Finite Group Databasebeta

← #15638583

Subgroups — #15638583

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#13082665C211yesmaximal, characteristic, complemented
2#13080555C211yesmaximal, characteristic, complemented
3#13080533C211yesmaximal, characteristic, complemented
4#13080503C212yesmaximal, complemented
5#13080481C211yesmaximal, characteristic, complemented
6#13080451C212yesmaximal, complemented
7#13080429C211yesmaximal, characteristic, complemented
8D4×#4326C211yesmaximal, characteristic, complemented
9#13080353C212yesmaximal, complemented
10#13080346C211yesmaximal, characteristic, complemented
11#13080334C211yesmaximal, characteristic, complemented
12#13080319C212yesmaximal, complemented
13D4×#4324C211yesmaximal, characteristic, complemented
14#13079592C211yesmaximal, characteristic, complemented
15#13079572C211yesmaximal, characteristic, complemented
16#13079404C212yesmaximal, complemented
17#13079393C212yesmaximal, complemented
18#13078687C211yesmaximal, characteristic, complemented
19#13078634C211yesmaximal, characteristic, complemented
20#13077834C212yesmaximal, complemented
21C2×#10622852C212yesmaximal, complemented
22#13077640C211yesmaximal, characteristic, complemented
23D4×C11×#41C211yesmaximal, characteristic, complemented
24C22×C11×#41C2212yes—
25C11×#550C2211yescharacteristic
26D4×Q8×C11C2211yescharacteristic
27C11×#548C2212yes—
28C11×#547—21no—
29C11×#547C2211yescharacteristic
30C11×#546—22no—
31C11×#546C2212yes—
32D42×C11—21no—
33D42×C11C2211yescharacteristic
34C11×#532—21no—
35C11×#532C2211yescharacteristic
36C11×#525—22no—
37C11×#525C2212yes—
38C4×C11×#41C2211yescharacteristic
39C2×C4×D4×C11—21no—
40C2×C4×D4×C11C2211yescharacteristic
41C2×#67003C2212yescomplemented
42C2×#67003C2212yescomplemented
43C22×#4326C2212yescomplemented
44#10623337—21no—
45C22×#4324C2212yescomplemented
46#10623322C2212yescomplemented
47C2×#66977C2212yescomplemented
48#10623095—22no—
49#10623092—21no—
50#10623086C2211yescharacteristic
51#10623083C2212yescomplemented
52#10623082C2211yescharacteristic, complemented
53#10623077—21no—
54#10623073C2211yescharacteristic, complemented
55#10623072C2212yescomplemented
56D4×Dic22C2211yescharacteristic
57#10623042—21no—
58#10623026—22no—
59#10623010C2211yescharacteristic, complemented
60#10623001C2211yescharacteristic, complemented
61#10622852C2211yescharacteristic
62#10622852C2212yes—
63#10622852C2212yescomplemented
64#10622852C2212yescomplemented
65#10622852C2212yescomplemented
66#10622852C2212yescomplemented
67#10622852C2212yescomplemented
68#10622852C2212yescomplemented
69#10622852C2212yescomplemented
70#10622851C2211yescharacteristic
71#10622851C2212yescomplemented
72#10622846C2212yescomplemented
73#10622846C2212yescomplemented
74#10622841C2212yescomplemented
75#10622840C2212yescomplemented
76C2×#66899C2212yescomplemented
77#10622831C2212yescomplemented
78#10622830C2212yescomplemented
79C2×#66896C2212yescomplemented
80C2×C22⋊(C11⋊C8)C2212yescomplemented
81C2×C22⋊(C11⋊C8)C2212yescomplemented
82#10622705C2211yescharacteristic, complemented
83#10622703C2211yescharacteristic, complemented
84#10622696C2211yescharacteristic, complemented
85#10622694C2211yescharacteristic, complemented
86#10622689C2211yescharacteristic, complemented
87#10622688C2211yescharacteristic, complemented
88#10622685C2211yescharacteristic, complemented
89#10622683C2211yescharacteristic, complemented
90#10622672C2212yescomplemented
91#10622669C2212yescomplemented
92#10622667C2212yescomplemented
93#10622667C2212yescomplemented
94#10622664C2212yescomplemented
