Finite Group Databasebeta

← #14917222

Subgroups — #14917222

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#13071754C212yesmaximal, complemented
4#13071678C212yesmaximal, complemented
5#13071659C211yesmaximal, characteristic, complemented
6#13071656C211yesmaximal, characteristic, complemented
7#13071631C211yesmaximal, characteristic, complemented
8#13071628C211yesmaximal, characteristic, complemented
9#13071593C212yesmaximal, complemented
10#13071508C211yesmaximal, characteristic, complemented
11#13071505C211yesmaximal, characteristic, complemented
12#13071437C211yesmaximal, characteristic, complemented
13D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071424C212yesmaximal, complemented
15#13071423C212yesmaximal, complemented
16#13071311C211yesmaximal, characteristic, complemented
17#13071305C211yesmaximal, characteristic, complemented
18#13071276C212yesmaximal, complemented
19#13071269C212yesmaximal, complemented
20#13071205C211yesmaximal, characteristic, complemented
21C4×#66983C211yesmaximal, characteristic, complemented
22#13071106C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yescomplemented
29C22×C42×C11C2211yescharacteristic, complemented
30C2×#66993C2212yes—
31C2×#66991C2211yescharacteristic
32C2×#66990C2212yes—
33C2×D4×Dic11C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11C2212yescomplemented
36C2×C4×C22⋊D11C2212yescomplemented
37C22×(C2×D11)⋊C4C2212yes—
38C2×#66979C2211yescharacteristic, complemented
39#10623138C4116yescomplemented
40C2×#66948C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66946C2212yescomplemented
43C2×#66945C2211yescharacteristic
44C2×#66945C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic, complemented
46C2×#66938C2212yes—
47C2×#66935C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C4×D44C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#389C2211yescharacteristic, complemented
52C11×#388C2212yescomplemented
53C11×#386C2212yescomplemented
54C11×#380C2211yescharacteristic, complemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56C4×C11×C22⋊C4C2212yescomplemented
57#10622834C2211yescharacteristic
58#10622834C2212yescomplemented
59#10622833C2212yescomplemented
60#10622826C2211yescharacteristic
61#10622826C2211yescharacteristic
62#10622826C2212yes—
63#10622826C2211yescharacteristic, complemented
64#10622826C2211yescharacteristic, complemented
65#10622826C2212yescomplemented
66#10622825C2211yescharacteristic, complemented
67#10622823C2212yescomplemented
68#10622603C2212yes—
69#10622602C2212yescomplemented
70#10622601C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic
73#10622598C2211yescharacteristic, complemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76C4⋊C4×Dic11C2212yescomplemented
77#10622586C2211yescharacteristic, complemented
78#10622571C2212yes—
79#10622571C2212yescomplemented
80#10622570C2212yes—
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622569C2212yes—
84#10622569C2212yes—
85#10622569C2212yescomplemented
86#10622569C2212yescomplemented
87#10622569C2212yescomplemented
88#10622568C2212yes—
89#10622568C2212yes—
90#10622564C2212yescomplemented
91#10622563C2212yescomplemented
92#10622558C2212yescomplemented
93#10622558C2212yescomplemented
94C22⋊C4×Dic11C2212yescomplemented
95#10622553C2212yes—
96#10622553C2212yescomplemented
97#10622552C2211yescharacteristic
98#10622552C2211yescharacteristic
99#10622552C2211yescharacteristic
100#10622552C2212yescomplemented
101C4×(C2×D11)⋊C4C2211yescharacteristic
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
104C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
105C4×(C2×D11)⋊C4C2212yescomplemented
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2212yescomplemented
109#10622542C2211yescharacteristic, complemented
110#10622542C2211yescharacteristic, complemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yes—
113#10622283C2212yescomplemented
114#10622283C2212yescomplemented
115#10622282C2212yes—
116#10622282C2212yescomplemented
117#10622281C2212yescomplemented
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622264C2212yescomplemented
122#10622264C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2312yes—
137C2×D4×D11—42no—
138C2×D4×D11—42no—
139C2×D4×D11C2×C418yescomplemented
140C2×#4339—42no—
141C2×#4339—42no—
142C2×#4339C2×C418yescomplemented
143C22×D44C2311yescharacteristic
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C11×#121C2×C418yescomplemented
153C4×D4×C11—42no—
154C4×D4×C11—44no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
164C2×C42×C11—42no—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177#66993C2×C4116yescomplemented
178#66991C2×C418yescomplemented
179#66990C2×C4116yescomplemented
180D4×Dic11—42no—
