Finite Group Databasebeta

← #14917766

Subgroups — #14917766

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#13071767C212yesmaximal, complemented
3#13071754C212yesmaximal, complemented
4#13071687C211yesmaximal, characteristic, complemented
5#13071685C211yesmaximal, characteristic, complemented
6#13071681C211yesmaximal, characteristic, complemented
7#13071661C212yesmaximal, complemented
8#13071596C212yesmaximal, complemented
9#13071455C211yesmaximal, characteristic, complemented
10#13071441C211yesmaximal, characteristic, complemented
11#13071437C211yesmaximal, characteristic, complemented
12D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
13#13071382C212yesmaximal, complemented
14#13071338C211yesmaximal, characteristic, complemented
15#13071326C211yesmaximal, characteristic, complemented
16#13071317C212yesmaximal, complemented
17#13071275C212yesmaximal, complemented
18#13071270C212yesmaximal, complemented
19#13071221C211yesmaximal, characteristic, complemented
20#13071180C211yesmaximal, characteristic, complemented
21C4×#66989C211yesmaximal, characteristic, complemented
22#13071109C211yesmaximal, characteristic, complemented
23C11×#2366C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C2×C11×#127C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yescomplemented
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×#66993C2211yescharacteristic
31C2×#66992C2212yes—
32C2×#66992C2212yes—
33C2×#66990C2212yes—
34C2×#66990C2212yes—
35C2×#66989C2211yescharacteristic
36C2×D4×Dic11C2211yescharacteristic
37C2×D4×Dic11C2211yescharacteristic, complemented
38C2×D4×Dic11C2212yescomplemented
39C22×(C2×D11)⋊C4C2212yes—
40#10623246C4116yescomplemented
41C2×#66946C2211yescharacteristic
42C2×#66940C2211yescharacteristic, complemented
43C2×(C22⋊D11)⋊C4C2212yescomplemented
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×#390C2212yescomplemented
53C11×#386C2212yescomplemented
54C11×#386C2212yescomplemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57#10622834C2211yescharacteristic
58#10622834C2212yescomplemented
59#10622834C2211yescharacteristic, complemented
60#10622833C2212yescomplemented
61#10622833C2212yescomplemented
62#10622826C2212yes—
63#10622826C2212yes—
64#10622826C2212yescomplemented
65#10622826C2212yescomplemented
66C4×C22⋊Dic11C2212yescomplemented
67C4×C22⋊Dic11C2212yescomplemented
68C2×C11⋊#95C2212yescomplemented
69#10622603C2211yescharacteristic
70#10622603C2211yescharacteristic
71#10622603C2212yescomplemented
72#10622602C2212yescomplemented
73#10622601C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622591C2211yescharacteristic, complemented
77#10622591C2211yescharacteristic, complemented
78#10622590C2211yescharacteristic, complemented
79#10622589C2211yescharacteristic, complemented
80#10622587C2211yescharacteristic, complemented
81#10622571C2212yes—
82#10622571C2212yes—
83#10622570C2212yes—
84#10622570C2212yes—
85#10622570C2212yescomplemented
86#10622570C2212yescomplemented
87#10622569C2212yes—
88#10622569C2212yes—
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622568C2212yes—
92#10622568C2212yes—
93#10622559C2212yescomplemented
94#10622559C2212yescomplemented
95#10622558C2212yescomplemented
96#10622558C2212yescomplemented
97#10622558C2212yescomplemented
98#10622558C2212yescomplemented
99#10622556C2212yescomplemented
100#10622555C2212yescomplemented
101C22⋊C4×Dic11C2212yescomplemented
102#10622553C2212yes—
103#10622553C2212yescomplemented
104#10622552C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic
107C4×(C2×D11)⋊C4C2212yescomplemented
108C4×C4⋊Dic11C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110#10622546C2212yescomplemented
111#10622545C2211yescharacteristic, complemented
112C42×Dic11C2211yescharacteristic, complemented
113#10622542C2211yescharacteristic, complemented
114#10622283C2211yescharacteristic
115#10622283C2211yescharacteristic
116#10622283C2212yescomplemented
