Finite Group Databasebeta

← #14917230

Subgroups — #14917230

Order 2816.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623138C211yesmaximal, characteristic
2#13071791C212yesmaximal, complemented
3#13071756C212yesmaximal, complemented
4#13071677C212yesmaximal, complemented
5#13071654C211yesmaximal, characteristic, complemented
6#13071636C211yesmaximal, characteristic, complemented
7#13071630C211yesmaximal, characteristic, complemented
8#13071598C212yesmaximal, complemented
9#13071508C211yesmaximal, characteristic, complemented
10#13071505C211yesmaximal, characteristic, complemented
11#13071437C211yesmaximal, characteristic, complemented
12D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
13#13071424C212yesmaximal, complemented
14#13071423C212yesmaximal, complemented
15#13071307C211yesmaximal, characteristic, complemented
16#13071303C211yesmaximal, characteristic, complemented
17#13071279C212yesmaximal, complemented
18#13071275C212yesmaximal, complemented
19#13071204C211yesmaximal, characteristic, complemented
20#13071132C211yesmaximal, characteristic, complemented
21C4×#66948C211yesmaximal, characteristic, complemented
22#13071102C211yesmaximal, characteristic, complemented
23C11×#2363C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×#66993C2212yes—
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2212yescomplemented
34C2×#66983C2211yescharacteristic
35C22×(C2×D11)⋊C4C2212yes—
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37#10623138C4116yescomplemented
38C2×#66948C2211yescharacteristic
39C2×#66946C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66938C2212yes—
42C2×#66935C2212yes—
43C2×(C22⋊D11)⋊C4C2212yescomplemented
44C2×(C22⋊D11)⋊C4C2212yescomplemented
45C2×C22⋊C4×D11C2212yes—
46C2×C4×D44C2211yescharacteristic
47C2×C4×D44C2212yescomplemented
48C2×#66925C2211yescharacteristic, complemented
49C2×C42×D11C2211yescharacteristic, complemented
50C11×#390C2211yescharacteristic
51C11×#390C2212yescomplemented
52C11×#389C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#386C2212yescomplemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56C4×C11×C22⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2212yescomplemented
58#10622834C2211yescharacteristic
59#10622833C2212yescomplemented
60#10622826C2212yes—
61#10622826C2212yescomplemented
62#10622823C2212yescomplemented
63C4×C22⋊Dic11C2211yescharacteristic, complemented
64#10622603C2212yes—
65#10622602C2212yescomplemented
66#10622601C2211yescharacteristic
67#10622601C2212yescomplemented
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic, complemented
71#10622600C2211yescharacteristic, complemented
72#10622598C2211yescharacteristic, complemented
73C4⋊C4×Dic11C2211yescharacteristic, complemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2212yescomplemented
76#10622586C2211yescharacteristic, complemented
77#10622571C2212yes—
78#10622571C2212yes—
79#10622571C2212yescomplemented
80#10622571C2212yescomplemented
81#10622570C2211yescharacteristic
82#10622570C2211yescharacteristic
83#10622570C2212yescomplemented
84#10622570C2212yescomplemented
85#10622569C2212yes—
86#10622569C2212yes—
87#10622569C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2211yescharacteristic, complemented
90#10622569C2211yescharacteristic, complemented
91#10622568C2212yes—
92#10622568C2212yes—
93#10622564C2212yescomplemented
94#10622563C2212yescomplemented
95#10622558C2212yescomplemented
96#10622558C2212yescomplemented
97C22⋊C4×Dic11C2212yescomplemented
98#10622553C2212yes—
99#10622553C2212yescomplemented
100#10622552C2211yescharacteristic
101#10622552C2212yes—
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2212yescomplemented
105C4×(C2×D11)⋊C4C2212yescomplemented
