Finite Group Databasebeta

← #14917771

Subgroups — #14917771

Order 2816.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623246C211yesmaximal, characteristic
2#13071774C212yesmaximal, complemented
3#13071754C212yesmaximal, complemented
4#13071689C211yesmaximal, characteristic, complemented
5#13071686C211yesmaximal, characteristic, complemented
6#13071678C211yesmaximal, characteristic, complemented
7#13071677C211yesmaximal, characteristic, complemented
8#13071664C212yesmaximal, complemented
9#13071596C212yesmaximal, complemented
10#13071455C211yesmaximal, characteristic, complemented
11#13071441C211yesmaximal, characteristic, complemented
12#13071437C211yesmaximal, characteristic, complemented
13D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071382C212yesmaximal, complemented
15#13071327C211yesmaximal, characteristic, complemented
16#13071317C212yesmaximal, complemented
17#13071279C212yesmaximal, complemented
18#13071272C212yesmaximal, complemented
19#13071226C211yesmaximal, characteristic, complemented
20#127×Dic11C211yesmaximal, characteristic, complemented
21#13071155C211yesmaximal, characteristic, complemented
22#13071111C211yesmaximal, characteristic, complemented
23C11×#2328C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C2×C11×#127C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×#66993C2211yescharacteristic
30C2×#66992C2212yes—
31C2×#66992C2212yes—
32C2×#66990C2212yes—
33C2×#66990C2212yes—
34C2×#66989C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C2×D4×Dic11C2212yescomplemented
37C2×D4×Dic11C2211yescharacteristic, complemented
38C2×D4×Dic11C2212yescomplemented
39C2×C4×C22⋊D11C2212yescomplemented
40C22×(C2×D11)⋊C4C2212yes—
41#10623246C4116yescomplemented
42C2×#66946C2211yescharacteristic
43C2×#66940C2211yescharacteristic, complemented
44C2×(C22⋊D11)⋊C4C2212yescomplemented
45C2×C22⋊C4×D11C2212yes—
46C2×#66928C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic, complemented
52C11×#386C2212yescomplemented
53C11×#386C2212yescomplemented
54C11×#386C2212yescomplemented
55C11×#386C2212yescomplemented
56C11×#382C2211yescharacteristic, complemented
57C11×#376C2211yescharacteristic, complemented
58#10622834C2211yescharacteristic
59#10622834C2212yescomplemented
60#10622834C2211yescharacteristic, complemented
61#10622834C2212yescomplemented
62#10622826C2212yes—
63#10622826C2212yes—
64#10622826C2212yescomplemented
65#10622823C2212yescomplemented
66C4×C22⋊Dic11C2212yescomplemented
67C2×C11⋊#95C2212yescomplemented
68#10622601C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71C4⋊C4×Dic11C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2211yescharacteristic, complemented
73#10622587C2211yescharacteristic, complemented
74#10622571C2212yes—
75#10622571C2212yes—
76#10622571C2212yescomplemented
77#10622570C2212yes—
78#10622570C2212yes—
79#10622570C2212yescomplemented
80#10622570C2212yescomplemented
81#10622569C2212yes—
82#10622569C2212yes—
83#10622569C2212yescomplemented
84#10622569C2212yescomplemented
85#10622568C2212yes—
86#10622568C2212yes—
87#10622559C2212yescomplemented
88#10622558C2212yescomplemented
89#10622558C2212yescomplemented
90#10622557C2212yescomplemented
91#10622557C2212yescomplemented
92#10622556C2212yescomplemented
93#10622555C2212yescomplemented
94C22⋊C4×Dic11C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96#10622552C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×(C2×D11)⋊C4C2211yescharacteristic
99#10622548C2211yescharacteristic, complemented