117#10622282C2212yes—
118#10622282C2212yescomplemented
119#10622281C2212yescomplemented
120#10622279C2212yescomplemented
121#10622268C2211yescharacteristic, complemented
122#10622268C2211yescharacteristic, complemented
123#10622265C2212yescomplemented
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—
152C4×D4×C11—44no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175#66993C2×C418yescomplemented
176#66992C2×C4116yescomplemented
177#66992C2×C4116yescomplemented
178#66990C2×C4116yescomplemented
179#66990C2×C4116yescomplemented
180#66989C2×C418yescomplemented
181D4×Dic11—42no—
182D4×Dic11—42no—
183D4×Dic11—44no—
184C2×(C2×D11)⋊C4—44no—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
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×Dic11C2311yescharacteristic
221#66946—42no—
222#66940—42no—
223(C22⋊D11)⋊C4—44no—
224(C22⋊D11)⋊C4—44no—
225C22⋊C4×D11—44no—
226#66928C2×C418yescomplemented
227C4×D44—42no—
228#66925C2×C418yescomplemented
229C4×Dic22—42no—
230C11×#95C2312yes—
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
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—24no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
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—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11C22×C418yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
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×C4⋊C4—22no—
342C11×C4⋊C4—41no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C42×C11—22no—
350C42×C11—22no—
351C42×C11—42no—
352C42×C11C22×C414yes—
353C22⋊Dic11—24no—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—42no—
359C22⋊Dic11C22×C418yes—
360C22⋊Dic11C22×C418yes—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—22no—
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)⋊C4—41no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—41no—
373(C2×D11)⋊C4C22×C414yes—
374(C2×D11)⋊C4C22×C414yes—
375(C2×D11)⋊C4C22×C418yes—
376(C2×D11)⋊C4C22×C418yes—
377C4⋊Dic11—22no—
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11—41no—
381Dic11⋊C4—42no—
382Dic11⋊C4—42no—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385Dic11⋊C4C22×C414yes—
386Dic11⋊C4C22×C414yes—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390C4×Dic11—22no—
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#2366D1111yescharacteristic, complemented
404#2364—112no—
405#2358—112no—
406#2341—111no—
407#2339—111no—
408D4×C22⋊C4—111no—
409D4×C22⋊C4—111no—
410#2333—112no—
411#2328—111no—
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—21no—
466C2×C4×C11—21no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—84no—
482C2×C4×C11—84no—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11H(5,𝔽2)12yes—
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—22no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—22no—
518C2×Dic11—48no—
519C2×Dic11—84no—
520C2×Dic11—84no—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C412yes—
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C414yes—
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—111no—
545C2×C4×D4—112no—
546C2×C4×D4—111no—
547C2×C4×D4—111no—
548C2×C4×D4—112no—
549C2×C4×D4—112no—
550C2×C4×D4—111no—
551C2×C4×D4C2×D1111yescharacteristic
552C2×C4×D4C2×D1112yescomplemented
553C2×C4×D4C2×D1111yescharacteristic, complemented
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391—111no—
559#390—111no—
560#390—112no—
561#390—111no—
562#390—111no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390—112no—
567#390—111no—
568#390C2×D1111yescharacteristic
569#390C2×D1111yescharacteristic, complemented
570#390C2×D1112yescomplemented
571#388—111no—
572#388—111no—
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#388—112no—
583#388—111no—
584#388—111no—
585#387—111no—
586#387—111no—
587#387—112no—
588#387—112no—
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#386—112no—
602#386—112no—
