Finite Group Databasebeta

← #14916549

Subgroups — #14916549

Order 2816.

2458 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13071756C212yesmaximal, complemented
3#13071753C212yesmaximal, complemented
4#13071745C212yesmaximal, complemented
5#13071744C212yesmaximal, complemented
6#13071567C211yesmaximal, characteristic, complemented
7#13071566C211yesmaximal, characteristic, complemented
8#13071566C211yesmaximal, characteristic, complemented
9#13071548C211yesmaximal, characteristic, complemented
10#13071547C211yesmaximal, characteristic, complemented
11#13071545C211yesmaximal, characteristic, complemented
12#13071538C211yesmaximal, characteristic, complemented
13#13071379C212yesmaximal, complemented
14#13071375C212yesmaximal, complemented
15#13071367C212yesmaximal, complemented
16#13071366C212yesmaximal, complemented
17#13071224C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071205C211yesmaximal, characteristic, complemented
20#13071204C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22#13070995C211yesmaximal, 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×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66945C2211yescharacteristic, complemented
41C2×C4⋊C4×D11C2211yescharacteristic, complemented
42C2×#66937C2211yescharacteristic
43C2×#66936C2211yescharacteristic
44C2×#66935C2211yescharacteristic
45C2×#66931C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66925C2211yescharacteristic
48C11×#390C2212yes—
49C11×#388C2212yes—
50C11×#388C2212yescomplemented
51C11×#384C2211yescharacteristic, complemented
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic, complemented
54C4×C11×C4⋊C4C2212yescomplemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56#10622833C2212yes—
57#10622825C2211yescharacteristic
58#10622825C2211yescharacteristic, complemented
59#10622603C2212yes—
60#10622603C2212yes—
61#10622603C2212yes—
62#10622603C2212yescomplemented
63#10622601C2212yes—
64#10622600C2211yescharacteristic
65#10622600C2211yescharacteristic
66#10622600C2211yescharacteristic
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic, complemented
71#10622600C2211yescharacteristic, complemented
72#10622594C2212yescomplemented
73#10622591C2212yescomplemented
74#10622591C2212yescomplemented
75#10622590C2211yescharacteristic, complemented
76#10622589C2211yescharacteristic, complemented
77C4⋊C4×Dic11C2212yescomplemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80#10622571C2212yes—
81#10622571C2212yes—
82#10622571C2212yescomplemented
83#10622570C2212yes—
84#10622570C2212yes—
85#10622570C2212yes—
86#10622569C2212yes—
87#10622569C2212yescomplemented
88#10622568C2212yes—
89#10622568C2212yes—
90#10622564C2212yes—
91#10622557C2212yes—
92#10622557C2212yes—
93#10622557C2212yescomplemented
94#10622556C2212yes—
95C22⋊C4×Dic11C2212yes—
96C22⋊C4×Dic11C2212yescomplemented
97C22⋊C4×Dic11C2212yescomplemented
98#10622553C2212yes—
99#10622553C2212yes—
100#10622553C2212yes—
101#10622553C2212yescomplemented
102#10622552C2212yes—
103C4×(C2×D11)⋊C4C2212yes—
104C4×(C2×D11)⋊C4C2212yes—
105C4×(C2×D11)⋊C4C2212yescomplemented
106#10622549C2211yescharacteristic, complemented
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108#10622546C2212yescomplemented
109C4×Dic11⋊C4C2212yescomplemented
110C4×Dic11⋊C4C2212yescomplemented
111#10622542C2212yescomplemented
112#10622283C2212yes—
113#10622282C2212yes—
114#10622279C2212yes—
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622277C2212yes—
119#10622268C2212yescomplemented
120#10622266C2212yescomplemented