106C4×C4⋊Dic11C2211yescharacteristic, complemented
107C4×Dic11⋊C4C2212yescomplemented
108#10622542C2212yescomplemented
109#10622541C2211yescharacteristic, complemented
110#10622283C2212yes—
111#10622283C2212yescomplemented
112#10622283C2212yescomplemented
113#10622282C2212yes—
114#10622282C2212yescomplemented
115#10622281C2212yescomplemented
116#10622278C2211yescharacteristic
117#10622278C2211yescharacteristic
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622264C2212yescomplemented
121#10622264C2212yescomplemented
122#10622259C2211yescharacteristic, complemented
123#10622259C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2312yes—
135C23×Dic11C2312yes—
136C2×D4×D11—42no—
137C2×D4×D11—42no—
138C2×D4×D11C2×C418yescomplemented
139C2×#4339—42no—
140C2×#4339—42no—
141C2×#4339C2×C418yescomplemented
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C11×#121C2×C418yescomplemented
153C4×D4×C11—42no—
154C11×#117—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176#66993C2×C4116yescomplemented
177#66991C2×C418yescomplemented
178#66990C2×C4116yescomplemented
179D4×Dic11—42no—
180D4×Dic11—44no—
181#66983C2×C418yescomplemented
182C2×(C2×D11)⋊C4—44no—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×C4⋊Dic11—42no—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220#66948C2×C418yescomplemented
221#66946—42no—
222#66945C2×C418yescomplemented
223#66938C2×C4116yescomplemented
224#66935C2×C4116yescomplemented
225(C22⋊D11)⋊C4—44no—
226(C22⋊D11)⋊C4—44no—
227C22⋊C4×D11—44no—
228C4×D44—44no—
229C4×D44—42no—
230#66925—42no—
231C42×D11—42no—
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
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⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34411—111nomaximal, Sylow
253C24×C11C2412yes—
254C24×C11C2411yescharacteristic
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—
264C23×D11C2411yescharacteristic
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11C22×C414yes—
270C2×D4×C11C22×C418yes—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C2×C22⋊D11—42no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—41no—
289C2×C22⋊D11—41no—
290C2×C22⋊D11—41no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11C22×C418yes—
297C2×C22⋊D11C22×C418yes—
298C2×C22⋊D11C22×C418yes—
299C2×C22⋊D11C22×C414yes—
300C2×C22⋊D11C22×C414yes—
301C22×Dic11—24no—
302C22×Dic11—42no—
303C22×Dic11—42no—
304C22×Dic11—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316D4×D11—416no—
317#4339—416no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44—42no—
321C2×D44—42no—
322C2×D44—41no—
323C2×D44—41no—
324C2×D44C22×C414yes—
325C2×D44C22×C414yes—
326C2×D44C22×C418yes—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×Dic22—41no—
346C2×Dic22—41no—
347C2×Dic22C22×C414yes—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4C22×C414yes—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—41no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4C22×C418yes—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—42no—
362C42×C11—42no—
363C22⋊Dic11—22no—
364C22⋊Dic11—42no—
365C22⋊Dic11—42no—
366C22⋊Dic11—42no—
367C22⋊Dic11—41no—
368C22⋊Dic11C22×C418yes—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—41no—
373(C2×D11)⋊C4—41no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—41no—
384(C2×D11)⋊C4—41no—
385(C2×D11)⋊C4C22×C418yes—
386(C2×D11)⋊C4C22×C418yes—
387(C2×D11)⋊C4C22×C418yes—
388C4⋊Dic11—24no—
389C4⋊Dic11—22no—
390C4⋊Dic11—22no—
391C4⋊Dic11—42no—
392C4⋊Dic11C22×C414yes—
393Dic11⋊C4—24no—
394Dic11⋊C4—41no—
395Dic11⋊C4—41no—
396Dic11⋊C4—42no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—41no—
400C4×Dic11—41no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C4×Dic11C22×C418yes—
405C2×#535—111no—
