Finite Group Databasebeta

← #14916554

Subgroups — #14916554

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#13071754C212yesmaximal, complemented
4#13071750C212yesmaximal, complemented
5#13071748C212yesmaximal, complemented
6#13071565C211yesmaximal, characteristic, complemented
7#13071563C211yesmaximal, characteristic, complemented
8#13071560C211yesmaximal, characteristic, complemented
9#13071560C211yesmaximal, characteristic, complemented
10#13071546C211yesmaximal, characteristic, complemented
11#13071542C211yesmaximal, characteristic, complemented
12#13071541C211yesmaximal, characteristic, complemented
13#13071382C212yesmaximal, complemented
14#13071376C212yesmaximal, complemented
15#13071373C212yesmaximal, complemented
16#13071370C212yesmaximal, complemented
17#13071226C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071209C211yesmaximal, characteristic, complemented
20#13071205C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22#13070995C211yesmaximal, characteristic, complemented
23C11×#2352C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C2×#66979C2211yescharacteristic, 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×#388C2212yes—
49C11×#387C2212yescomplemented
50C11×#386C2212yes—
51C11×#382C2211yescharacteristic, complemented
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic, complemented
54C4×C11×C4⋊C4C2211yescharacteristic, complemented
55C4×C11×C22⋊C4C2212yescomplemented
56#10622834C2212yes—
57#10622826C2212yes—
58#10622826C2212yes—
59#10622826C2212yescomplemented
60#10622825C2211yescharacteristic
61#10622825C2211yescharacteristic, complemented
62C4×C22⋊Dic11C2212yescomplemented
63#10622603C2212yes—
64#10622601C2212yes—
65#10622600C2211yescharacteristic
66#10622600C2211yescharacteristic
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic, complemented
72#10622600C2211yescharacteristic, complemented
73#10622591C2212yescomplemented
74#10622590C2211yescharacteristic, complemented
75#10622589C2211yescharacteristic, complemented
76C4⋊C4×Dic11C2212yescomplemented
77C4⋊C4×Dic11C2211yescharacteristic, complemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79#10622587C2212yescomplemented
80#10622570C2212yes—
81#10622570C2212yes—
82#10622570C2212yes—
83#10622569C2212yes—
84#10622569C2212yescomplemented
85#10622568C2212yes—
86#10622568C2212yes—
87#10622564C2212yes—
88#10622564C2212yescomplemented
89#10622558C2212yes—
90#10622558C2212yes—
91#10622558C2212yescomplemented
92#10622556C2212yes—
93C22⋊C4×Dic11C2212yes—
94#10622553C2212yes—
95#10622552C2212yes—
96C4×(C2×D11)⋊C4C2212yes—
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2212yescomplemented
99#10622548C2211yescharacteristic, complemented
100C4×C4⋊Dic11C2212yescomplemented
101C4×C4⋊Dic11C2211yescharacteristic, complemented
102#10622546C2212yescomplemented
103#10622546C2212yescomplemented
104#10622283C2212yes—
105#10622283C2212yes—
106#10622283C2212yes—
107#10622283C2212yescomplemented
108#10622282C2212yes—
109#10622282C2212yes—
110#10622282C2212yes—
111#10622282C2212yescomplemented
112#10622279C2212yes—
113#10622279C2212yescomplemented
114#10622278C2212yes—
115#10622278C2212yes—
116#10622277C2212yes—
117#10622268C2212yescomplemented
118#10622268C2212yescomplemented
119#10622267C2212yescomplemented
120#10622265C2212yescomplemented
121#10622262C2212yescomplemented
122#10622262C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
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—
151C2×C11×C4⋊C4—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C42×C11C2312yes—
164C2×C42×C11C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172#66992C2×C418yes—
173#66990C2×C418yescomplemented
174C4×C22⋊D11C2×C418yescomplemented
175C4×C22⋊D11C2×C418yescomplemented
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193#66979—42no—
194#66979—42no—
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×C4×Dic11C2312yes—
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×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
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—41no—
285C2×C22⋊D11—41no—
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×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⋊C4C22×C414yes—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4C22×C414yes—
347C11×C22⋊C4C22×C414yes—
348C42×C11—42no—
349C42×C11—42no—
350C42×C11C22×C414yes—
351C22⋊Dic11—42no—
352C22⋊Dic11—42no—
353C22⋊Dic11—42no—
354C22⋊Dic11—42no—
355C22⋊Dic11C22×C414yes—
356C22⋊Dic11C22×C414yes—
357(C2×D11)⋊C4—42no—
358(C2×D11)⋊C4—42no—
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)⋊C4C22×C414yes—
369(C2×D11)⋊C4C22×C414yes—
370(C2×D11)⋊C4C22×C414yes—
371(C2×D11)⋊C4C22×C414yes—
372(C2×D11)⋊C4C22×C414yes—
373(C2×D11)⋊C4C22×C414yes—
374C4⋊Dic11—22no—
375C4⋊Dic11—22no—
376C4⋊Dic11—22no—
377C4⋊Dic11—22no—
378C4⋊Dic11—42no—
379C4⋊Dic11—42no—
380C4⋊Dic11C22×C414yes—
381Dic11⋊C4—42no—
382Dic11⋊C4—42no—
383Dic11⋊C4—42no—
384Dic11⋊C4C22×C414yes—
385Dic11⋊C4C22×C414yes—
386Dic11⋊C4C22×C414yes—
387Dic11⋊C4C22×C414yes—
388C4×Dic11—42no—
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#2354—111no—
406#2352—111no—
407#2352—111no—
408#2352—111no—
409#2352D1111yescharacteristic, complemented
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×C11—84no—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C412yes—
489C2×C4×C11C23×C412yes—
490C2×C4×C11C23×C412yes—
491C2×C4×C11C23×C412yes—
492C2×C4×C11H(5,𝔽2)12yes—
493C2×C4×C11H(5,𝔽2)12yes—
494C22⋊D11—44no—
495C22⋊D11—44no—
496C22⋊D11—44no—
497C22⋊D11—44no—
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—21no—
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—22no—
520C2×Dic11—44no—
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×#117—111no—