121#10622265C2212yescomplemented
122#10622265C2212yescomplemented
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×C418yes—
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×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×Dic22C2311yescharacteristic
149C4×D4×C11C2×C418yescomplemented
150C11×#117—42no—
151C11×#117—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2312yes—
167C2×C42×C11C2312yes—
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174#66992C2×C418yes—
175#66990C2×C418yescomplemented
176C4×C22⋊D11C2×C418yescomplemented
177C4×C22⋊D11C2×C418yescomplemented
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
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⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
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#66945—42no—
221#66945—42no—
222#66945—42no—
223C4⋊C4×D11—42no—
224#66937C2×C418yes—
225#66936C2×C418yescomplemented
226#66935C2×C418yescomplemented
227#66931C2×C418yescomplemented
228C4×D44C2×C418yescomplemented
229#66925C2×C418yescomplemented
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
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—
250#34361—111nomaximal, Sylow
251C24×C11C2411yescharacteristic
252C24×C11C2411yescharacteristic
253C23×D11—41no—
254C23×D11—41no—
255C23×D11—41no—
256C23×D11—41no—
257C23×D11—41no—
258C23×D11—41no—
259C23×D11C22×C414yes—
260C23×D11C2411yescharacteristic
261C23×D11C2411yescharacteristic
262C23×D11C2411yescharacteristic
263C2×D4×C11—41no—
264C2×D4×C11—41no—
265C2×D4×C11C22×C414yes—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11C22×C414yes—
271C22×C4×C11C22×C414yes—
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C22×C4×C11C2412yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—41no—
282C2×C22⋊D11—41no—
283C2×C22⋊D11—41no—
284C2×C22⋊D11—41no—
285C2×C22⋊D11—41no—
286C2×C22⋊D11—41no—
287C2×C22⋊D11—41no—
288C2×C22⋊D11—41no—
289C2×C22⋊D11C22×C414yes—
290C2×C22⋊D11C22×C414yes—
291C2×C22⋊D11C22×C414yes—
292C2×C22⋊D11C22×C414yes—
293C22×Dic11—41no—
294C22×Dic11—41no—
295C22×Dic11—42no—
296C22×Dic11—42no—
297C22×Dic11—42no—
298C22×Dic11C22×C414yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2412yes—
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2411yescharacteristic
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308#4339—416no—
309C2×D44—41no—
310C2×D44—41no—
311C2×D44—41no—
312C2×D44—41no—
313C2×D44C22×C414yes—
314C2×D44C22×C414yes—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—41no—
322C2×C4×D11—41no—
323C2×C4×D11—41no—
324C2×C4×D11—41no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—416no—
329C2×C4×D11C22×C414yes—
330C2×C4×D11C22×C414yes—
331C2×C4×D11C22×C414yes—
332C2×C4×D11C22×C414yes—
333C2×C4×D11C22×C414yes—
334C2×Dic22—41no—
335C2×Dic22—41no—
336C2×Dic22C22×C414yes—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—42no—
342C11×C4⋊C4—42no—
343C11×C4⋊C4C22×C414yes—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4C22×C414yes—
349C11×C22⋊C4C22×C414yes—
350C42×C11—42no—
351C42×C11—42no—
352C42×C11—42no—
353C42×C11C22×C414yes—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11C22×C414yes—
358C22⋊Dic11C22×C414yes—
359(C2×D11)⋊C4—42no—
360(C2×D11)⋊C4—42no—
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—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4C22×C414yes—
371(C2×D11)⋊C4C22×C414yes—
372(C2×D11)⋊C4C22×C414yes—
373(C2×D11)⋊C4C22×C414yes—
374(C2×D11)⋊C4C22×C414yes—
375(C2×D11)⋊C4C22×C414yes—
376C4⋊Dic11—22no—
377C4⋊Dic11—22no—
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11—42no—