95#10622664C2212yescomplemented
96#10622664C2212yescomplemented
97#10622663C2212yescomplemented
98#10622661C2212yescomplemented
99#10622660C2212yescomplemented
100#10622658C2212yescomplemented
101#10622656C2212yescomplemented
102#10622654C2212yescomplemented
103#10622654C2212yescomplemented
104#10622654C2212yescomplemented
105#10622653C2212yescomplemented
106#10622651C2212yescomplemented
107#10622650C2212yescomplemented
108#10622648C2212yescomplemented
109#10622646C2212yescomplemented
110#10622644C2211yescharacteristic, complemented
111C4×#4326C2212yescomplemented
112C4×#4326C2211yescharacteristic, complemented
113#10622641C2211yescharacteristic, complemented
114C4×#4325C2211yescharacteristic, complemented
115#10622635C2211yescharacteristic, complemented
116#10622633C2211yescharacteristic, complemented
117#10622632C2211yescharacteristic, complemented
118C4×#4324C2211yescharacteristic, complemented
119C4×#4324C2212yescomplemented
120#10622629C2211yescharacteristic, complemented
121C4×#4323C2211yescharacteristic, complemented
122D4×C11⋊C8C2211yescharacteristic
123D4×C11⋊C8C2211yescharacteristic
124D4×C11⋊C8C2211yescharacteristic, complemented
125D4×C11⋊C8C2211yescharacteristic, complemented
126D4×C11⋊C8C2212yescomplemented
127D4×C11⋊C8C2212yescomplemented
128#10622622C2211yescharacteristic, complemented
129#10622620C2211yescharacteristic, complemented
130#10622616C2211yescharacteristic, complemented
131#10622609C2211yescharacteristic, complemented
132#10622609C2212yescomplemented
133#10622538C2211yescharacteristic, complemented
134#10622538C2211yescharacteristic, complemented
135C2×C11×#41—22no—
136C2×C11×#41—22no—
137C2×C11×#41—44no—
138C2×C11×#41—44no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2312yes—
141C2×C11×#41C2312yes—
142C2×C11×#41C2312yes—
143C22×Q8×C11C2312yes—
144C22×D4×C11—22no—
145C22×D4×C11—21no—
146C22×D4×C11D411yescharacteristic
147C22×D4×C11C2312yes—
148C23×C4×C11—22no—
149C23×C4×C11C2312yes—
150C2×#4341—21no—
151C2×#4339C2312yes—
152C22×Dic22C2312yes—
153C11×C4⋊Q8—21no—
154C11×C4⋊Q8C2311yescharacteristic
155C11×#127—21no—
156C11×#127C2311yescharacteristic
157C11×#124—22no—
158C11×#124C2312yes—
159C11×#123—22no—
160C11×#123—22no—
161C11×#123—22no—
162C11×C22⋊Q8—22no—
163C11×C22⋊Q8—22no—
164C11×C22⋊Q8C2312yes—
165C11×C22⋊Q8C2312yes—
166C11×#121—22no—
167C11×#121—21no—
168C11×#121—21no—
169C11×#121—21no—
170C11×#121—21no—
171C11×#121—22no—
172C11×#121—22no—
173C11×#121C2312yes—
174C11×#121C2312yes—
175C11×#120—22no—
176C11×#120—22no—
177C11×#120—22no—
178C4×Q8×C11C2311yescharacteristic
179C4×Q8×C11C2311yescharacteristic
180C4×D4×C11—21no—
181C4×D4×C11—22no—
182C4×D4×C11—21no—
183C4×D4×C11—21no—
184C4×D4×C11—22no—
185C4×D4×C11—21no—
186C4×D4×C11—22no—
187C4×D4×C11—21no—
188C4×D4×C11—21no—
189C4×D4×C11D411yescharacteristic
190C4×D4×C11D411yescharacteristic
191C4×D4×C11D412yes—
192C4×D4×C11C2311yescharacteristic
193C4×D4×C11C2311yescharacteristic
194C4×D4×C11C2311yescharacteristic
195C4×D4×C11C2312yes—
196C4×D4×C11C2311yescharacteristic
197C11×#117—21no—
198C11×#117C2311yescharacteristic
199C2×C11×C4⋊C4—21no—
200C2×C11×C4⋊C4D411yescharacteristic
201C2×C11×C22⋊C4—22no—
202C2×C11×C22⋊C4D412yes—
203C2×C42×C11—21no—
204C2×C42×C11C2311yescharacteristic
205#67006—22no—
206C2×C22⋊Dic11—22no—
207#67003—44no—
208#67003—44no—
209C2×#4326—44no—
210C2×#4326C2311yescharacteristic
211C2×#4326C2312yes—
212C2×#4326C2312yes—
213C2×#4326C2312yes—
214C2×#4326C2312yes—
215C2×#4325C2311yescharacteristic
216C2×#4325C2312yes—
217#66992—22no—
218#66991—21no—
219#66989—21no—
220#66988—22no—