603#386C2×D1112yescomplemented
604#386C2×D1112yescomplemented
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#384—111no—
610#382—111no—
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⋊C4C2×D1111yescharacteristic, complemented
620C4×C4⋊C4C2×D1111yescharacteristic, complemented
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—112no—
628#376—111no—
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—41no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—41no—
664C2×D11—42no—
665C2×D11—41no—
666C2×D11—816no—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—42no—
671C4×C11—41no—
672C4×C11—41no—
673C4×C11—41no—
674C4×C11—42no—
675C4×C11#51814yes—
676Dic11—24no—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—41no—
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—44no—
724C4×D4—442no—
725C4×D4—444no—
726C4×D4—444no—
727C4×D4—442no—
728C4×D4—442no—
729C4×D4—442no—
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—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4C22×D1111yescharacteristic
743C2×C4⋊C4C22×D1111yescharacteristic
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—111no—
754C2×C22⋊C4—111no—
755C2×C22⋊C4—112no—
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—111no—
787C2×C42—111no—
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1112yes—
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—111no—
801#95—111no—
802#95—112no—
803#95—111no—
804#95—111no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—111no—
811#95C22×D1111yescharacteristic
812#95C22×D1112yes—
813#95C22×D1111yescharacteristic
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—24no—
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—118no—
880C22×C4—114no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—112no—
886C22×C4—224no—
887C22×C4—224no—
888C22×C4—222no—
889C22×C4—222no—
890C22×C4—442no—
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×D1111yescharacteristic
903C22×C4C23×D1112yes—
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—22no—
914C4⋊C4—41no—
915C4⋊C4—114no—
916C4⋊C4—114no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—222no—
920C4⋊C4—442no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—442no—
924C4⋊C4—441no—
925C22⋊C4—24no—
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—224no—
939C22⋊C4—222no—
940C22⋊C4—224no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—441no—
948C22⋊C4—441no—
949C22⋊C4—442no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C42—22no—
956C42—22no—
957C42—42no—
958C42—114no—
959C42—222no—
960C42—222no—
961C42—222no—
962C42—222no—
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—221no—
985C23—222no—
986C23—222no—
987C23—221no—
988C23—222no—
989C23—221no—
990C23—221no—
991C23—222no—
992C23—221no—
993C23—222no—
994C23—222no—
995C23—221no—
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—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—112no—
1040C2×C4—112no—
1041C2×C4—114no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—221no—
1045C2×C4—221no—
1046C2×C4—222no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—222no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—228no—
1055C2×C4—222no—
1056C2×C4—221no—
1057C2×C4—222no—
1058C2×C4—221no—
1059C2×C4—221no—
1060C2×C4—221no—
1061C2×C4—222no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—448no—
1071C2×C4—884no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4—884no—
1075C2×C4C22×C4×D1112yes—
1076C2×C4C22×C4×D1112yes—
1077C2×C4C22×C4×D1112yes—
1078C2×C4#6703712yes—
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—222no—
1099C22—224no—
1100C22—222no—
1101C22—442no—
1102C22—441no—
1103C22—441no—
1104C22—442no—
1105C22—442no—
1106C22—441no—
1107C22—441no—
1108C22—442no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6703711yescharacteristic
1113C22C2×#6704211yescharacteristic
1114C22#1062345311yescharacteristic