381C4⋊Dic11C22×C414yes—
382Dic11⋊C4—42no—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385Dic11⋊C4C22×C414yes—
386Dic11⋊C4C22×C414yes—
387Dic11⋊C4C22×C414yes—
388Dic11⋊C4C22×C414yes—
389C4×Dic11—42no—
390C4×Dic11—42no—
391C4×Dic11—42no—
392C4×Dic11—42no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11—42no—
396C4×Dic11C22×C414yes—
397C2×#525—111no—
398#2375—112no—
399#2375—112no—
400#2374—112no—
401#2374—112no—
402#2354—111no—
403#2354—111no—
404#2354—111no—
405#2354D1111yescharacteristic, complemented
406#2352—111no—
407#2352—111no—
408#2352—111no—
409#2352—111no—
410#2333—112no—
411#2333—112no—
412#2332—112no—
413#2332—112no—
414#2314—111no—
415#2314—111no—
416#2311—111no—
417#2311—111no—
418#2280—111no—
419#2280—111no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—21no—
426C23×C11—21no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11C23×C412yes—
433C23×C11C23×C412yes—
434C23×C11C2511yescharacteristic
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—21no—
441C22×D11—21no—
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—44no—
454C22×D11—44no—
455C22×D11—44no—
456C22×D11—44no—
457C22×D11—44no—
458C22×D11—44no—
459C22×D11—44no—
460C22×D11C23×C412yes—
461C22×D11C23×C412yes—
462C22×D11C23×C412yes—
463D4×C11—44no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—28no—
473C2×C4×C11—28no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C412yes—
489C2×C4×C11C23×C412yes—
490C2×C4×C11C23×C412yes—
491C2×C4×C11H(5,𝔽2)12yes—
492C2×C4×C11H(5,𝔽2)12yes—
493C22⋊D11—44no—
494C22⋊D11—44no—
495C22⋊D11—44no—
496C22⋊D11—44no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—44no—
520C2×Dic11—84no—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C412yes—
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C412yes—
526D44—44no—
527D44—44no—
528C4×D11—28no—
529C4×D11—28no—
530C4×D11—28no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—84no—
534Dic22—44no—
535C22×#41—111no—
536C24×C4—111no—
537#525—1116no—
538C2×#123—111no—
539C2×#123—111no—
540C2×C22⋊Q8—111no—
541C2×C22⋊Q8—111no—
542C2×#121—111no—
543C2×#121—111no—
544C2×#120—111no—
545C2×#120—111no—
546C2×C4×D4—111no—
547C2×C4×D4—111no—
548C2×C4×D4—111no—
549C2×C4×D4C2×D1111yescharacteristic
550C2×#117—111no—
551C2×#117—111no—
552C2×#117—111no—
553C2×#117—111no—
554C2×#117—111no—
555C2×#117C2×D1111yescharacteristic
556C2×#117C2×D1111yescharacteristic, complemented
557C22×C4⋊C4—111no—
558C22×C4⋊C4—111no—
559#391—112no—
560#391—112no—
561#390—112no—
562#390—112no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390C2×D1112yes—
567#388—112no—
568#388—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388C2×D1112yes—
582#388C2×D1112yescomplemented
583#387—112no—
584#387—112no—
585#387—112no—
586#387—112no—
587#387—112no—
588#387—112no—
589#387—112no—
590#387—112no—
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#384—111no—
600#384C2×D1111yescharacteristic, complemented
601#382—111no—
602#382—111no—
603#381—112no—
604#381—112no—
605#380—111no—
606#380—111no—
607#380—111no—
608#380—111no—
609#380—111no—
610#380—111no—
611#380—111no—
612#380—111no—
613#380—111no—
614#380—111no—
615#380C2×D1111yescharacteristic
616#380C2×D1111yescharacteristic, complemented
617#379—112no—
618#379—112no—
619C4×C4⋊C4—111no—
620C4×C4⋊C4—111no—
621C4×C4⋊C4—112no—
622C4×C4⋊C4—111no—
623C4×C4⋊C4—112no—
624C4×C4⋊C4—112no—
625C4×C4⋊C4C2×D1111yescharacteristic, complemented
626C4×C4⋊C4C2×D1112yescomplemented
627C4×C22⋊C4—112no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4—112no—