221D4×Dic11—21no—
222C2×#4324—44no—
223C2×#4324C2311yescharacteristic
224C2×#4324C2312yes—
225C2×#4324C2312yes—
226C2×#4324C2312yes—
227C2×#4324C2312yes—
228C2×#4323C2311yescharacteristic
229C2×#4323C2312yes—
230#66983C2311yescharacteristic
231#66983C2312yes—
232#66982—21no—
233#66982—22no—
234C4×C22⋊D11—21no—
235C4×C22⋊D11—22no—
236C4×C22⋊D11—22no—
237#66979—21no—
238#66979C2312yes—
239C2×C4⋊Dic11C2312yes—
240#66977—21no—
241#66977—22no—
242#66977—22no—
243#66977C2312yes—
244#66977C2311yescharacteristic
245#66977C2312yes—
246#66977C2312yes—
247#66977C2312yes—
248C2×Dic11⋊C4—22no—
249C22×C11⋊C8C2312yes—
250C22×C11⋊C8C2312yes—
251C22×C11⋊C8C2312yes—
252C22×C11⋊C8C2312yes—
253#66950—21no—
254#66949—22no—
255C4⋊C4×D11—21no—
256#66942—22no—
257#66941—21no—
258#66940—21no—
259#66939—22no—
260#66938—22no—
261#66936—22no—
262(C22⋊D11)⋊C4—22no—
263#66932—22no—
264#66932—22no—
265#66931—22no—
266#66930—22no—
267#66929—21no—
268#66928C2311yescharacteristic
269C4×D44C2311yescharacteristic
270#66925—21no—
271#66923—21no—
272#66923C2311yescharacteristic
273#66922C2311yescharacteristic
274#66922C2311yescharacteristic
275C4×Dic22—21no—
276C4×Dic22C2312yes—
277C4×Dic22C2311yescharacteristic
278#66899C2311yescharacteristic
279#66899C2312yes—
280#66899C2312yes—
281#66899C2312yes—
282#66899C2312yes—
283#66899C2311yescharacteristic
284#66899C2312yes—
285#66896C2311yescharacteristic
286#66896C2312yes—
287#66896C2312yes—
288#66896C2312yes—
289#66896C2312yes—
290#66896C2311yescharacteristic
291#66896C2312yes—
292C22⋊(C11⋊C8)C2311yescharacteristic
293C22⋊(C11⋊C8)C2312yes—
294C22⋊(C11⋊C8)C2311yescharacteristic
295C22⋊(C11⋊C8)C2312yes—
296C22⋊(C11⋊C8)C2312yes—
297C22⋊(C11⋊C8)C2312yes—
298C22⋊(C11⋊C8)C2312yes—
299#66874C2311yescharacteristic
300#66874C2311yescharacteristic
301#66874C2312yes—
302#66874C2312yes—
303#66873C2311yescharacteristic
304#66873C2311yescharacteristic
305#66872C2311yescharacteristic
306#66872C2312yes—
307#66872C2311yescharacteristic
308#66871C2312yes—
309#66871C2311yescharacteristic
310#66871C2311yescharacteristic
311C4⋊(C11⋊C8)C2311yescharacteristic
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4×C11⋊C8C2311yescharacteristic
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2312yes—
318#61568—111nomaximal, Sylow
319C24×C11—22no—
320C24×C11C2×D412yes—
321C11×#41—22no—
322C11×#41—22no—
323C11×#41—24no—
324C11×#41—24no—
325C11×#41—42no—
326C11×#41—42no—
327C11×#41—42no—
328C11×#41—42no—
329C11×#41—48no—
330C11×#41—48no—
331C2×Q8×C11—22no—
332C2×Q8×C11—24no—
333C2×Q8×C11—42no—
334C2×Q8×C11C2412yes—
335C2×Q8×C11C2411yescharacteristic
336C2×D4×C11—21no—
337C2×D4×C11—24no—
338C2×D4×C11—24no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—22no—
346C2×D4×C11—21no—
347C2×D4×C11—42no—
348C2×D4×C11—48no—
349C2×D4×C11—44no—
350C2×D4×C11C2×D412yes—
351C2×D4×C11C2×D411yescharacteristic
352C2×D4×C11C2×D411yescharacteristic
353C2×D4×C11C2412yes—
354C2×D4×C11C2411yescharacteristic
355C22×C4×C11—21no—
356C22×C4×C11—22no—
357C22×C4×C11—21no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—21no—
362C22×C4×C11—42no—
363C22×C4×C11—42no—
364C22×C4×C11—48no—
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2×D412yes—
367C22×C4×C11C2×D412yes—
368C22×C4×C11C2×D412yes—
369C22×C4×C11C2×D411yescharacteristic
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2412yes—
372C22×C4×C11C2412yes—
373C2×C22⋊D11—22no—
374C2×C22⋊D11—21no—
375C2×C22⋊D11—22no—
376C22×Dic11—22no—
377C22×Dic11—22no—
378#4341—44no—
379#4339—42no—
380#4339—42no—
381C2×D44C2411yescharacteristic
382C2×C4×D11—21no—
383C2×C4×D11—22no—
