no—
1122D4—444no—
1123D4—444no—
1124D4—444no—
1125D4—442no—
1126D4—881no—
1127D4—882no—
1128D4—882no—
1129D4#6704212yes—
1130C2×C4—24no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—81no—
1144C2×C4—112no—
1145C2×C4—112no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—442no—
1154C2×C4—442no—
1155C2×C4—444no—
1156C2×C4—444no—
1157C2×C4—444no—
1158C2×C4—444no—
1159C2×C4—442no—
1160C2×C4—444no—
1161C2×C4—882no—
1162C2×C4—882no—
1163C2×C4C2×D4×D1111yescharacteristic
1164C2×C4C2×D4×D1111yescharacteristic
1165C2×C4C2×D4×D1111yescharacteristic
1166C2×C4C2×D4×D1111yescharacteristic
1167C2×C4C2×D4×D1111yescharacteristic
1168C2×C4C24×D1111yescharacteristic
1169C8—21no—
1170C8—21no—
1171C8—21no—
1172C8—21no—
1173C8—222no—
1174C8—222no—
1175C22—21no—
1176C22—21no—
1177C22—22no—
1178C22—21no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—114no—
1185C22—222no—
1186C22—222no—
1187C22—222no—
1188C22—222no—
1189C22—222no—
1190C22—442no—
1191C22—442no—
1192C22—442no—
1193C22—884no—
1194C22—888no—
1195C22C22×D4×D1111yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—21no—
1199C4—22no—
1200C4—21no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—222no—
1207C4—222no—
1208C4—442no—
1209C4—442no—
1210C4—442no—
1211C4D11×#13512yes—
1212C4C2×#6704211yescharacteristic
1213C4C2×#6704211yescharacteristic
1214C2—41no—
1215C2—42no—
1216C2—81no—
1217C2—224no—
1218C2—442no—
1219C2—882no—
1220C2#1308224911yescharacteristic
1221C2C2×D11×#13511yescharacteristic
1222C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3102C2
socleC22×C11C23×D4
hypercenter#3102D11
hypocenterC11#61568
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #13082667C2semidirect
2. #41×D44C2semidirect
3. #13080557C2semidirect
4. #13080535C2semidirect
5. #13080500C2semidirect
6. #13080483C2semidirect
7. #13080448C2semidirect
8. #13080431C2semidirect
9. Q16×D44C2semidirect
10. #13080352C2semidirect
11. #13080347C2semidirect
12. #13080337C2semidirect
13. #13080329C2semidirect
14. SD16×D44C2semidirect
15. #13079588C2semidirect
16. #13079574C2semidirect
17. #13079407C2semidirect
18. #13079401C2semidirect
19. #13078687C2semidirect
20. #13077831C2semidirect
21. D11×#452C2semidirect
22. #13077639C2semidirect
23. C11×#3102C2semidirect
25. C11×#529C22semidirect
27. C2×Q16×D11C22semidirect
28. C2×#66969C22semidirect
29. C2×SD16×D11C22semidirect
30. C2×#66965C22semidirect
32. #10623225C22semidirect
33. #10623208C22semidirect
35. D11×C22⋊Q8C22semidirect
36. #10623137C22semidirect
37. #10623115C22semidirect
44. #10623086C22semidirect
60. #10623001C22semidirect
61. C11×#485C22semidirect
62. C11×#482C22semidirect
63. C11×#479C22semidirect
64. C11×#478C22semidirect
65. C11×#464C22semidirect
66. C11×#463C22semidirect
69. C4×C11×Q16C22semidirect
70. C4×C11×SD16C22semidirect
71. C4×C11×SD16C22semidirect
72. C4×C11×D8C22semidirect
73. C11×#431C22semidirect
75. #10622800C22semidirect
76. #10622786C22semidirect
77. #10622783C22semidirect
78. #10622769C22semidirect
79. #10622681C22semidirect
80. #10622672C22semidirect
81. #10622660C22semidirect
82. #10622650C22semidirect
83. #10622644C22semidirect
84. #10622644C22semidirect
85. C4×#4326C22semidirect
86. #10622640C22semidirect
87. #10622633C22semidirect
88. #10622632C22semidirect
89. #10622632C22semidirect
90. C4×#4324C22semidirect
91. #10622628C22semidirect
92. #10622620C22semidirect
93. #10622609C22semidirect
94. #10622538C22semidirect
95. #10622500C22semidirect
96. #10622500C22semidirect
97. #10622498C22semidirect
98. #10622495C22semidirect
99. #10622480C22semidirect
100. #10622477C22semidirect
101. #10622477C22semidirect
102. #10622475C22semidirect
103. #10622458C22semidirect
104. #10622458C22semidirect
105. #10622447C22semidirect
106. #10622447C22semidirect
107. #10622426C22semidirect
108. #10622423C22semidirect
109. #10622421C22semidirect
110. #10622421C22semidirect
111. #10622420C22semidirect
112. #10622419C22semidirect
113. #10622417C22semidirect
114. D11×#103C22semidirect
115. #10622396C22semidirect
116. #10622396C22semidirect
117. #10622394C22semidirect
118. #10622391C22semidirect
119. #10622389C22semidirect
120. #10622388C22semidirect
121. #10622385C22semidirect
122. D11×#102C22semidirect
123. #10622346C22semidirect
124. #10622346C22semidirect
125. D11×C22⋊C8C22semidirect
126. D11×C22⋊C8C22semidirect
127. #10622312C22semidirect
128. #10622307C22semidirect
129. #10622306C22semidirect
132. C8×D44C22semidirect
133. C8×D44C22semidirect
134. #10622294C22semidirect
494. #3102D11semidirect
562. D44#135semidirect
615. #529C2×D11semidirect
632. #485C2×D11semidirect
635. #482C2×D11semidirect
637. #479C2×D11semidirect
638. #478C2×D11semidirect
651. #464C2×D11semidirect
652. #463C2×D11semidirect
679. C4×Q16C2×D11semidirect
681. C4×SD16C2×D11semidirect
682. C4×SD16C2×D11semidirect
683. C4×D8C2×D11semidirect
691. #431C2×D11semidirect
1085. C11#61568semidirect

Maximal subgroups

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

subgroupindex
#130826672
#41×D442
#130805572
#130805352
#130805002
#130804832
#130804482
#130804312
Q16×D442
#130803522
#130803472
#130803372
#130803292
SD16×D442
#130795882
#130795742
#130794072
#130794012
#130786872
#130778312
D11×#4522
#130776392
C11×#31022
#6156811