556C2×#117C2×D1111yescharacteristic
557C22×C4⋊C4—111no—
558C22×C4⋊C4C2×D1111yescharacteristic, complemented
559#391—112no—
560#391—112no—
561#390—112no—
562#390—112no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390—112no—
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#388—112no—
582#388C2×D1112yes—
583#387—112no—
584#387—112no—
585#387—112no—
586#387—112no—
587#387—112no—
588#387—112no—
589#387—112no—
590#387C2×D1112yescomplemented
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—112no—
597#386—112no—
598#386C2×D1112yes—
599#384—111no—
600#384—111no—
601#382—111no—
602#382C2×D1111yescharacteristic, complemented
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⋊C4—112no—
626C4×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4C2×D1112yescomplemented
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—442no—
717C23×C4—442no—
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1111yescharacteristic
720C23×C4C22×D1112yes—
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—118no—
735#117—442no—
736#117—442no—
737#117—442no—
738#117—442no—
739#117—442no—
740C2×C4⋊C4—42no—
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—111no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—442no—
756C2×C4⋊C4C22×D1111yescharacteristic
757C2×C4⋊C4C22×D1111yescharacteristic
758C2×C4⋊C4C22×D1111yescharacteristic
759C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4—112no—
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×C42—112no—
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#95C22×D1112yes—
818#95C22×D1112yes—
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—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—111no—
879C22×C4—111no—
880C22×C4—111no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—114no—
884C22×C4—114no—
885C22×C4—114no—
886C22×C4—114no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—112no—
890C22×C4—112no—
891C22×C4—112no—
892C22×C4—112no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—222no—
899C22×C4—4416no—
900C22×C4—441no—
901C22×C4—441no—
902C22×C4—441no—
903C22×C4—441no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4—442no—
907C22×C4—441no—
908C22×C4—441no—
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—114no—
926C4⋊C4—114no—
927C4⋊C4—114no—
928C4⋊C4—114no—
929C4⋊C4—114no—
930C4⋊C4—222no—
931C4⋊C4—222no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—442no—
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—114no—
944C22⋊C4—114no—
945C22⋊C4—114no—
946C22⋊C4—114no—
947C22⋊C4—114no—
948C22⋊C4—114no—
949C22⋊C4—114no—
950C22⋊C4—114no—
951C22⋊C4—442no—
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—114no—
971C42—442no—
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—84no—
1055C2×C4—112no—
1056C2×C4—112no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—112no—
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—221no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—228no—
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—222no—
1085C2×C4—444no—
1086C2×C4—444no—
1087C2×C4—444no—
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#1308287311yescharacteristic
1166C2#1308287711yescharacteristic
1167C2#1308288011yescharacteristic
1168C2#1308289011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2352C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2352D11
hypocenterC11#34361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13071756C2semidirect
3. #13071754C2semidirect
4. #13071750C2semidirect
5. #13071748C2semidirect
6. #13071565C2semidirect
7. #13071563C2semidirect
8. #13071560C2semidirect
9. #13071560C2semidirect
10. #13071546C2semidirect
11. #13071542C2semidirect
12. #13071541C2semidirect
13. #13071382C2semidirect
14. #13071376C2semidirect
15. #13071373C2semidirect
16. #13071370C2semidirect
17. #13071226C2semidirect
18. #13071221C2semidirect
19. #13071209C2semidirect
20. #13071205C2semidirect
21. #13070998C2semidirect
22. #13070995C2semidirect
23. C11×#2352C2semidirect
28. C22×C11×C4⋊C4C22semidirect
34. C2×#66979C22semidirect
35. #10623078C4semidirect
40. C2×#66945C22semidirect
41. C2×C4⋊C4×D11C22semidirect
49. C11×#387C22semidirect
51. C11×#382C22semidirect
53. C11×#380C22semidirect
54. C4×C11×C4⋊C4C22semidirect
55. C4×C11×C22⋊C4C22semidirect
59. #10622826C22semidirect
61. #10622825C22semidirect
62. C4×C22⋊Dic11C22semidirect
71. #10622600C22semidirect
72. #10622600C22semidirect
73. #10622591C22semidirect
74. #10622590C22semidirect
75. #10622589C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. #10622587C22semidirect
84. #10622569C22semidirect
88. #10622564C22semidirect
91. #10622558C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. #10622548C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. C4×C4⋊Dic11C22semidirect
102. #10622546C22semidirect
103. #10622546C22semidirect
107. #10622283C22semidirect
111. #10622282C22semidirect
113. #10622279C22semidirect
117. #10622268C22semidirect
118. #10622268C22semidirect
119. #10622267C22semidirect
120. #10622265C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622259C22semidirect
141. C22×C4×D11C2×C4semidirect
149. C4×D4×C11C2×C4semidirect
173. #66990C2×C4semidirect
174. C4×C22⋊D11C2×C4semidirect
175. 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
409. #2352D11semidirect
558. C22×C4⋊C4C2×D11semidirect
590. #387C2×D11semidirect
602. #382C2×D11semidirect
616. #380C2×D11semidirect
626. C4×C4⋊C4C2×D11semidirect
634. C4×C22⋊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
#130717542
#130717502
#130717482
#130715652
#130715632
#130715602
#130715462
#130715422
#130715412
#130713822
#130713762
#130713732
#130713702
#130712262
#130712212
#130712092
#130712052
#130709982
#130709952
C11×#23522
#3436111