Finite Group Databasebeta

← #14916563

Subgroups — #14916563

Order 2816.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13071783C212yesmaximal, complemented
3#13071767C212yesmaximal, complemented
4#13071700C212yesmaximal, complemented
5#13071660C212yesmaximal, complemented
6#13071560C211yesmaximal, characteristic, complemented
7#13071548C211yesmaximal, characteristic, complemented
8#13071546C211yesmaximal, characteristic, complemented
9#13071546C211yesmaximal, characteristic, complemented
10#13071545C211yesmaximal, characteristic, complemented
11#13071516C211yesmaximal, characteristic, complemented
12#13071512C211yesmaximal, characteristic, complemented
13#13071404C212yesmaximal, complemented
14#13071400C212yesmaximal, complemented
15#13071275C212yesmaximal, complemented
16#13071269C212yesmaximal, complemented
17#13071224C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071205C211yesmaximal, characteristic, complemented
20#13071204C211yesmaximal, characteristic, complemented
21#13070995C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2354C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic, complemented
35#10623078C4116yescomplemented
36C2×#66949C2211yescharacteristic
37C2×#66947C2211yescharacteristic
38C2×#66946C2212yes—
39C2×#66945C2211yescharacteristic, complemented
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic, complemented
43C2×#66937C2211yescharacteristic
44C2×#66936C2211yescharacteristic
45C2×#66935C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×#66931C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C2×#66925C2211yescharacteristic
51C11×#390C2212yes—
52C11×#388C2212yes—
53C11×#388C2212yescomplemented
54C11×#384C2211yescharacteristic, complemented
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic, complemented
57C4×C11×C4⋊C4C2212yescomplemented
58C4×C11×C4⋊C4C2211yescharacteristic, complemented
59#10622833C2212yes—
60#10622825C2211yescharacteristic
61#10622825C2211yescharacteristic, complemented
62#10622603C2212yes—
63#10622603C2212yes—
64#10622602C2212yes—
65#10622602C2212yescomplemented
66#10622600C2211yescharacteristic
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic, complemented
73#10622600C2211yescharacteristic, complemented
74#10622594C2212yescomplemented
75#10622591C2212yescomplemented
76#10622591C2212yescomplemented
77#10622590C2211yescharacteristic, complemented
78#10622589C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81#10622586C2212yescomplemented
82#10622571C2212yes—
83#10622571C2212yescomplemented
84#10622570C2212yes—
85#10622570C2212yes—
86#10622569C2212yes—
87#10622569C2212yes—
88#10622569C2212yescomplemented
89#10622568C2212yes—
90#10622564C2212yes—
91#10622559C2212yescomplemented
92#10622558C2212yes—
93#10622558C2212yes—
94#10622558C2212yescomplemented
95#10622556C2212yes—
96#10622555C2212yes—
97C22⋊C4×Dic11C2212yescomplemented
98#10622553C2212yes—
99#10622553C2212yescomplemented
100#10622552C2212yes—
101C4×(C2×D11)⋊C4C2212yes—
102C4×(C2×D11)⋊C4C2212yes—
103C4×(C2×D11)⋊C4C2212yes—
104C4×(C2×D11)⋊C4C2212yes—
105C4×(C2×D11)⋊C4C2212yescomplemented
106#10622549C2211yescharacteristic, complemented
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108#10622546C2212yescomplemented
109#10622546C2212yescomplemented
110#10622546C2212yescomplemented
111#10622542C2212yescomplemented
112#10622282C2212yes—
113#10622282C2212yescomplemented
114#10622281C2212yes—
115#10622280C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118D11×#95C2212yes—
119#10622266C2212yescomplemented
120#10622265C2212yescomplemented
121#10622262C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C2×#4339—42no—
135C2×#4339—42no—
136C2×#4339C2×C418yescomplemented
137C22×D44C2311yescharacteristic
138C22×D44C2311yescharacteristic
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C4×D4×C11C2×C418yescomplemented
152C11×#117—42no—
153C11×#117—42no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C42×C11C2312yes—