406#2380—112no—
407#2375—112no—
408#2366—112no—
409#2363—111no—
410#2363D1111yescharacteristic, complemented
411#2361—111no—
412#2361—111no—
413#2358—112no—
414#2347—111no—
415#2347—111no—
416D4×C22⋊C4—111no—
417D4×C22⋊C4—111no—
418#2337—112no—
419#2337—112no—
420#2324—111no—
421#2324—111no—
422#2321—112no—
423#2321—112no—
424#2311—111no—
425C4×#121—111no—
426C4×#121—111no—
427#2297—111no—
428C23×C11—21no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—22no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11C23×C414yes—
441C23×C11C23×C412yes—
442C23×C11C2511yescharacteristic
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—22no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—22no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—21no—
461C22×D11—48no—
462C22×D11—48no—
463C22×D11—48no—
464C22×D11—84no—
465C22×D11—84no—
466C22×D11—84no—
467C22×D11—84no—
468C22×D11C23×C412yes—
469C22×D11C23×C414yes—
470C22×D11C23×C412yes—
471D4×C11—28no—
472D4×C11—48no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—28no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—84no—
496C2×C4×C11C23×C414yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11H(5,𝔽2)12yes—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C22⋊D11—48no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—84no—
531C2×Dic11—84no—
532C2×Dic11C23×C412yes—
533C2×Dic11C23×C414yes—
534C2×Dic11C23×C412yes—
535C2×Dic11H(5,𝔽2)12yes—
536D44—28no—
537D44—48no—
538D44—44no—
539C4×D11—28no—
540C4×D11—28no—
541C4×D11—44no—
542C4×D11—44no—
543C4×D11—84no—
544C4×D11—84no—
545Dic22—44no—
546C22×#41—111no—
547C23×D4—111no—
548#535—1116no—
549C2×#127—112no—
550C2×#124—112no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#121—111no—
554C2×#121C2×D1111yescharacteristic
555C2×#120—112no—
556C2×#120—112no—
557C2×C4×D4—112no—
558C2×C4×D4—111no—
559C2×C4×D4—111no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4—112no—
564C2×C4×D4C2×D1111yescharacteristic
565C2×#117—111no—
566C2×#117—111no—
567C2×#117C2×D1111yescharacteristic, complemented
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C22⋊C4—112no—
571C22×C42—111no—
572#391—112no—
573#391—111no—
574#391—111no—
575#390—111no—
576#390—112no—
577#390—111no—
578#390—111no—
579#390—111no—
580#390—112no—
581#390—112no—
582#390—112no—
583#390—111no—
584#390C2×D1111yescharacteristic
585#390C2×D1112yescomplemented
586#389—111no—
587#389—111no—
588#389—111no—
589#389C2×D1111yescharacteristic, complemented
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388—112no—
599#388—112no—
600#388—112no—
601#388C2×D1112yescomplemented
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—111no—
613#386—112no—
614#386—111no—
615#386—112no—
616#386—111no—
617#386—111no—
618#386—112no—
619#386C2×D1112yescomplemented
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#383—112no—
625#383—112no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380—111no—
630#379—112no—
631#379—112no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—112no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—111no—
636C4×C4⋊C4—112no—
637C4×C4⋊C4C2×D1111yescharacteristic, complemented
638C4×C22⋊C4—111no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4C2×D1112yescomplemented
645C4×C22⋊C4C2×D1111yescharacteristic, complemented
646C22×C11—22no—
647C22×C11—24no—
648C22×C11—22no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—22no—
652C22×C11—42no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—41no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11C24×C411yescharacteristic
661C22×C11C2×H(5,𝔽2)11yescharacteristic
662C22×C11C2×H(5,𝔽2)11yescharacteristic
663C22×C11C2×H(5,𝔽2)11yescharacteristic
664C22×C11C2×H(5,𝔽2)11yescharacteristic