384C2×Dic22—21no—
385C2×Dic22—22no—
386C2×Dic22—42no—
387C2×Dic22—42no—
388C2×Dic22C2412yes—
389C2×Dic22C2411yescharacteristic
390C11×C4⋊C4—21no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4C2×D411yescharacteristic
397C11×C4⋊C4C2×D411yescharacteristic
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2411yescharacteristic
400C11×C4⋊C4C2411yescharacteristic
401C11×C22⋊C4—22no—
402C11×C22⋊C4—21no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—21no—
407C11×C22⋊C4—21no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4C2×D412yes—
411C11×C22⋊C4C2×D412yes—
412C11×C22⋊C4C2×D412yes—
413C11×C22⋊C4C2×D412yes—
414C42×C11—21no—
415C42×C11—21no—
416C42×C11—21no—
417C42×C11C2×D411yescharacteristic
418C42×C11C2×D411yescharacteristic
419C42×C11C2411yescharacteristic
420C42×C11C2411yescharacteristic
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11—22no—
424C22⋊Dic11—22no—
425C22⋊Dic11—22no—
426C22⋊Dic11—21no—
427#4326—22no—
428#4326—24no—
429#4326—42no—
430#4326—42no—
431#4326—42no—
432#4325—22no—
433#4325—42no—
434#4324—22no—
435#4324—24no—
436#4324—42no—
437#4324—42no—
438#4324—42no—
439#4323—22no—
440#4323—42no—
441(C2×D11)⋊C4—21no—
442(C2×D11)⋊C4—21no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—21no—
445(C2×D11)⋊C4—22no—
446C4⋊Dic11—21no—
447C4⋊Dic11—21no—
448C4⋊Dic11—21no—
449C4⋊Dic11—22no—
450C4⋊Dic11C2412yes—
451C4⋊Dic11C2411yescharacteristic
452C4⋊Dic11C2411yescharacteristic
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—21no—
456Dic11⋊C4—21no—
457Dic11⋊C4—21no—
458Dic11⋊C4—21no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462C4×Dic11—22no—
463C4×Dic11—21no—
464C4×Dic11—22no—
465C2×C11⋊C8—42no—
466C2×C11⋊C8—42no—
467C2×C11⋊C8—42no—
468C2×C11⋊C8—42no—
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2412yes—
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2412yes—
474C2×C11⋊C8C2411yescharacteristic
475#3520—111no—
476D4×#41D1111yescharacteristic, complemented
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#3102—111no—
495#3002—112no—
496C2×#452—112no—
497#2972—111no—
498C23×C11—21no—
499C23×C11—24no—
500C23×C11—22no—
501C23×C11—42no—
502C23×C11—42no—
503C23×C11—44no—
504C23×C11—44no—
505C23×C11—82no—
506C23×C11C22×D412yes—
507C23×C11C22×D411yescharacteristic
508C23×C11C22×D412yes—
509C22×D11—21no—
510Q8×C11—21no—
511Q8×C11—22no—
512Q8×C11—22no—
513Q8×C11—44no—
514Q8×C11H(5,𝔽2)12yes—
515D4×C11—24no—
516D4×C11—24no—
517D4×C11—22no—
518D4×C11—21no—
519D4×C11—22no—
520D4×C11—22no—
521D4×C11—44no—
522D4×C11—44no—
523D4×C11—44no—
524D4×C11—44no—
525D4×C11—44no—
526D4×C11—42no—
527D4×C11—81no—
528D4×C11—82no—
529D4×C11#13514yescomplemented
530D4×C11H(5,𝔽2)12yes—
531C2×C4×C11—24no—
532C2×C4×C11—21no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—22no—
543C2×C4×C11—42no—
544C2×C4×C11—42no—
545C2×C4×C11—42no—
546C2×C4×C11—41no—
547C2×C4×C11—44no—
548C2×C4×C11—44no—
549C2×C4×C11—44no—
550C2×C4×C11—44no—
551C2×C4×C11—42no—
552C2×C4×C11—81no—
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D412yes—
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C2511yescharacteristic
561C22⋊D11—42no—
562C22⋊D11—44no—
563C22⋊D11—82no—
564C2×Dic11—21no—
565C2×Dic11—22no—
566C2×Dic11—22no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—44no—
570C2×Dic11—82no—
571D44—21no—
572D44—21no—
573C4×D11—42no—
574C4×D11—82no—
575Dic22—21no—
576Dic22—22no—
577Dic22—22no—
578Dic22—21no—
579Dic22—42no—
580Dic22—82no—
581C11⋊C8—21no—
582C11⋊C8—22no—
583C11⋊C8—21no—
584C11⋊C8—22no—
585C11⋊C8—21no—
586C11⋊C8—21no—
587C22×#41C2×D1112yes—