635C22×C11—22no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—22no—
641C22×C11—41no—
642C22×C11—41no—
643C22×C11—41no—
644C22×C11—41no—
645C22×C11—41no—
646C22×C11—41no—
647C22×C11—41no—
648C22×C11—41no—
649C22×C11C24×C411yescharacteristic
650C22×C11C2×H(5,𝔽2)11yescharacteristic
651C22×C11C2×H(5,𝔽2)11yescharacteristic
652C22×C11#58511yescharacteristic
653C22×C11#58511yescharacteristic
654C22×C11#58511yescharacteristic
655C22×C11#58511yescharacteristic
656C2×D11—22no—
657C2×D11—22no—
658C2×D11—22no—
659C2×D11—22no—
660C2×D11—22no—
661C2×D11—22no—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—416no—
666C2×D11—41no—
667C2×D11—41no—
668C2×D11—41no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11—41no—
672C2×D11—41no—
673C2×D11—41no—
674C2×D11—41no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—41no—
678C4×C11—22no—
679C4×C11—22no—
680C4×C11—22no—
681C4×C11—22no—
682C4×C11—42no—
683C4×C11—42no—
684C4×C11—42no—
685C4×C11—42no—
686C4×C11#51814yes—
687Dic11—22no—
688Dic11—22no—
689Dic11—22no—
690Dic11—22no—
691Dic11—22no—
692Dic11—42no—
693Dic11—42no—
694Dic11—42no—
695Dic11—42no—
696C25—111no—
697C2×#41—118no—
698C2×#41—442no—
699C2×#41—442no—
700C22×Q8—111no—
701C22×D4—111no—
702C22×D4—111no—
703C22×D4—111no—
704C22×D4—111no—
705C22×D4—111no—
706C22×D4—111no—
707C22×D4C22×D1111yescharacteristic
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—118no—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—112no—
716C23×C4—112no—
717C23×C4—442no—
718C23×C4—442no—
719C23×C4C22×D1111yescharacteristic
720C23×C4C22×D1111yescharacteristic
721#123—118no—
722#123—118no—
723C22⋊Q8—118no—
724C22⋊Q8—118no—
725#121—118no—
726#121—118no—
727#120—118no—
728#120—118no—
729C4×D4—118no—
730C4×D4—118no—
731C4×D4—118no—
732C4×D4C4×D1118yescomplemented
733#117—42no—
734#117—42no—
735#117—118no—
736#117—442no—
737#117—442no—
738#117—442no—
739#117—442no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—442no—
754C2×C4⋊C4—442no—
755C2×C4⋊C4C22×D1111yescharacteristic
756C2×C4⋊C4C22×D1111yescharacteristic
757C2×C4⋊C4C22×D1111yescharacteristic
758C2×C4⋊C4C22×D1111yescharacteristic
759C2×C4⋊C4C22×D1112yes—
760C2×C4⋊C4C22×D1112yes—
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C22⋊C4—111no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4C22×D1112yes—
785C2×C22⋊C4C22×D1112yes—
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1112yes—
788C2×C22⋊C4C22×D1111yescharacteristic
789C2×C22⋊C4C22×D1111yescharacteristic
790C2×C42—111no—
791C2×C42—112no—
792C2×C42—112no—
793C2×C42—112no—
794C2×C42—112no—
795C2×C42—112no—
796C2×C42—112no—
797C2×C42—112no—
798C2×C42C22×D1112yes—
799C2×C42C22×D1112yes—
800C2×C42C22×D1112yes—
801C2×C42C22×D1111yescharacteristic
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95C22×D1112yes—
820#95C22×D1112yes—
821#95C22×D1112yes—
822C2×C11—42no—
823C2×C11—42no—
824C2×C11C2×#51811yescharacteristic
825C2×C11#342811yescharacteristic
826C2×C11#342811yescharacteristic
827C2×C11#353911yescharacteristic
828C2×C11#353911yescharacteristic
829C2×C11#354011yescharacteristic
830C2×C11#354011yescharacteristic
831D11—42no—
832D11—42no—
833D11—42no—
834C24—111no—
835C24—111no—
836C24—111no—
837C24—114no—
838C24—441no—
839C24—441no—
840C24—441no—
841C24—441no—
842C24—441no—
843C24—441no—
844C24C23×D1111yescharacteristic
845C24C23×D1111yescharacteristic
846#41—4416no—
847C2×Q8—114no—
848C2×Q8—441no—
849C2×Q8—441no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—114no—
853C2×D4—114no—
854C2×D4—114no—
855C2×D4—114no—