100C4×Dic11⋊C4C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2211yescharacteristic, complemented
102C42×Dic11C2211yescharacteristic, complemented
103#10622542C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622283C2212yes—
106#10622283C2212yescomplemented
107#10622283C2212yescomplemented
108#10622282C2211yescharacteristic
109#10622282C2211yescharacteristic
110#10622282C2211yescharacteristic
111#10622282C2211yescharacteristic
112#10622282C2212yescomplemented
113#10622282C2212yescomplemented
114#10622281C2212yescomplemented
115#10622281C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622268C2212yescomplemented
119#10622268C2212yescomplemented
120#10622265C2211yescharacteristic, complemented
121#10622265C2211yescharacteristic, complemented
122#10622265C2211yescharacteristic, complemented
123#10622265C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C23×C4×C11C2312yes—
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C23×Dic11C2312yes—
136C23×Dic11C2312yes—
137C23×Dic11C2312yes—
138C2×#4341—42no—
139C2×#4341—42no—
140C2×#4341C2×C418yescomplemented
141C2×D4×D11—42no—
142C2×D4×D11—42no—
143C2×D4×D11C2×C418yescomplemented
144C22×D44C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×Dic22C2311yescharacteristic
149C11×#127C2×C418yescomplemented
150C4×D4×C11—42no—
151C4×D4×C11—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171#66993C2×C418yescomplemented
172#66992C2×C4116yescomplemented
173#66992C2×C4116yescomplemented
174#66990C2×C4116yescomplemented
175#66990C2×C4116yescomplemented
176#66989C2×C418yescomplemented
177D4×Dic11—42no—
178D4×Dic11—42no—
179D4×Dic11—44no—
180D4×Dic11—44no—
181C4×C22⋊D11—44no—
182C2×(C2×D11)⋊C4—44no—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222#66946—42no—
223#66940—42no—
224(C22⋊D11)⋊C4—44no—
225C22⋊C4×D11—44no—
226#66928C2×C418yescomplemented
227C4×D44—42no—
228#66925C2×C418yescomplemented
229C4×Dic22—42no—
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34438—111nomaximal, Sylow
253C24×C11C2412yes—
254C24×C11C2412yes—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11—42no—
261C23×D11C22×C418yes—
262C23×D11C2411yescharacteristic
263C23×D11C2412yes—
264C2×D4×C11—22no—
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11—42no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C22×C414yes—
273C2×D4×C11C22×C414yes—
274C2×D4×C11C22×C418yes—
275C2×D4×C11C22×C418yes—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11C22×C418yes—
300C2×C22⋊D11C22×C418yes—
301C2×C22⋊D11C22×C418yes—
302C2×C22⋊D11C22×C418yes—
303C22×Dic11—24no—
304C22×Dic11—24no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11C22×C418yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322#4341—416no—
323D4×D11—416no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44C22×C414yes—
327C2×C4×D11—24no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11C22×C414yes—
336C2×Dic22—22no—
337C2×Dic22—22no—
338C2×Dic22C22×C414yes—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C42×C11—22no—
348C42×C11—22no—
349C42×C11C22×C414yes—
350C22⋊Dic11—24no—
351C22⋊Dic11—24no—
352C22⋊Dic11—42no—
353C22⋊Dic11—42no—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11C22×C418yes—
357C22⋊Dic11C22×C418yes—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—41no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—41no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4C22×C414yes—
371(C2×D11)⋊C4C22×C414yes—
372(C2×D11)⋊C4C22×C418yes—
373(C2×D11)⋊C4C22×C418yes—
374C4⋊Dic11—22no—
375C4⋊Dic11—22no—
376C4⋊Dic11—42no—
377C4⋊Dic11—42no—