665C22×C11#58511yescharacteristic
666C22×C11#58511yescharacteristic
667C2×D11—22no—
668C2×D11—24no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—24no—
673C2×D11—24no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—41no—
677C2×D11—42no—
678C2×D11—41no—
679C2×D11—42no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—42no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—42no—
688C2×D11—816no—
689C4×C11—22no—
690C4×C11—24no—
691C4×C11—22no—
692C4×C11—41no—
693C4×C11—41no—
694C4×C11—42no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11#51814yes—
698Dic11—22no—
699Dic11—22no—
700Dic11—24no—
701Dic11—22no—
702Dic11—42no—
703Dic11—42no—
704Dic11—41no—
705Dic11—41no—
706Dic11—41no—
707C25—112no—
708C2×#41—118no—
709C2×#41—442no—
710C2×#41—442no—
711C22×Q8—111no—
712C22×D4—112no—
713C22×D4—112no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—118no—
718C22×D4—111no—
719C22×D4—112no—
720C22×D4—111no—
721C22×D4—442no—
722C22×D4—442no—
723C22×D4C22×D1111yescharacteristic
724C22×D4C22×D1112yes—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—112no—
728C23×C4—112no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4C22×D1111yescharacteristic
734C23×C4C22×D1112yes—
735#127—1116no—
736#124—1116no—
737#121—118no—
738#121—118no—
739#121—118no—
740#121C4×D1118yescomplemented
741#120—1116no—
742#120—1116no—
743C4×D4—42no—
744C4×D4—442no—
745C4×D4—444no—
746C4×D4—442no—
747C4×D4—442no—
748C4×D4—444no—
749C4×D4—444no—
750C4×D4—444no—
751#117—42no—
752#117—118no—
753#117—442no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—442no—
764C2×C4⋊C4C22×D1111yescharacteristic
765C2×C4⋊C4C22×D1111yescharacteristic
766C2×C4⋊C4C22×D1112yes—
767C2×C4⋊C4C22×D1111yescharacteristic
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
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—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—444no—
794C2×C22⋊C4—444no—
795C2×C22⋊C4C22×D1112yes—
796C2×C22⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4C22×D1112yes—
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1111yescharacteristic
801C2×C22⋊C4C22×D1112yes—
802C2×C42—112no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—111no—
809C2×C42—111no—
810C2×C42—442no—
811C2×C42C22×D1111yescharacteristic
812C2×C42C22×D1111yescharacteristic
813C2×C42C22×D1112yes—
814C2×C42C22×D1112yes—
815#95—111no—
816#95—111no—
817#95—111no—
818#95—112no—
819#95—112no—
820#95—111no—
821#95—111no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—111no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95C22×D1111yescharacteristic
832#95C22×D1112yes—
833#95C22×D1111yescharacteristic
834#95C22×D1112yes—
835C2×C11—44no—
836C2×C11—42no—
837C2×C11C2×#51811yescharacteristic
838C2×C11C4×H(5,𝔽2)11yescharacteristic
839C2×C11C4×H(5,𝔽2)11yescharacteristic
840C2×C11#353711yescharacteristic
841C2×C11#354011yescharacteristic
842C2×C11#354611yescharacteristic
843C2×C11#354611yescharacteristic
844D11—42no—
845D11—44no—
846D11—42no—
847C24—111no—
848C24—112no—
849C24—111no—
850C24—118no—
851C24—442no—
852C24—442no—
853C24—442no—
854C24—442no—
855C24—442no—
856C24—442no—
857C24C23×D1112yes—
858C24C23×D1111yescharacteristic
859#41—4416no—
860C2×Q8—114no—
861C2×Q8—441no—
862C2×Q8—441no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—114no—
868C2×D4—118no—
869C2×D4—118no—
870C2×D4—118no—
871C2×D4—114no—
872C2×D4—114no—
873C2×D4—114no—
874C2×D4—118no—
875C2×D4—222no—
876C2×D4—222no—
877C2×D4—442no—
878C2×D4—441no—
879C2×D4—441no—
880C2×D4—442no—
881C2×D4—4416no—
882C2×D4—442no—
883C2×D4—442no—
884C2×D4—442no—
885C2×D4—442no—
886C2×D4—441no—
887C2×D4—441no—
888C2×D4—441no—
889C2×D4—441no—
890C2×D4—442no—
891C2×D4—442no—
892C2×D4C2×C4×D1114yes—