181#66983C2×C418yescomplemented
182C4×C22⋊D11—44no—
183C4×C22⋊D11—44no—
184C2×(C2×D11)⋊C4—44no—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205#66979—42no—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222#66948C2×C418yescomplemented
223#66946—42no—
224#66946—44no—
225#66945—42no—
226#66945C2×C418yescomplemented
227C4⋊C4×D11—42no—
228#66938C2×C4116yescomplemented
229#66935C2×C4116yescomplemented
230C22⋊C4×D11—44no—
231C4×D44—42no—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
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—22no—
274C22×C4×C11—22no—
275C22×C4×C11—24no—
276C22×C4×C11—41no—
277C22×C4×C11—41no—
278C22×C4×C11—41no—
279C22×C4×C11—41no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C22×C414yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—41no—
295C2×C22⋊D11—41no—
296C2×C22⋊D11—41no—
297C2×C22⋊D11—41no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11C22×C418yes—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C414yes—
306C2×C22⋊D11C22×C414yes—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319D4×D11—416no—
320#4339—416no—
321C2×D44—22no—
322C2×D44—22no—
323C2×D44—42no—
324C2×D44—42no—
325C2×D44—41no—
326C2×D44—41no—
327C2×D44C22×C414yes—
328C2×D44C22×C414yes—
329C2×D44C22×C418yes—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
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—24no—
351C11×C4⋊C4C22×C414yes—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4C22×C418yes—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—41no—
360C42×C11—41no—
361C42×C11—42no—
362C22⋊Dic11—42no—
363C22⋊Dic11—41no—
364C22⋊Dic11—41no—
365C22⋊Dic11—42no—
366C22⋊Dic11—42no—
367C22⋊Dic11—42no—
368C22⋊Dic11C22×C418yes—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—22no—
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—41no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—41no—
384(C2×D11)⋊C4—41no—
385(C2×D11)⋊C4—41no—
386(C2×D11)⋊C4C22×C418yes—
387(C2×D11)⋊C4C22×C418yes—
388(C2×D11)⋊C4C22×C418yes—
389C4⋊Dic11—22no—
390C4⋊Dic11—22no—
391C4⋊Dic11—42no—
392C4⋊Dic11—41no—
393C4⋊Dic11—41no—
394C4⋊Dic11C22×C414yes—
395Dic11⋊C4—24no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—42no—
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#2363—111no—
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×#121D1111yescharacteristic, complemented
427#2297—111no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—21no—
434C23×C11—22no—
435C23×C11—21no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—21no—
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—21no—
456C22×D11—22no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—22no—
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—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—28no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—44no—
495C2×C4×C11—44no—
496C2×C4×C11—84no—
497C2×C4×C11C23×C414yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11H(5,𝔽2)12yes—
502C2×C4×C11H(5,𝔽2)12yes—
503C2×C4×C11H(5,𝔽2)12yes—
504C22⋊D11—44no—
505C22⋊D11—44no—
506C22⋊D11—48no—
507C22⋊D11—48no—
508C22⋊D11—48no—
509C2×Dic11—22no—
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—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—84no—
534C2×Dic11C23×C412yes—
535C2×Dic11C23×C414yes—
536C2×Dic11C23×C412yes—
537D44—28no—
538D44—48no—
539D44—44no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—84no—
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—111no—
558C2×C4×D4—112no—
559C2×C4×D4—112no—
560C2×C4×D4—112no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4C2×D1111yescharacteristic
564C2×C4×D4C2×D1112yescomplemented
565C2×#117—111no—
566C2×#117—111no—
567C2×#117—111no—
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C22⋊C4—112no—
571C22×C42C2×D1111yescharacteristic, complemented
572#391—111no—
573#391—111no—
574#391—112no—
575#390—111no—
576#390—112no—
577#390—111no—
578#390—112no—
579#390—112no—
580#390—112no—
581#390—111no—
582#390—111no—
583#390—112no—
584#390—111no—
585#390C2×D1111yescharacteristic
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—111no—
605#386—111no—
606#386—111no—
607#386—112no—
608#386—111no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386—112no—
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#380C2×D1111yescharacteristic, complemented
630#379—112no—
631#379—112no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—112no—
635C4×C4⋊C4—112no—
636C4×C4⋊C4—111no—
637C4×C4⋊C4C2×D1111yescharacteristic, complemented
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4C2×D1112yescomplemented
646C22×C11—22no—
647C22×C11—24no—
648C22×C11—22no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—22no—
652C22×C11—41no—
653C22×C11—42no—