378Dic11⋊C4—22no—
379Dic11⋊C4—22no—
380Dic11⋊C4—42no—
381Dic11⋊C4—42no—
382Dic11⋊C4—41no—
383Dic11⋊C4—41no—
384Dic11⋊C4C22×C414yes—
385Dic11⋊C4C22×C414yes—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390C4×Dic11—42no—
391C4×Dic11—42no—
392C4×Dic11—42no—
393C4×Dic11—41no—
394C4×Dic11—41no—
395C4×Dic11—42no—
396C4×Dic11C22×C414yes—
397C2×#535—111no—
398#2377—112no—
399#2375—112no—
400#2367—111no—
401#2367—111no—
402#2366—111no—
403#2366—111no—
404#2364—112no—
405#2358—112no—
406#2341—111no—
407#2339—111no—
408D4×C22⋊C4—111no—
409D4×C22⋊C4—111no—
410#2333—112no—
411#2328D1111yescharacteristic, complemented
412#2326—111no—
413#2325—112no—
414#2321—112no—
415#2321—112no—
416#2314—111no—
417C4×#127—111no—
418C4×#124—111no—
419#2298—111no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11C23×C414yes—
433C23×C11C23×C414yes—
434C23×C11C2511yescharacteristic
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—21no—
442C22×D11—21no—
443C22×D11—22no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—22no—
447C22×D11—48no—
448C22×D11—48no—
449C22×D11—48no—
450C22×D11—84no—
451C22×D11—84no—
452C22×D11—84no—
453C22×D11—84no—
454C22×D11C23×C412yes—
455C22×D11C23×C414yes—
456D4×C11—28no—
457D4×C11—28no—
458D4×C11—48no—
459D4×C11—48no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—84no—
483C2×C4×C11—84no—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C2×C4×C11H(5,𝔽2)12yes—
489C22⋊D11—48no—
490C22⋊D11—48no—
491C22⋊D11—48no—
492C22⋊D11—48no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—48no—
518C2×Dic11—84no—
519C2×Dic11—84no—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C412yes—
523C2×Dic11C23×C414yes—
524C2×Dic11H(5,𝔽2)12yes—
525C2×Dic11H(5,𝔽2)12yes—
526D44—28no—
527C4×D11—28no—
528C4×D11—84no—
529C4×D11—84no—
530Dic22—28no—
531C22×#41—111no—
532C23×D4—111no—
533#535—1116no—
534C2×#127—111no—
535C2×#127C2×D1111yescharacteristic
536C2×#124—111no—
537C2×#124—111no—
538C2×#121—112no—
539C2×#121—112no—
540C2×#120—112no—
541C2×#120—112no—
542C2×C4×Q8—111no—
543C2×C4×Q8—111no—
544C2×C4×D4—112no—
545C2×C4×D4—111no—
546C2×C4×D4—111no—
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—111no—
550C2×C4×D4—112no—
551C2×C4×D4—111no—
552C2×C4×D4C2×D1111yescharacteristic
553C2×C4×D4C2×D1111yescharacteristic, complemented
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391—111no—
559#390—112no—
560#390—111no—
561#390—111no—
562#390—112no—
563#390—111no—
564#390—112no—
565#390—112no—
566#390—112no—
567#390—112no—
568#390—111no—
569#390C2×D1111yescharacteristic
570#390C2×D1111yescharacteristic, complemented
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—111no—
578#388—111no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—111no—
583#388—111no—
584#388—112no—
585#387—112no—
586#387—112no—
587#387—111no—
588#387—111no—
589#387—111no—
590#387—111no—
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—112no—
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#386C2×D1112yescomplemented
602#386C2×D1112yescomplemented
603#386C2×D1112yescomplemented
604#386C2×D1112yescomplemented
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#384—111no—
610#382C2×D1111yescharacteristic, complemented
611#381—112no—
612#380—111no—
613#380—111no—
614#380—112no—
615#379—112no—
616#379—112no—
617C4×C4⋊C4—111no—
618C4×C4⋊C4—111no—
619C4×C4⋊C4—111no—
620C4×C4⋊C4—111no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—111no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4—112no—
628#376C2×D1111yescharacteristic, complemented
629C2×#95—112no—