893C2×D4C2×C4×D1118yes—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—111no—
900C22×C4—112no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—112no—
908C22×C4—112no—
909C22×C4—111no—
910C22×C4—222no—
911C22×C4—224no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—224no—
918C22×C4—441no—
919C22×C4—441no—
920C22×C4—441no—
921C22×C4—441no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4C2×C4×D1114yes—
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1112yes—
936C22×C4C23×D1112yes—
937C22×C4C23×D1111yescharacteristic
938C22×C4C23×D1112yes—
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—42no—
945C4⋊C4—114no—
946C4⋊C4—224no—
947C4⋊C4—222no—
948C4⋊C4—222no—
949C4⋊C4—224no—
950C4⋊C4—442no—
951C4⋊C4—441no—
952C4⋊C4—441no—
953C4⋊C4—442no—
954C4⋊C4C2×C4×D1114yes—
955C22⋊C4—24no—
956C22⋊C4—22no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—41no—
960C22⋊C4—42no—
961C22⋊C4—118no—
962C22⋊C4—118no—
963C22⋊C4—118no—
964C22⋊C4—118no—
965C22⋊C4—222no—
966C22⋊C4—224no—
967C22⋊C4—222no—
968C22⋊C4—222no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4—442no—
972C22⋊C4—441no—
973C22⋊C4—441no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—441no—
980C22⋊C4—442no—
981C22⋊C4—441no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—441no—
986C22⋊C4C2×C4×D1118yes—
987C42—22no—
988C42—22no—
989C42—42no—
990C42—42no—
991C42—118no—
992C42—222no—
993C42—222no—
994C42—441no—
995C42—441no—
996C42—442no—
997C42—442no—
998C42—442no—
999C11#3441111yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—21no—
1009C23—22no—
1010C23—22no—
1011C23—21no—
1012C23—112no—
1013C23—114no—
1014C23—112no—
1015C23—221no—
1016C23—222no—
1017C23—221no—
1018C23—221no—
1019C23—221no—
1020C23—222no—
1021C23—222no—
1022C23—221no—
1023C23—221no—
1024C23—222no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—222no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—222no—
1033C23—448no—
1034C23—448no—
1035C23—448no—
1036C23—884no—
1037C23—884no—
1038C23—884no—
1039C23—884no—
1040C23C22×C4×D1114yes—
1041C23C22×C4×D1112yes—
1042C23C24×D1111yescharacteristic
1043Q8—444no—
1044D4—28no—
1045D4—48no—
1046D4—228no—
1047D4—444no—
1048D4—448no—
1049D4—448no—
1050D4—444no—
1051D4—444no—
1052D4—448no—
1053D4—448no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—28no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—84no—
1077C2×C4—112no—
1078C2×C4—114no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—222no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—228no—
1090C2×C4—228no—
1091C2×C4—221no—
1092C2×C4—221no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—444no—
1107C2×C4—444no—
1108C2×C4—884no—
1109C2×C4—884no—
1110C2×C4—884no—
1111C2×C4—884no—
1112C2×C4C22×C4×D1114yes—
1113C2×C4C22×C4×D1112yes—
1114C2×C4C22×C4×D1112yes—
1115C2×C4#6703712yes—
1116C2×C4#6704212yes—
1117C2×C4#6704212yes—
1118C22—22no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—22no—
1123C22—24no—
1124C22—42no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—42no—
1129C22—41no—
1130C22—41no—
1131C22—42no—
1132C22—222no—
1133C22—222no—
1134C22—224no—
1135C22—222no—
1136C22—224no—
1137C22—222no—
1138C22—222no—
1139C22—224no—
1140C22—222no—
1141C22—441no—
1142C22—441no—
1143C22—442no—
1144C22—442no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—442no—
1149C22—441no—
1150C22—441no—
1151C22—442no—
1152C22—441no—
1153C22—8816no—
1154C22C23×C4×D1111yescharacteristic
1155C22C2×#6703711yescharacteristic
1156C22C2×#6704211yescharacteristic
1157C22C2×#6704211yescharacteristic
1158C22#1062345311yescharacteristic
1159C22D11×H(5,𝔽2)11yescharacteristic
1160C22#1062345511yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—41no—
1165C4—42no—
1166C4—41no—
1167C4—41no—
1168C4—42no—