169C2×C42×C11C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176#66992C2×C418yescomplemented
177#66990C2×C418yescomplemented
178C4×C22⋊D11C2×C418yescomplemented
179C4×C22⋊D11C2×C418yescomplemented
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195#66979—42no—
196C2×C4⋊Dic11—42no—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218#66949C2×C418yescomplemented
219#66947C2×C418yescomplemented
220#66946—44no—
221#66945—42no—
222C4⋊C4×D11—42no—
223C4⋊C4×D11—42no—
224C4⋊C4×D11—42no—
225#66937C2×C418yes—
226#66936C2×C418yescomplemented
227#66935C2×C418yescomplemented
228(C22⋊D11)⋊C4—44no—
229C22⋊C4×D11—44no—
230#66931C2×C418yescomplemented
231C4×D44C2×C418yescomplemented
232#66925C2×C418yescomplemented
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34362—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C24×C11C2411yescharacteristic
256C23×D11—22no—
257C23×D11—22no—
258C23×D11—41no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11C22×C414yes—
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C2×D4×C11—41no—
267C2×D4×C11—41no—
268C2×D4×C11C22×C414yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11C22×C414yes—
274C22×C4×C11C22×C414yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—22no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—41no—
287C2×C22⋊D11—41no—
288C2×C22⋊D11—41no—
289C2×C22⋊D11—41no—
290C2×C22⋊D11—41no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11C22×C414yes—
293C2×C22⋊D11C22×C414yes—
294C2×C22⋊D11C22×C414yes—
295C2×C22⋊D11C22×C414yes—
296C22×Dic11—41no—
297C22×Dic11—41no—
298C22×Dic11—42no—
299C22×Dic11—42no—
300C22×Dic11—42no—
301C22×Dic11C22×C414yes—
302C22×Dic11C2412yes—
303C22×Dic11C2412yes—
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311#4339—416no—
312C2×D44—22no—
313C2×D44—22no—
314C2×D44—41no—
315C2×D44—41no—
316C2×D44C22×C414yes—
317C2×D44C22×C414yes—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—41no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—416no—
338C2×C4×D11C22×C414yes—
339C2×C4×D11C22×C414yes—
340C2×C4×D11C22×C414yes—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×Dic22—41no—
344C2×Dic22—41no—
345C2×Dic22C22×C414yes—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4—42no—
352C11×C4⋊C4C22×C414yes—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4C22×C414yes—
358C11×C22⋊C4C22×C414yes—
359C42×C11—42no—
360C42×C11—42no—
361C42×C11—42no—
362C42×C11C22×C414yes—
363C22⋊Dic11—42no—
364C22⋊Dic11—42no—
365C22⋊Dic11—42no—
366C22⋊Dic11C22×C414yes—
367C22⋊Dic11C22×C414yes—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C414yes—
379(C2×D11)⋊C4C22×C414yes—
380(C2×D11)⋊C4C22×C414yes—
381(C2×D11)⋊C4C22×C414yes—
382(C2×D11)⋊C4C22×C414yes—
383C4⋊Dic11—22no—
384C4⋊Dic11—22no—
385C4⋊Dic11—22no—
386C4⋊Dic11—22no—
387C4⋊Dic11—42no—
388C4⋊Dic11C22×C414yes—
389Dic11⋊C4—42no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4—42no—
393Dic11⋊C4—42no—
394Dic11⋊C4C22×C414yes—
395Dic11⋊C4C22×C414yes—
396Dic11⋊C4C22×C414yes—
397Dic11⋊C4C22×C414yes—
398C4×Dic11—42no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11C22×C414yes—
404C2×#525—111no—
405#2378—112no—
406#2377—112no—
407#2368—112no—
408#2364—112no—
409#2354—111no—
410#2354D1111yescharacteristic, complemented
411#2352—111no—
412#2352—111no—
413#2352—111no—
414#2352—111no—
415D4×C4⋊C4—111no—
416D4×C4⋊C4—111no—
417#2335—112no—
418#2335—112no—
419#2321—112no—
420#2321—112no—
421#2314—111no—
422#2314—111no—
423#2311—111no—
424#2311—111no—
425#2280—111no—
426C2×#380—111no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11C23×C412yes—
440C23×C11C23×C412yes—
441C23×C11C2511yescharacteristic
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—28no—
459C22×D11—44no—
460C22×D11—44no—
461C22×D11—44no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11C23×C412yes—
466C22×D11C23×C412yes—
467C22×D11C23×C412yes—
468C22×D11H(5,𝔽2)12yes—
469C22×D112−1+412yes—