630C43—111no—
631C22×C11—24no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11C24×C411yescharacteristic
646C22×C11C2×H(5,𝔽2)11yescharacteristic
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C22×C11C2×H(5,𝔽2)11yescharacteristic
649C22×C11C2×H(5,𝔽2)11yescharacteristic
650C22×C11#58511yescharacteristic
651C22×C11#58511yescharacteristic
652C2×D11—22no—
653C2×D11—24no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—41no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—41no—
662C2×D11—41no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—41no—
666C2×D11—816no—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—41no—
670C4×C11—42no—
671C4×C11—41no—
672C4×C11—41no—
673C4×C11—42no—
674C4×C11—41no—
675C4×C11#51814yes—
676Dic11—24no—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—22no—
682Dic11—42no—
683Dic11—42no—
684Dic11—41no—
685Dic11—41no—
686C25—112no—
687C2×#41—118no—
688C2×#41—442no—
689C2×#41—442no—
690C22×Q8—111no—
691C22×D4—112no—
692C22×D4—112no—
693C22×D4—112no—
694C22×D4—112no—
695C22×D4—118no—
696C22×D4—111no—
697C22×D4—442no—
698C22×D4—442no—
699C22×D4C22×D1111yescharacteristic
700C22×D4C22×D1111yescharacteristic
701C22×D4C22×D1112yes—
702C22×D4C22×D1112yes—
703C23×C4—112no—
704C23×C4—111no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4C22×D1112yes—
710C23×C4C22×D1112yes—
711#127—118no—
712#127C4×D1118yescomplemented
713#124—118no—
714#124—118no—
715#121—1116no—
716#121—1116no—
717#120—1116no—
718#120—1116no—
719C4×Q8—442no—
720C4×Q8—442no—
721C4×D4—42no—
722C4×D4—42no—
723C4×D4—442no—
724C4×D4—444no—
725C4×D4—442no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—444no—
729C4×D4—444no—
730C4×D4—444no—
731#117—118no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4C22×D1111yescharacteristic
745C2×C4⋊C4C22×D1111yescharacteristic
746C2×C22⋊C4—112no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—111no—
755C2×C22⋊C4—111no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—444no—
771C2×C22⋊C4—444no—
772C2×C22⋊C4C22×D1112yes—
773C2×C22⋊C4C22×D1112yes—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1112yes—
778C2×C42—111no—
779C2×C42—111no—
780C2×C42—111no—
781C2×C42—111no—
782C2×C42—111no—
783C2×C42—112no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—111no—
788C2×C42—111no—
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1111yescharacteristic
791C2×C42C22×D1111yescharacteristic
792#95—111no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—111no—
800#95—112no—
801#95—111no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—111no—
807#95—111no—
808#95C22×D1111yescharacteristic
809#95C22×D1111yescharacteristic
810#95C22×D1111yescharacteristic
811#95C22×D1111yescharacteristic
812#95C22×D1112yes—
813#95C22×D1112yes—
814C2×C11—44no—
815C2×C11—44no—
816C2×C11C2×#51811yescharacteristic
817C2×C11C4×H(5,𝔽2)11yescharacteristic
818C2×C11C4×H(5,𝔽2)11yescharacteristic
819C2×C11#354311yescharacteristic
820C2×C11#354611yescharacteristic
821C2×C11#355811yescharacteristic
822C2×C11#356211yescharacteristic
823D11—44no—
824D11—42no—
825C24—111no—
826C24—112no—
827C24—118no—
828C24—442no—
829C24—442no—
830C24—442no—
831C24—442no—
832C24—442no—
833C24—442no—
834C24C23×D1112yes—
835C24C23×D1112yes—
836#41—4416no—
837C2×Q8—114no—
838C2×Q8—222no—
839C2×Q8—222no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—118no—
849C2×D4—118no—
850C2×D4—118no—
851C2×D4—118no—
852C2×D4—114no—
853C2×D4—222no—
854C2×D4—222no—
855C2×D4—4416no—
856C2×D4—442no—
857C2×D4—442no—
858C2×D4—442no—