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#550C2×D1111yescharacteristic
597D4×Q8—111no—
598D4×Q8C2×D1111yescharacteristic
599#548—112no—
600#548C2×D1112yes—
601#547—21no—
602#547—111no—
603#547—111no—
604#547C2×D1111yescharacteristic
605#546—22no—
606#546—221no—
607#546C2×D1112yes—
608D42—21no—
609D42C2×D1111yescharacteristic
610#542—221no—
611#539—222no—
612#533—111no—
613#532—21no—
614#532C2×D1111yescharacteristic
615#529—111no—
616#525—22no—
617#525—112no—
618#525C2×D1112yes—
619C2×C22⋊Q8—112no—
620#520—221no—
621C4×#41C2×D1111yescharacteristic
622C2×C4×D4—21no—
623C2×C4×D4C2×D1111yescharacteristic
624#495—112no—
625#494—111no—
626#492—111no—
627#488—112no—
628#487—111no—
629#486—111no—
630#485—112no—
631#485—111no—
632#485—112no—
633#483—112no—
634#482—112no—
635#482—111no—
636#480—112no—
637#479—111no—
638#478—111no—
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#464—111no—
652#463—111no—
653#462—111no—
654#462—111no—
655#461—111no—
656#461—111no—
657#460—111no—
658#459—111no—
659#452—111no—
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#452—112no—
669#451—112no—
670#451—112no—
671#450—112no—
672#449—111no—
673#449—112no—
674#449—112no—
675#448—112no—
676#448—112no—
677#447—112no—
678C4×Q16—111no—
679C4×Q16—112no—
680C4×SD16—111no—
681C4×SD16—111no—
682C4×SD16—112no—
683C4×D8—111no—
684C8×D4—111no—
685C8×D4—111no—
686C8×D4—112no—
687C8×D4—111no—
688C8×D4—111no—
689C8×D4—112no—
690#431—111no—
691#431—111no—
692#416—112no—
693#416—112no—
694C2×#103—112no—
695C2×#102—112no—
696C2×C22⋊C8—112no—
697C2×C22⋊C8—112no—
698C22×C11—22no—
699C22×C11—22no—
700C22×C11—21no—
701C22×C11—22no—
702C22×C11—21no—
703C22×C11—22no—
704C22×C11—22no—
705C22×C11—21no—
706C22×C11—22no—
707C22×C11—41no—
708C22×C11—41no—
709C22×C11—42no—
710C22×C11—42no—
711C22×C11—42no—
712C22×C11—84no—
713C22×C11—88no—
714C22×C11C2×#13514yes—
715C22×C11C23×D411yescharacteristic
716C2×D11—41no—
717C2×D11—41no—
718C2×D11—41no—
719C4×C11—21no—
720C4×C11—21no—
721C4×C11—21no—
722C4×C11—22no—
723C4×C11—22no—
724C4×C11—22no—
725C4×C11—21no—
726C4×C11—41no—
727C4×C11—42no—
728C4×C11—41no—
729C4×C11C2×#13512yes—
730C4×C11C2×H(5,𝔽2)11yescharacteristic
731C4×C11C2×H(5,𝔽2)11yescharacteristic
732Dic11—41no—
733Dic11—41no—
734Dic11—42no—
735Dic11—42no—
736Dic11—41no—
737C2×#41—22no—
738C2×#41—22no—
739C2×#41—44no—
740C2×#41—44no—
741C2×#41—112no—
742C2×#41—221no—
743C2×#41C22×D1111yescharacteristic
744C2×#41C22×D1112yes—
745C2×#41C22×D1112yes—
746C2×#41C22×D1112yes—
747C22×Q8—112no—
748C22×Q8C22×D1112yes—
749C22×D4—22no—
750C22×D4—21no—
751C22×D4C22⋊D1111yescharacteristic
752C22×D4C22×D1112yes—
753C23×C4—22no—
754C23×C4C22×D1112yes—
755#135—444no—
756#135—444no—
757C2×Q16—111no—
758C2×Q16—112no—
759C2×Q16—112no—
760C2×Q16—112no—
761C2×Q16—112no—
762C2×Q16—444no—
763C2×SD16—111no—
764C2×SD16—111no—
765C2×SD16—112no—
766C2×SD16—112no—
767C2×SD16—112no—
768C2×SD16—112no—
769C2×SD16—112no—
770C2×SD16—444no—
771C2×D8—111no—
772C2×D8—112no—
773C22×C8—112no—
774C22×C8—112no—
775C22×C8—112no—
776C22×C8—112no—
777C4⋊Q8—21no—
778C4⋊Q8—111no—
779C4⋊Q8—111no—
780C4⋊Q8—221no—
781C4⋊Q8C22×D1111yescharacteristic
782#127—21no—
783#127C22×D1111yescharacteristic
784#126—222no—
785#126—222no—
786#126—221no—
787#125—111no—
788#125—222no—
789#125—221no—
790#124—22no—
791#124—111no—
792#124—221no—
793#124—222no—
794#124C22×D1112yes—
795#123—22no—
796#123—22no—
797#123—22no—
798#123—222no—
799#123—222no—
800#123—221no—
801#123—222no—
802#123—222no—
803C22⋊Q8—22no—
804C22⋊Q8—22no—
805C22⋊Q8—111no—
806C22⋊Q8—112no—
807C22⋊Q8—112no—
808C22⋊Q8—112no—