470D4×C11—44no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—28no—
480C2×C4×C11—28no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11C23×C412yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C22⋊D11—28no—
501C22⋊D11—44no—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—44no—
527C2×Dic11—84no—
528C2×Dic11C23×C412yes—
529C2×Dic11C23×C412yes—
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C412yes—
532C2×Dic11C23×C412yes—
533D44—28no—
534D44—44no—
535C4×D11—28no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—84no—
541C4×D11—84no—
542C4×D11—84no—
543Dic22—44no—
544C22×#41—111no—
545C24×C4—111no—
546#525—1116no—
547C2×#123—111no—
548C2×#123—111no—
549C2×C22⋊Q8—111no—
550C2×C22⋊Q8—111no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#120—111no—
554C2×#120—111no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—112no—
558C2×C4×D4—112no—
559C2×C4×D4—111no—
560C2×C4×D4C2×D1111yescharacteristic
561C2×#117—111no—
562C2×#117—111no—
563C2×#117—111no—
564C2×#117C2×D1111yescharacteristic
565C2×#117C2×D1111yescharacteristic, complemented
566C22×C4⋊C4—111no—
567C22×C4⋊C4—111no—
568C22×C4⋊C4—111no—
569C22×C4⋊C4—111no—
570C22×C22⋊C4—112no—
571#391—112no—
572#391—112no—
573#390—112no—
574#390—112no—
575#390—112no—
576#390C2×D1112yes—
577#389—112no—
578#389—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388C2×D1112yes—
590#388C2×D1112yescomplemented
591#387—112no—
592#387—112no—
593#387—112no—
594#387—112no—
595#387—112no—
596#387—112no—
597#387—112no—
598#387—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#385—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#384—111no—
612#384C2×D1111yescharacteristic, complemented
613#382—111no—
614#382—111no—
615#381—112no—
616#380—111no—
617#380—111no—
618#380—111no—
619#380—111no—
620#380—111no—
621#380—111no—
622#380—111no—
623#380—111no—
624#380—111no—
625#380—111no—
626#380—112no—
627#380—112no—
628#380C2×D1111yescharacteristic
629#380C2×D1111yescharacteristic, complemented
630#379—112no—
631C4×C4⋊C4—111no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—112no—
635C4×C4⋊C4C2×D1111yescharacteristic, complemented
636C4×C4⋊C4C2×D1112yescomplemented
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C2×#95—112no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—41no—
658C22×C11C24×C411yescharacteristic
659C22×C11C2×H(5,𝔽2)11yescharacteristic
660C22×C11C2×H(5,𝔽2)11yescharacteristic
661C22×C11C2×H(5,𝔽2)11yescharacteristic
662C22×C11C2×2−1+411yescharacteristic
663C22×C11#58511yescharacteristic
664C22×C11#58511yescharacteristic
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—416no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11#52014yes—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—22no—
690C4×C11—22no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11—42no—
695C4×C11#51814yes—
696Dic11—22no—
697Dic11—22no—
698Dic11—22no—
699Dic11—22no—
700Dic11—22no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C2×#41—118no—
707C2×#41—442no—
708C2×#41—442no—
709C22×Q8—111no—
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4C22×D1111yescharacteristic
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—118no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—112no—
727C23×C4—112no—
728C23×C4—442no—
729C23×C4—442no—
730C23×C4C22×D1111yescharacteristic
731C23×C4C22×D1111yescharacteristic
732#123—118no—
733#123—118no—
734C22⋊Q8—118no—
735C22⋊Q8—118no—
736#121—118no—
737#121—118no—
738#120—118no—
739#120—118no—
740C4×D4—118no—
741C4×D4—118no—
742C4×D4—118no—
743C4×D4—444no—
744C4×D4—444no—
745C4×D4C4×D1118yescomplemented
746#117—42no—
747#117—42no—
748#117—118no—
749#117—442no—
750#117—442no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—442no—
767C2×C4⋊C4—442no—
768C2×C4⋊C4—442no—
769C2×C4⋊C4—442no—
770C2×C4⋊C4C22×D1111yescharacteristic
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1111yescharacteristic
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1112yes—