856C2×D4—114no—
857C2×D4—114no—
858C2×D4—441no—
859C2×D4—441no—
860C2×D4—441no—
861C2×D4—441no—
862C2×D4—441no—
863C2×D4—441no—
864C2×D4—441no—
865C2×D4—441no—
866C2×D4—441no—
867C2×D4—441no—
868C2×D4—441no—
869C2×D4—441no—
870C2×D4C2×C4×D1114yes—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—111no—
880C22×C4—114no—
881C22×C4—114no—
882C22×C4—114no—
883C22×C4—114no—
884C22×C4—114no—
885C22×C4—114no—
886C22×C4—112no—
887C22×C4—112no—
888C22×C4—112no—
889C22×C4—112no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—4416no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—441no—
900C22×C4—441no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—441no—
905C22×C4—441no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4C2×C4×D1114yes—
910C22×C4C2×C4×D1114yes—
911C22×C4C23×D1112yes—
912C22×C4C23×D1112yes—
913C22×C4C23×D1112yes—
914C22×C4C23×D1112yes—
915C22×C4C23×D1111yescharacteristic
916C22×C4C23×D1111yescharacteristic
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1111yescharacteristic
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—114no—
927C4⋊C4—114no—
928C4⋊C4—114no—
929C4⋊C4—114no—
930C4⋊C4—114no—
931C4⋊C4—222no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—222no—
935C4⋊C4—442no—
936C4⋊C4—442no—
937C4⋊C4—442no—
938C4⋊C4—442no—
939C4⋊C4C2×C4×D1114yes—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—114no—
945C22⋊C4—114no—
946C22⋊C4—114no—
947C22⋊C4—114no—
948C22⋊C4—114no—
949C22⋊C4—114no—
950C22⋊C4—114no—
951C22⋊C4—114no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C22⋊C4—442no—
956C22⋊C4—442no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4—442no—
961C22⋊C4—442no—
962C22⋊C4—442no—
963C22⋊C4—442no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4C2×C4×D1114yes—
967C22⋊C4C2×C4×D1114yes—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—114no—
972C42—442no—
973C42—442no—
974C42—442no—
975C42—442no—
976C42—442no—
977C42—442no—
978C42—442no—
979C42C2×C4×D1114yes—
980C11#3436111yescharacteristic, complemented, Sylow
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—112no—
994C23—112no—
995C23—112no—
996C23—221no—
997C23—221no—
998C23—221no—
999C23—221no—
1000C23—221no—
1001C23—221no—
1002C23—221no—
1003C23—221no—
1004C23—221no—
1005C23—221no—
1006C23—221no—
1007C23—221no—
1008C23—221no—
1009C23—221no—
1010C23—221no—
1011C23—221no—
1012C23—221no—
1013C23—221no—
1014C23—444no—
1015C23—444no—
1016C23—444no—
1017C23—444no—
1018C23—444no—
1019C23—444no—
1020C23—444no—
1021C23C22×C4×D1112yes—
1022C23C22×C4×D1112yes—
1023C23C24×D1111yescharacteristic
1024Q8—444no—
1025D4—44no—
1026D4—444no—
1027D4—444no—
1028D4—444no—
1029D4—444no—
1030D4—444no—
1031D4—444no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—112no—
1055C2×C4—112no—
1056C2×C4—112no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—221no—
1060C2×C4—221no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—228no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—444no—
1085C2×C4—444no—
1086C2×C4—444no—
1087C2×C4—884no—
1088C2×C4—884no—
1089C2×C4C22×C4×D1112yes—
1090C2×C4C22×C4×D1112yes—
1091C2×C4C22×C4×D1112yes—
1092C2×C4C22×C4×D1112yes—
1093C2×C4C22×C4×D1112yes—
1094C2×C4#6703712yes—
1095C2×C4#6704212yes—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—222no—
1111C22—222no—
1112C22—222no—
1113C22—222no—
1114C22—222no—
1115C22—222no—
1116C22—222no—
1117C22—222no—
1118C22—222no—
1119C22—4416no—
1120C22—441no—
1121C22—441no—
1122C22—441no—
1123C22—441no—
1124C22—441no—
1125C22—441no—
1126C22—441no—
1127C22—441no—
1128C22—441no—