809C22⋊Q8—112no—
810C22⋊Q8—222no—
811C22⋊Q8—222no—
812C22⋊Q8—221no—
813C22⋊Q8—222no—
814C22⋊Q8—221no—
815C22⋊Q8—222no—
816C22⋊Q8C22×D1112yes—
817C22⋊Q8C22×D1112yes—
818#121—22no—
819#121—21no—
820#121—21no—
821#121—21no—
822#121—21no—
823#121—22no—
824#121—22no—
825#121—111no—
826#121—112no—
827#121—222no—
828#121—221no—
829#121C22×D1112yes—
830#121C22×D1112yes—
831#120—22no—
832#120—22no—
833#120—22no—
834#120—222no—
835C4×Q8—111no—
836C4×Q8—112no—
837C4×Q8—221no—
838C4×Q8—221no—
839C4×Q8C22×D1111yescharacteristic
840C4×Q8C22×D1111yescharacteristic
841C4×D4—21no—
842C4×D4—22no—
843C4×D4—21no—
844C4×D4—21no—
845C4×D4—22no—
846C4×D4—21no—
847C4×D4—22no—
848C4×D4—21no—
849C4×D4—21no—
850C4×D4—111no—
851C4×D4—221no—
852C4×D4—222no—
853C4×D4—222no—
854C4×D4—221no—
855C4×D4—222no—
856C4×D4C22⋊D1111yescharacteristic
857C4×D4C22⋊D1112yes—
858C4×D4C22⋊D1111yescharacteristic
859C4×D4C22×D1111yescharacteristic
860C4×D4C22×D1111yescharacteristic
861C4×D4C22×D1111yescharacteristic
862C4×D4C22×D1112yes—
863C4×D4C22×D1111yescharacteristic
864#117—21no—
865#117—112no—
866#117—221no—
867#117—222no—
868#117—221no—
869#117C22×D1111yescharacteristic
870C2×C4⋊C4—21no—
871C2×C4⋊C4—112no—
872C2×C4⋊C4—222no—
873C2×C4⋊C4—221no—
874C2×C4⋊C4C22⋊D1111yescharacteristic
875C2×C22⋊C4—22no—
876C2×C22⋊C4—222no—
877C2×C22⋊C4C22⋊D1112yes—
878C2×C42—21no—
879C2×C42C22×D1111yescharacteristic
880#107—111no—
881#107—112no—
882#107—111no—
883#106—112no—
884#106—111no—
885#106—111no—
886C4⋊C8—111no—
887C4⋊C8—111no—
888C4⋊C8—111no—
889C4⋊C8—111no—
890#103—111no—
891#103—112no—
892#103—112no—
893#103—112no—
894#103—111no—
895#103—112no—
896#103—112no—
897#103—111no—
898#103—112no—
899#103—112no—
900#103—111no—
901#102—111no—
902#102—112no—
903#102—112no—
904#102—112no—
905#102—111no—
906#102—112no—
907#102—112no—
908#102—111no—
909#102—111no—
910C22⋊C8—111no—
911C22⋊C8—112no—
912C22⋊C8—111no—
913C22⋊C8—112no—
914C22⋊C8—112no—
915C22⋊C8—112no—
916C22⋊C8—112no—
917C4×C8—111no—
918C4×C8—111no—
919C4×C8—112no—
920C2×C11—24no—
921C2×C11—42no—
922C2×C11—41no—
923C2×C11—42no—
924C2×C11—82no—
925C2×C11#348411yescharacteristic
926C2×C11C22×#13511yescharacteristic
927C2×C11#358611yescharacteristic
928D11—81no—
929C24—22no—
930C24C2×C22⋊D1112yes—
931#41—22no—
932#41—22no—
933#41—24no—
934#41—24no—
935#41—42no—
936#41—42no—
937#41—42no—
938#41—42no—
939#41—48no—
940#41—48no—
941#41—442no—
942#41—442no—
943#41—444no—
944C2×Q8—22no—
945C2×Q8—24no—
946C2×Q8—42no—
947C2×Q8—111no—
948C2×Q8—112no—
949C2×Q8—221no—
950C2×Q8—222no—
951C2×Q8—442no—
952C2×Q8—442no—
953C2×Q8C23×D1112yes—
954C2×Q8C23×D1111yescharacteristic
955C2×D4—21no—
956C2×D4—24no—
957C2×D4—24no—
958C2×D4—22no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—21no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—42no—
967C2×D4—48no—
968C2×D4—44no—
969C2×D4—111no—
970C2×D4—221no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4C2×C22⋊D1112yes—
974C2×D4C2×C22⋊D1111yescharacteristic
975C2×D4C2×C22⋊D1111yescharacteristic
976C2×D4C23×D1112yes—
977C2×D4C23×D1111yescharacteristic
978C22×C4—21no—
979C22×C4—22no—
980C22×C4—21no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—21no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—48no—
988C22×C4—222no—
989C22×C4—222no—
990C22×C4—221no—
991C22×C4—222no—
992C22×C4C2×C22⋊D1111yescharacteristic
993C22×C4C2×C22⋊D1111yescharacteristic
994C22×C4C2×C22⋊D1112yes—
995C22×C4C2×C22⋊D1112yes—
996C22×C4C2×C22⋊D1112yes—
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1112yes—
999C22×C4C23×D1112yes—
1000Q16—222no—
1001Q16—224no—