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—444no—
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C22⋊C4C22×D1111yescharacteristic
804C2×C42—111no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42C22×D1112yes—
811C2×C42C22×D1112yes—
812C2×C42C22×D1112yes—
813C2×C42C22×D1111yescharacteristic
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95C22×D1112yes—
832#95C22×D1112yes—
833#95C22×D1112yes—
834C2×C11—42no—
835C2×C11—42no—
836C2×C11C2×#51811yescharacteristic
837C2×C11C2×#52011yescharacteristic
838C2×C11#342811yescharacteristic
839C2×C11#354111yescharacteristic
840C2×C11#354111yescharacteristic
841C2×C11#354211yescharacteristic
842C2×C11#354211yescharacteristic
843D11—24no—
844D11—42no—
845D11—42no—
846C24—111no—
847C24—111no—
848C24—111no—
849C24—114no—
850C24—222no—
851C24—222no—
852C24—441no—
853C24—441no—
854C24—441no—
855C24—441no—
856C24C23×D1111yescharacteristic
857C24C23×D1111yescharacteristic
858#41—4416no—
859C2×Q8—114no—
860C2×Q8—441no—
861C2×Q8—441no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—114no—
865C2×D4—114no—
866C2×D4—114no—
867C2×D4—114no—
868C2×D4—114no—
869C2×D4—114no—
870C2×D4—222no—
871C2×D4—222no—
872C2×D4—222no—
873C2×D4—222no—
874C2×D4—441no—
875C2×D4—441no—
876C2×D4—441no—
877C2×D4—441no—
878C2×D4—441no—
879C2×D4—441no—
880C2×D4—441no—
881C2×D4—441no—
882C2×D4C2×C4×D1114yes—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—111no—
890C22×C4—111no—
891C22×C4—111no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—114no—
895C22×C4—114no—
896C22×C4—114no—
897C22×C4—114no—
898C22×C4—112no—
899C22×C4—112no—
900C22×C4—112no—
901C22×C4—112no—
902C22×C4—224no—
903C22×C4—224no—
904C22×C4—222no—
905C22×C4—222no—
906C22×C4—222no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—4416no—
911C22×C4—441no—
912C22×C4—441no—
913C22×C4—441no—
914C22×C4—441no—
915C22×C4—442no—
916C22×C4—442no—
917C22×C4—442no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—441no—
923C22×C4—441no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4C2×C4×D1114yes—
928C22×C4C2×C4×D1114yes—
929C22×C4C23×D1112yes—
930C22×C4C23×D1112yes—
931C22×C4C23×D1112yes—
932C22×C4C23×D1112yes—
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1111yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—114no—
945C4⋊C4—114no—
946C4⋊C4—114no—
947C4⋊C4—114no—
948C4⋊C4—114no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4C2×C4×D1114yes—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—114no—
965C22⋊C4—114no—
966C22⋊C4—114no—
967C22⋊C4—114no—
968C22⋊C4—114no—
969C22⋊C4—114no—
970C22⋊C4—114no—
971C22⋊C4—114no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4C2×C4×D1114yes—
985C22⋊C4C2×C4×D1114yes—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—114no—
990C42—442no—
991C42—442no—
992C42—442no—
993C42—442no—
994C42—442no—
995C42C2×C4×D1114yes—
996C11#3436211yescharacteristic, complemented, Sylow
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—112no—
1010C23—112no—
1011C23—112no—
1012C23—112no—
1013C23—112no—
1014C23—228no—
1015C23—221no—
1016C23—221no—
1017C23—221no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—221no—
1023C23—221no—
1024C23—221no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—444no—
1032C23—444no—
1033C23—444no—
1034C23—444no—
1035C23—444no—
1036C23—444no—
1037C23C22×C4×D1112yes—
1038C23C22×C4×D1112yes—
1039C23C24×D1111yescharacteristic
1040Q8—444no—
1041D4—44no—
1042D4—228no—
1043D4—228no—
1044D4—444no—
1045D4—444no—
1046D4—444no—
1047D4—444no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—112no—
1071C2×C4—112no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—112no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—228no—
1086C2×C4—228no—
1087C2×C4—228no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—444no—
1101C2×C4—444no—
1102C2×C4—444no—
1103C2×C4—884no—
1104C2×C4—884no—
1105C2×C4—884no—
1106C2×C4—884no—
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1112yes—