1169C4—222no—
1170C4—222no—
1171C4—224no—
1172C4—222no—
1173C4—441no—
1174C4—441no—
1175C4—441no—
1176C4—442no—
1177C4—442no—
1178C4#1062307614yes—
1179C2—44no—
1180C2—42no—
1181C2—442no—
1182C2—444no—
1183C2—442no—
1184C2C2×#1062307611yescharacteristic
1185C2#1308182011yescharacteristic
1186C2C4×#6704211yescharacteristic
1187C2#1308285211yescharacteristic
1188C2#1308288611yescharacteristic
1189C2#1308297611yescharacteristic
1190C2#1308298011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2363C2
socle, cosocleC23×C11C25
prime radicalC2×#10623138C2
hypercenter#2363D11
hypocenterC11#34411
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. #13071791C2semidirect
3. #13071756C2semidirect
4. #13071677C2semidirect
5. #13071654C2semidirect
6. #13071636C2semidirect
7. #13071630C2semidirect
8. #13071598C2semidirect
9. #13071508C2semidirect
10. #13071505C2semidirect
11. #13071437C2semidirect
12. D4×(C2×D11)⋊C4C2semidirect
13. #13071424C2semidirect
14. #13071423C2semidirect
15. #13071307C2semidirect
16. #13071303C2semidirect
17. #13071279C2semidirect
18. #13071275C2semidirect
19. #13071204C2semidirect
20. #13071132C2semidirect
21. C4×#66948C2semidirect
22. #13071102C2semidirect
23. C11×#2363C2semidirect
28. C2×C11×#117C22semidirect
33. C2×D4×Dic11C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. #10623138C4semidirect
43. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×C4×D44C22semidirect
48. C2×#66925C22semidirect
49. C2×C42×D11C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
54. C11×#386C22semidirect
55. C4×C11×C4⋊C4C22semidirect
56. C4×C11×C22⋊C4C22semidirect
57. C4×C11×C22⋊C4C22semidirect
59. #10622833C22semidirect
61. #10622826C22semidirect
62. #10622823C22semidirect
63. C4×C22⋊Dic11C22semidirect
65. #10622602C22semidirect
67. #10622601C22semidirect
70. #10622600C22semidirect
71. #10622600C22semidirect
72. #10622598C22semidirect
73. C4⋊C4×Dic11C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. #10622586C22semidirect
79. #10622571C22semidirect
80. #10622571C22semidirect
83. #10622570C22semidirect
84. #10622570C22semidirect
87. #10622569C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
93. #10622564C22semidirect
94. #10622563C22semidirect
95. #10622558C22semidirect
96. #10622558C22semidirect
97. C22⋊C4×Dic11C22semidirect
99. #10622553C22semidirect
104. C4×(C2×D11)⋊C4C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. C4×C4⋊Dic11C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. #10622542C22semidirect
109. #10622541C22semidirect
111. #10622283C22semidirect
112. #10622283C22semidirect
114. #10622282C22semidirect
115. #10622281C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622264C22semidirect
121. #10622264C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
138. C2×D4×D11C2×C4semidirect
141. C2×#4339C2×C4semidirect
152. C11×#121C2×C4semidirect
176. #66993C2×C4semidirect
177. #66991C2×C4semidirect
178. #66990C2×C4semidirect
181. #66983C2×C4semidirect
220. #66948C2×C4semidirect
222. #66945C2×C4semidirect
223. #66938C2×C4semidirect
224. #66935C2×C4semidirect
410. #2363D11semidirect
567. C2×#117C2×D11semidirect
585. #390C2×D11semidirect
589. #389C2×D11semidirect
601. #388C2×D11semidirect
619. #386C2×D11semidirect
637. C4×C4⋊C4C2×D11semidirect
644. C4×C22⋊C4C2×D11semidirect
645. C4×C22⋊C4C2×D11semidirect
740. #121C4×D11semidirect
999. C11#34411semidirect

Maximal subgroups

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

subgroupindex
C2×#106231382
#130717912
#130717562
#130716772
#130716542
#130716362
#130716302
#130715982
#130715082
#130715052
#130714372
D4×(C2×D11)⋊C42
#130714242
#130714232
#130713072
#130713032
#130712792
#130712752
#130712042
#130711322
C4×#669482
#130711022
C11×#23632
#3441111