1002Q16—442no—
1003Q16—442no—
1004Q16—442no—
1005SD16—222no—
1006SD16—222no—
1007SD16—224no—
1008SD16—442no—
1009SD16—442no—
1010SD16—442no—
1011SD16—442no—
1012D8—222no—
1013D8—442no—
1014C2×C8—111no—
1015C2×C8—111no—
1016C2×C8—112no—
1017C2×C8—111no—
1018C2×C8—111no—
1019C2×C8—112no—
1020C2×C8—442no—
1021C2×C8—442no—
1022C2×C8—442no—
1023C2×C8—442no—
1024C4⋊C4—21no—
1025C4⋊C4—22no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—22no—
1030C4⋊C4—111no—
1031C4⋊C4—112no—
1032C4⋊C4—111no—
1033C4⋊C4—222no—
1034C4⋊C4—221no—
1035C4⋊C4—222no—
1036C4⋊C4—221no—
1037C4⋊C4—222no—
1038C4⋊C4—222no—
1039C4⋊C4—221no—
1040C4⋊C4—221no—
1041C4⋊C4—221no—
1042C4⋊C4—222no—
1043C4⋊C4—221no—
1044C4⋊C4—222no—
1045C4⋊C4—221no—
1046C4⋊C4C2×C22⋊D1111yescharacteristic
1047C4⋊C4C2×C22⋊D1111yescharacteristic
1048C4⋊C4C2×C22⋊D1112yes—
1049C4⋊C4C23×D1111yescharacteristic
1050C4⋊C4C23×D1111yescharacteristic
1051C22⋊C4—22no—
1052C22⋊C4—21no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—21no—
1057C22⋊C4—21no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—221no—
1061C22⋊C4—222no—
1062C22⋊C4—222no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—221no—
1067C22⋊C4—221no—
1068C22⋊C4—221no—
1069C22⋊C4—222no—
1070C22⋊C4—221no—
1071C22⋊C4C2×C22⋊D1112yes—
1072C22⋊C4C2×C22⋊D1112yes—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—222no—
1079C42—222no—
1080C42—221no—
1081C42C2×C22⋊D1111yescharacteristic
1082C42C2×C22⋊D1111yescharacteristic
1083C42C23×D1111yescharacteristic
1084C42C23×D1111yescharacteristic
1085C11#6156811yescharacteristic, complemented, Sylow
1086C23—21no—
1087C23—24no—
1088C23—22no—
1089C23—42no—
1090C23—42no—
1091C23—44no—
1092C23—44no—
1093C23—82no—
1094C23—221no—
1095C23C22×C22⋊D1112yes—
1096C23C22×C22⋊D1111yescharacteristic
1097C23C22×C22⋊D1112yes—
1098Q8—21no—
1099Q8—22no—
1100Q8—22no—
1101Q8—44no—
1102Q8—221no—
1103Q8—222no—
1104Q8—222no—
1105Q8—221no—
1106Q8—442no—
1107Q8—882no—
1108Q8#6703712yes—
1109D4—24no—
1110D4—24no—
1111D4—22no—
1112D4—21no—
1113D4—22no—
1114D4—22no—
1115D4—44no—
1116D4—44no—
1117D4—44no—
1118D4—44no—
1119D4—44no—
1120D4—42no—
1121D4—81no—
1122D4—82no—
1123D4—221no—
1124D4—221no—
1125D4—442no—
1126D4—444no—
1127D4—882no—
1128D4#6700314yescomplemented
1129D4#6703712yes—
1130C2×C4—24no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—42no—
1151C2×C4—81no—
1152C2×C4—221no—
1153C2×C4—222no—
1154C2×C4—221no—
1155C2×C4—222no—
1156C2×C4—221no—
1157C2×C4—444no—
1158C2×C4—442no—
1159C2×C4—882no—
1160C2×C4—882no—
1161C2×C4C22×C22⋊D1111yescharacteristic
1162C2×C4C22×C22⋊D1111yescharacteristic
1163C2×C4C22×C22⋊D1112yes—
1164C2×C4C22×C22⋊D1111yescharacteristic
1165C2×C4C22×C22⋊D1111yescharacteristic
1166C2×C4C22×C22⋊D1112yes—
1167C2×C4C22×C22⋊D1111yescharacteristic
1168C2×C4C24×D1111yescharacteristic
1169C8—221no—
1170C8—222no—
1171C8—221no—
1172C8—221no—
1173C8—222no—
1174C8—221no—
1175C22—22no—
1176C22—22no—
1177C22—21no—
1178C22—22no—
1179C22—21no—
1180C22—22no—
1181C22—22no—
1182C22—21no—
1183C22—22no—
1184C22—41no—
1185C22—41no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—84no—
1190C22—88no—
1191C22—441no—
1192C22—441no—
1193C22—441no—
1194C22C2×#6700314yes—
1195C22C23×C22⋊D1111yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—21no—
1199C4—22no—
1200C4—22no—
1201C4—22no—
1202C4—21no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—441no—
1207C4—442no—
1208C4—441no—
1209C4—441no—
1210C4—442no—
1211C4C2×#6700312yes—
1212C4C2×#6703711yescharacteristic
1213C4C2×#6703711yescharacteristic
1214C2—24no—
1215C2—41no—
1216C2—42no—
1217C2—42no—
1218C2—82no—