1110C2×C4C22×C4×D1112yes—
1111C2×C4C22×C4×D1112yes—
1112C2×C4#6703712yes—
1113C2×C4#6704212yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—114no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—222no—
1133C22—222no—
1134C22—222no—
1135C22—222no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—4416no—
1142C22—441no—
1143C22—441no—
1144C22—441no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22C23×C4×D1111yescharacteristic
1151C22C2×#6703711yescharacteristic
1152C22C2×#6704211yescharacteristic
1153C22#1062345311yescharacteristic
1154C22#1062345311yescharacteristic
1155C22D11×H(5,𝔽2)11yescharacteristic
1156C22D11×2−1+411yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—222no—
1166C4—222no—
1167C4—222no—
1168C4—222no—
1169C4—222no—
1170C4—442no—
1171C4—442no—
1172C4—442no—
1173C4—442no—
1174C4#1062307614yes—
1175C2—42no—
1176C2—42no—
1177C2—224no—
1178C2—442no—
1179C2—442no—
1180C2C2×#1062307611yescharacteristic
1181C2D11×#52011yescharacteristic
1182C2#1308181711yescharacteristic
1183C2#1308289911yescharacteristic
1184C2#1308291611yescharacteristic
1185C2#1308292211yescharacteristic
1186C2#1308293911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2354C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2354D11
hypocenterC11#34362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13071783C2semidirect
3. #13071767C2semidirect
4. #13071700C2semidirect
5. #13071660C2semidirect
6. #13071560C2semidirect
7. #13071548C2semidirect
8. #13071546C2semidirect
9. #13071546C2semidirect
10. #13071545C2semidirect
11. #13071516C2semidirect
12. #13071512C2semidirect
13. #13071404C2semidirect
14. #13071400C2semidirect
15. #13071275C2semidirect
16. #13071269C2semidirect
17. #13071224C2semidirect
18. #13071221C2semidirect
19. #13071205C2semidirect
20. #13071204C2semidirect
21. #13070995C2semidirect
22. D11×#380C2semidirect
23. C11×#2354C2semidirect
28. C2×C11×#117C22semidirect
34. C22×C4⋊Dic11C22semidirect
35. #10623078C4semidirect
39. C2×#66945C22semidirect
42. C2×C4⋊C4×D11C22semidirect
53. C11×#388C22semidirect
54. C11×#384C22semidirect
56. C11×#380C22semidirect
57. C4×C11×C4⋊C4C22semidirect
58. C4×C11×C4⋊C4C22semidirect
61. #10622825C22semidirect
65. #10622602C22semidirect
72. #10622600C22semidirect
73. #10622600C22semidirect
74. #10622594C22semidirect
75. #10622591C22semidirect
76. #10622591C22semidirect
77. #10622590C22semidirect
78. #10622589C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622586C22semidirect
83. #10622571C22semidirect
88. #10622569C22semidirect
91. #10622559C22semidirect
94. #10622558C22semidirect
97. C22⋊C4×Dic11C22semidirect
99. #10622553C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. #10622549C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. #10622546C22semidirect
109. #10622546C22semidirect
110. #10622546C22semidirect
111. #10622542C22semidirect
113. #10622282C22semidirect
119. #10622266C22semidirect
120. #10622265C22semidirect
121. #10622262C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
136. C2×#4339C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
151. C4×D4×C11C2×C4semidirect
176. #66992C2×C4semidirect
177. #66990C2×C4semidirect
178. C4×C22⋊D11C2×C4semidirect
179. C4×C22⋊D11C2×C4semidirect
218. #66949C2×C4semidirect
219. #66947C2×C4semidirect
226. #66936C2×C4semidirect
227. #66935C2×C4semidirect
230. #66931C2×C4semidirect
231. C4×D44C2×C4semidirect
232. #66925C2×C4semidirect
410. #2354D11semidirect
565. C2×#117C2×D11semidirect
590. #388C2×D11semidirect
612. #384C2×D11semidirect
629. #380C2×D11semidirect
635. C4×C4⋊C4C2×D11semidirect
636. C4×C4⋊C4C2×D11semidirect
745. C4×D4C4×D11semidirect
996. C11#34362semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
#130717832
#130717672
#130717002
#130716602
#130715602
#130715482
#130715462
#130715452
#130715162
#130715122
#130714042
#130714002
#130712752
#130712692
#130712242
#130712212
#130712052
#130712042
#130709952
D11×#3802
C11×#23542
#3436211