1129C22—441no—
1130C22—441no—
1131C22—441no—
1132C22C23×C4×D1111yescharacteristic
1133C22C2×#6703711yescharacteristic
1134C22C2×#6704211yescharacteristic
1135C22#1062345311yescharacteristic
1136C22#1062345311yescharacteristic
1137C22#1062345511yescharacteristic
1138C22#1062345711yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—222no—
1148C4—222no—
1149C4—222no—
1150C4—222no—
1151C4—222no—
1152C4—442no—
1153C4—442no—
1154C4—442no—
1155C4—442no—
1156C4#1062307614yes—
1157C2—42no—
1158C2—42no—
1159C2—442no—
1160C2—442no—
1161C2—442no—
1162C2C2×#1062307611yescharacteristic
1163C2#1308181611yescharacteristic
1164C2#1308181711yescharacteristic
1165C2#1308286711yescharacteristic
1166C2#1308287111yescharacteristic
1167C2#1308288611yescharacteristic
1168C2#1308289211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2354C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2354D11
hypocenterC11#34361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13071756C2semidirect
3. #13071753C2semidirect
4. #13071745C2semidirect
5. #13071744C2semidirect
6. #13071567C2semidirect
7. #13071566C2semidirect
8. #13071566C2semidirect
9. #13071548C2semidirect
10. #13071547C2semidirect
11. #13071545C2semidirect
12. #13071538C2semidirect
13. #13071379C2semidirect
14. #13071375C2semidirect
15. #13071367C2semidirect
16. #13071366C2semidirect
17. #13071224C2semidirect
18. #13071221C2semidirect
19. #13071205C2semidirect
20. #13071204C2semidirect
21. #13070998C2semidirect
22. #13070995C2semidirect
23. C11×#2354C2semidirect
28. C2×C11×#117C22semidirect
34. C22×C4⋊Dic11C22semidirect
35. #10623078C4semidirect
40. C2×#66945C22semidirect
41. C2×C4⋊C4×D11C22semidirect
50. C11×#388C22semidirect
51. C11×#384C22semidirect
53. C11×#380C22semidirect
54. C4×C11×C4⋊C4C22semidirect
55. C4×C11×C4⋊C4C22semidirect
58. #10622825C22semidirect
62. #10622603C22semidirect
70. #10622600C22semidirect
71. #10622600C22semidirect
72. #10622594C22semidirect
73. #10622591C22semidirect
74. #10622591C22semidirect
75. #10622590C22semidirect
76. #10622589C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
82. #10622571C22semidirect
87. #10622569C22semidirect
93. #10622557C22semidirect
96. C22⋊C4×Dic11C22semidirect
97. C22⋊C4×Dic11C22semidirect
101. #10622553C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. #10622549C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. #10622546C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. C4×Dic11⋊C4C22semidirect
111. #10622542C22semidirect
115. #10622279C22semidirect
119. #10622268C22semidirect
120. #10622266C22semidirect
121. #10622265C22semidirect
122. #10622265C22semidirect
123. #10622259C22semidirect
141. C22×C4×D11C2×C4semidirect
149. C4×D4×C11C2×C4semidirect
175. #66990C2×C4semidirect
176. C4×C22⋊D11C2×C4semidirect
177. C4×C22⋊D11C2×C4semidirect
218. #66949C2×C4semidirect
219. #66947C2×C4semidirect
225. #66936C2×C4semidirect
226. #66935C2×C4semidirect
227. #66931C2×C4semidirect
228. C4×D44C2×C4semidirect
229. #66925C2×C4semidirect
405. #2354D11semidirect
556. C2×#117C2×D11semidirect
582. #388C2×D11semidirect
600. #384C2×D11semidirect
616. #380C2×D11semidirect
625. C4×C4⋊C4C2×D11semidirect
626. C4×C4⋊C4C2×D11semidirect
732. C4×D4C4×D11semidirect
980. C11#34361semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
#130717562
#130717532
#130717452
#130717442
#130715672
#130715662
#130715482
#130715472
#130715452
#130715382
#130713792
#130713752
#130713672
#130713662
#130712242
#130712212
#130712052
#130712042
#130709982
#130709952
C11×#23542
#3436111