859C2×D4—442no—
860C2×D4—442no—
861C2×D4—442no—
862C2×D4—442no—
863C2×D4—442no—
864C2×D4C2×C4×D1114yes—
865C2×D4C2×C4×D1114yes—
866C2×D4C2×C4×D1118yes—
867C2×D4C2×C4×D1118yes—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—111no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—111no—
878C22×C4—112no—
879C22×C4—111no—
880C22×C4—118no—
881C22×C4—114no—
882C22×C4—111no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—112no—
886C22×C4—224no—
887C22×C4—224no—
888C22×C4—224no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—442no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4—442no—
896C22×C4—442no—
897C22×C4—442no—
898C22×C4—442no—
899C22×C4—442no—
900C22×C4—442no—
901C22×C4—442no—
902C22×C4C23×D1112yes—
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1112yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—114no—
914C4⋊C4—114no—
915C4⋊C4—222no—
916C4⋊C4—222no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—442no—
920C4⋊C4—442no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—441no—
924C4⋊C4—441no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—118no—
932C22⋊C4—118no—
933C22⋊C4—114no—
934C22⋊C4—114no—
935C22⋊C4—118no—
936C22⋊C4—118no—
937C22⋊C4—222no—
938C22⋊C4—222no—
939C22⋊C4—224no—
940C22⋊C4—224no—
941C22⋊C4—224no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—441no—
949C22⋊C4—442no—
950C22⋊C4—441no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C42—22no—
956C42—22no—
957C42—114no—
958C42—222no—
959C42—222no—
960C42—222no—
961C42—222no—
962C42—442no—
963C42—442no—
964C42—442no—
965C42—442no—
966C42—441no—
967C42—441no—
968C42C2×C4×D1114yes—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—112no—
983C23—114no—
984C23—222no—
985C23—221no—
986C23—222no—
987C23—221no—
988C23—221no—
989C23—221no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—221no—
994C23—221no—
995C23—222no—
996C23—448no—
997C23—448no—
998C23—448no—
999C23—884no—
1000C23—884no—
1001C23—884no—
1002C23—884no—
1003C23C22×C4×D1114yes—
1004C23C22×C4×D1114yes—
1005C23C24×D1111yescharacteristic
1006Q8—228no—
1007D4—28no—
1008D4—28no—
1009D4—48no—
1010D4—48no—
1011D4—228no—
1012D4—448no—
1013D4—448no—
1014D4—448no—
1015D4—448no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—112no—
1041C2×C4—112no—
1042C2×C4—114no—
1043C2×C4—112no—
1044C2×C4—112no—
1045C2×C4—112no—
1046C2×C4—221no—
1047C2×C4—222no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—228no—
1059C2×C4—221no—
1060C2×C4—221no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—448no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4—884no—
1075C2×C4—884no—
1076C2×C4C22×C4×D1112yes—
1077C2×C4C22×C4×D1112yes—
1078C2×C4C22×C4×D1112yes—
1079C2×C4#6703712yes—
1080C2×C4#6704212yes—
1081C22—24no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—222no—
1096C22—224no—
1097C22—224no—
1098C22—224no—
1099C22—222no—
1100C22—222no—
1101C22—442no—
1102C22—441no—
1103C22—441no—
1104C22—442no—
1105C22—441no—
1106C22—442no—
1107C22—442no—
1108C22—441no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6704211yescharacteristic
1113C22D11×H(5,𝔽2)11yescharacteristic
1114C22D11×H(5,𝔽2)11yescharacteristic
1115C22#1062345511yescharacteristic
1116C22#1062345511yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—42no—
1123C4—41no—
1124C4—42no—
1125C4—222no—
1126C4—222no—
1127C4—224no—
1128C4—222no—
1129C4—222no—
1130C4—222no—
1131C4—442no—
1132C4—442no—
1133C4—441no—
1134C4—441no—
1135C4#1062307614yes—
1136C2—44no—
1137C2—44no—
1138C2—442no—
1139C2—444no—