1219C2—881no—
1220C2#1308225111yescharacteristic
1221C2C22×#6700311yescharacteristic
1222C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingD4×C11×#41C2
socleC22×C11C23×D4
hypercenterD4×#41D11
hypocenterC11#61568
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. #13082665C2semidirect
2. #13080555C2semidirect
3. #13080533C2semidirect
4. #13080503C2semidirect
5. #13080481C2semidirect
6. #13080451C2semidirect
7. #13080429C2semidirect
8. D4×#4326C2semidirect
9. #13080353C2semidirect
10. #13080346C2semidirect
11. #13080334C2semidirect
12. #13080319C2semidirect
13. D4×#4324C2semidirect
14. #13079592C2semidirect
15. #13079572C2semidirect
16. #13079404C2semidirect
17. #13079393C2semidirect
18. #13078687C2semidirect
19. #13078634C2semidirect
20. #13077834C2semidirect
21. C2×#10622852C2semidirect
22. #13077640C2semidirect
23. D4×C11×#41C2semidirect
41. C2×#67003C22semidirect
42. C2×#67003C22semidirect
43. C22×#4326C22semidirect
45. C22×#4324C22semidirect
46. #10623322C22semidirect
47. C2×#66977C22semidirect
51. #10623083C22semidirect
52. #10623082C22semidirect
54. #10623073C22semidirect
55. #10623072C22semidirect
59. #10623010C22semidirect
60. #10623001C22semidirect
63. #10622852C22semidirect
64. #10622852C22semidirect
65. #10622852C22semidirect
66. #10622852C22semidirect
67. #10622852C22semidirect
68. #10622852C22semidirect
69. #10622852C22semidirect
71. #10622851C22semidirect
72. #10622846C22semidirect
73. #10622846C22semidirect
74. #10622841C22semidirect
75. #10622840C22semidirect
76. C2×#66899C22semidirect
77. #10622831C22semidirect
78. #10622830C22semidirect
79. C2×#66896C22semidirect
80. C2×C22⋊(C11⋊C8)C22semidirect
81. C2×C22⋊(C11⋊C8)C22semidirect
82. #10622705C22semidirect
83. #10622703C22semidirect
84. #10622696C22semidirect
85. #10622694C22semidirect
86. #10622689C22semidirect
87. #10622688C22semidirect
88. #10622685C22semidirect
89. #10622683C22semidirect
90. #10622672C22semidirect
91. #10622669C22semidirect
92. #10622667C22semidirect
93. #10622667C22semidirect
94. #10622664C22semidirect
95. #10622664C22semidirect
96. #10622664C22semidirect
97. #10622663C22semidirect
98. #10622661C22semidirect
99. #10622660C22semidirect
100. #10622658C22semidirect
101. #10622656C22semidirect
102. #10622654C22semidirect
103. #10622654C22semidirect
104. #10622654C22semidirect
105. #10622653C22semidirect
106. #10622651C22semidirect
107. #10622650C22semidirect
108. #10622648C22semidirect
109. #10622646C22semidirect
110. #10622644C22semidirect
111. C4×#4326C22semidirect
112. C4×#4326C22semidirect
113. #10622641C22semidirect
114. C4×#4325C22semidirect
115. #10622635C22semidirect
116. #10622633C22semidirect
117. #10622632C22semidirect
118. C4×#4324C22semidirect
119. C4×#4324C22semidirect
120. #10622629C22semidirect
121. C4×#4323C22semidirect
124. D4×C11⋊C8C22semidirect
125. D4×C11⋊C8C22semidirect
126. D4×C11⋊C8C22semidirect
127. D4×C11⋊C8C22semidirect
128. #10622622C22semidirect
129. #10622620C22semidirect
130. #10622616C22semidirect
131. #10622609C22semidirect
132. #10622609C22semidirect
133. #10622538C22semidirect
134. #10622538C22semidirect
476. D4×#41D11semidirect
529. D4×C11#135semidirect
1085. C11#61568semidirect
1128. D4#67003semidirect

Maximal subgroups

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

subgroupindex
#130826652
#130805552
#130805332
#130805032
#130804812
#130804512
#130804292
D4×#43262
#130803532
#130803462
#130803342
#130803192
D4×#43242
#130795922
#130795722
#130794042
#130793932
#130786872
#130786342
#130778342
C2×#106228522
#130776402
D4×C11×#412
#6156811