1115C22D11×H(5,𝔽2)11yescharacteristic
1116C22#1062345511yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—42no—
1125C4—222no—
1126C4—222no—
1127C4—224no—
1128C4—222no—
1129C4—222no—
1130C4—441no—
1131C4—442no—
1132C4—441no—
1133C4—441no—
1134C4—442no—
1135C4#1062307614yes—
1136C2—44no—
1137C2—44no—
1138C2—442no—
1139C2—444no—
1140C2C2×#1062307611yescharacteristic
1141C2#1308182011yescharacteristic
1142C2C4×#6703711yescharacteristic
1143C2#1308294011yescharacteristic
1144C2#1308297511yescharacteristic
1145C2#1308313011yescharacteristic
1146C2#1308320211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2366C2
socle, cosocleC23×C11C25
prime radicalC2×#10623246C2
hypercenter#2366D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2366

Complements

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

NH ≅ G/Ntype
2. #13071767C2semidirect
3. #13071754C2semidirect
4. #13071687C2semidirect
5. #13071685C2semidirect
6. #13071681C2semidirect
7. #13071661C2semidirect
8. #13071596C2semidirect
9. #13071455C2semidirect
10. #13071441C2semidirect
11. #13071437C2semidirect
12. D4×(C2×D11)⋊C4C2semidirect
13. #13071382C2semidirect
14. #13071338C2semidirect
15. #13071326C2semidirect
16. #13071317C2semidirect
17. #13071275C2semidirect
18. #13071270C2semidirect
19. #13071221C2semidirect
20. #13071180C2semidirect
21. C4×#66989C2semidirect
22. #13071109C2semidirect
23. C11×#2366C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C4×D4×C11C22semidirect
37. C2×D4×Dic11C22semidirect
38. C2×D4×Dic11C22semidirect
40. #10623246C4semidirect
42. C2×#66940C22semidirect
43. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
49. C2×C4×Dic22C22semidirect
51. C11×#390C22semidirect
52. C11×#390C22semidirect
53. C11×#386C22semidirect
54. C11×#386C22semidirect
55. C4×C11×C4⋊C4C22semidirect
56. C4×C11×C4⋊C4C22semidirect
58. #10622834C22semidirect
59. #10622834C22semidirect
60. #10622833C22semidirect
61. #10622833C22semidirect
64. #10622826C22semidirect
65. #10622826C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. C4×C22⋊Dic11C22semidirect
68. C2×C11⋊#95C22semidirect
71. #10622603C22semidirect
72. #10622602C22semidirect
76. #10622591C22semidirect
77. #10622591C22semidirect
78. #10622590C22semidirect
79. #10622589C22semidirect
80. #10622587C22semidirect
85. #10622570C22semidirect
86. #10622570C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
93. #10622559C22semidirect
94. #10622559C22semidirect
95. #10622558C22semidirect
96. #10622558C22semidirect
97. #10622558C22semidirect
98. #10622558C22semidirect
99. #10622556C22semidirect
100. #10622555C22semidirect
101. C22⋊C4×Dic11C22semidirect
103. #10622553C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×C4⋊Dic11C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. #10622546C22semidirect
111. #10622545C22semidirect
112. C42×Dic11C22semidirect
113. #10622542C22semidirect
116. #10622283C22semidirect
118. #10622282C22semidirect
119. #10622281C22semidirect
120. #10622279C22semidirect
121. #10622268C22semidirect
122. #10622268C22semidirect
123. #10622265C22semidirect
140. C2×#4341C2×C4semidirect
143. C2×D4×D11C2×C4semidirect
149. C11×#127C2×C4semidirect
175. #66993C2×C4semidirect
176. #66992C2×C4semidirect
177. #66992C2×C4semidirect
178. #66990C2×C4semidirect
179. #66990C2×C4semidirect
180. #66989C2×C4semidirect
226. #66928C2×C4semidirect
228. #66925C2×C4semidirect
403. #2366D11semidirect
552. C2×C4×D4C2×D11semidirect
553. C2×C4×D4C2×D11semidirect
569. #390C2×D11semidirect
570. #390C2×D11semidirect
603. #386C2×D11semidirect
604. #386C2×D11semidirect
619. C4×C4⋊C4C2×D11semidirect
620. C4×C4⋊C4C2×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
#130717672
#130717542
#130716872
#130716852
#130716812
#130716612
#130715962
#130714552
#130714412
#130714372
D4×(C2×D11)⋊C42
#130713822
#130713382
#130713262
#130713172
#130712752
#130712702
#130712212
#130711802
C4×#669892
#130711092
C11×#23662
#3443811