1140C2C2×#1062307611yescharacteristic
1141C2#1308182011yescharacteristic
1142C2#1308182011yescharacteristic
1143C2#1308294511yescharacteristic
1144C2#1308297711yescharacteristic
1145C2#1308313411yescharacteristic
1146C2#1308320611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2328C2
socle, cosocleC23×C11C25
prime radicalC2×#10623246C2
hypercenter#2328D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #13071774C2semidirect
3. #13071754C2semidirect
4. #13071689C2semidirect
5. #13071686C2semidirect
6. #13071678C2semidirect
7. #13071677C2semidirect
8. #13071664C2semidirect
9. #13071596C2semidirect
10. #13071455C2semidirect
11. #13071441C2semidirect
12. #13071437C2semidirect
13. D4×(C2×D11)⋊C4C2semidirect
14. #13071382C2semidirect
15. #13071327C2semidirect
16. #13071317C2semidirect
17. #13071279C2semidirect
18. #13071272C2semidirect
19. #13071226C2semidirect
20. #127×Dic11C2semidirect
21. #13071155C2semidirect
22. #13071111C2semidirect
23. C11×#2328C2semidirect
28. C2×C4×D4×C11C22semidirect
36. C2×D4×Dic11C22semidirect
37. C2×D4×Dic11C22semidirect
38. C2×D4×Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
41. #10623246C4semidirect
43. C2×#66940C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
49. C2×C4×Dic22C22semidirect
51. C11×#390C22semidirect
52. C11×#386C22semidirect
53. C11×#386C22semidirect
54. C11×#386C22semidirect
55. C11×#386C22semidirect
56. C11×#382C22semidirect
57. C11×#376C22semidirect
59. #10622834C22semidirect
60. #10622834C22semidirect
61. #10622834C22semidirect
64. #10622826C22semidirect
65. #10622823C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. C2×C11⋊#95C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. #10622587C22semidirect
76. #10622571C22semidirect
79. #10622570C22semidirect
80. #10622570C22semidirect
83. #10622569C22semidirect
84. #10622569C22semidirect
87. #10622559C22semidirect
88. #10622558C22semidirect
89. #10622558C22semidirect
90. #10622557C22semidirect
91. #10622557C22semidirect
92. #10622556C22semidirect
93. #10622555C22semidirect
94. C22⋊C4×Dic11C22semidirect
95. C22⋊C4×Dic11C22semidirect
99. #10622548C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C42×Dic11C22semidirect
103. #10622542C22semidirect
106. #10622283C22semidirect
107. #10622283C22semidirect
112. #10622282C22semidirect
113. #10622282C22semidirect
114. #10622281C22semidirect
115. #10622281C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622268C22semidirect
119. #10622268C22semidirect
120. #10622265C22semidirect
121. #10622265C22semidirect
122. #10622265C22semidirect
123. #10622265C22semidirect
140. C2×#4341C2×C4semidirect
143. C2×D4×D11C2×C4semidirect
149. C11×#127C2×C4semidirect
171. #66993C2×C4semidirect
172. #66992C2×C4semidirect
173. #66992C2×C4semidirect
174. #66990C2×C4semidirect
175. #66990C2×C4semidirect
176. #66989C2×C4semidirect
226. #66928C2×C4semidirect
228. #66925C2×C4semidirect
411. #2328D11semidirect
553. C2×C4×D4C2×D11semidirect
570. #390C2×D11semidirect
601. #386C2×D11semidirect
602. #386C2×D11semidirect
603. #386C2×D11semidirect
604. #386C2×D11semidirect
610. #382C2×D11semidirect
628. #376C2×D11semidirect
712. #127C4×D11semidirect
969. C11#34438semidirect

Maximal subgroups

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

subgroupindex
C2×#106232462
#130717742
#130717542
#130716892
#130716862
#130716782
#130716772
#130716642
#130715962
#130714552
#130714412
#130714372
D4×(C2×D11)⋊C42
#130713822
#130713272
#130713172
#130712792
#130712722
#130712262
#127×Dic112
#130711552
#130711112
C11×#23282
#3443811