654C22×C11—41no—
655C22×C11—42no—
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—41no—
680C2×D11—42no—
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—22no—
693C4×C11—42no—
694C4×C11—41no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11#51814yes—
698Dic11—22no—
699Dic11—22no—
700Dic11—24no—
701Dic11—42no—
702Dic11—41no—
703Dic11—41no—
704Dic11—41no—
705Dic11—42no—
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—112no—
730C23×C4—112no—
731C23×C4C22×D1111yescharacteristic
732C23×C4C22×D1111yescharacteristic
733C23×C4C22×D1112yes—
734C23×C4C22×D1111yescharacteristic
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—44no—
745C4×D4—442no—
746C4×D4—442no—
747C4×D4—442no—
748C4×D4—444no—
749C4×D4—444no—
750C4×D4—444no—
751#117—118no—
752#117—442no—
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—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—112no—
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—112no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
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—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—444no—
796C2×C22⋊C4—444no—
797C2×C22⋊C4C22×D1112yes—
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C42—42no—
803C2×C42—112no—
804C2×C42—111no—
805C2×C42—111no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42C22×D1111yescharacteristic
811C2×C42C22×D1111yescharacteristic
812C2×C42C22×D1112yes—
813C2×C42C22×D1111yescharacteristic
814C2×C42C22×D1111yescharacteristic
815#95—111no—
816#95—111no—
817#95—111no—
818#95—111no—
819#95—112no—
820#95—111no—
821#95—111no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—111no—
826#95—111no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95C22×D1112yes—
833#95C22×D1112yes—
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—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—111no—
906C22×C4—112no—
907C22×C4—111no—
908C22×C4—114no—
909C22×C4—114no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—112no—
913C22×C4—112no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—224no—
921C22×C4—442no—
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×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—114no—
946C4⋊C4—222no—
947C4⋊C4—222no—
948C4⋊C4—224no—
949C4⋊C4—442no—
950C4⋊C4—441no—
951C4⋊C4—441no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4C2×C4×D1114yes—
955C22⋊C4—24no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—118no—
960C22⋊C4—118no—
961C22⋊C4—118no—
962C22⋊C4—118no—
963C22⋊C4—222no—
964C22⋊C4—222no—
965C22⋊C4—222no—
966C22⋊C4—224no—
967C22⋊C4—222no—
968C22⋊C4—442no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4—442no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—441no—
976C22⋊C4—441no—
977C22⋊C4—442no—
978C22⋊C4—441no—
979C22⋊C4—441no—
980C22⋊C4—442no—
981C22⋊C4—441no—
982C22⋊C4—441no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4C2×C4×D1118yes—
987C42—22no—
988C42—22no—
989C42—41no—
990C42—41no—
991C42—42no—
992C42—118no—
993C42—222no—
994C42—222no—
995C42—442no—
996C42—442no—
997C42—442no—
998C42—442no—
999C11#3441111yescharacteristic, complemented, Sylow
1000C23—22no—
1001C23—21no—
1002C23—22no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—112no—
1013C23—114no—
1014C23—112no—
1015C23—221no—
1016C23—221no—
1017C23—222no—
1018C23—222no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—222no—
1023C23—221no—
1024C23—221no—
1025C23—222no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—222no—
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—21no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—28no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—84no—
1078C2×C4—112no—
1079C2×C4—114no—
1080C2×C4—112no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—222no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—222no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—221no—
1090C2×C4—222no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—884no—
1108C2×C4—884no—
1109C2×C4—884no—
1110C2×C4—884no—
1111C2×C4C22×C4×D1114yes—
1112C2×C4C22×C4×D1112yes—
1113C2×C4C22×C4×D1112yes—
1114C2×C4#6703712yes—
1115C2×C4#6703712yes—
1116C2×C4#6704212yes—
1117C2×C4#6704212yes—
1118C22—22no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—22no—
1123C22—24no—
1124C22—41no—
1125C22—42no—
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—442no—
1143C22—441no—
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×#6703711yescharacteristic
1157C22C2×#6704211yescharacteristic
1158C22C2×#6704211yescharacteristic
1159C22#1062345311yescharacteristic
1160C22#1062345311yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—22no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—42no—
1169C4—222no—
1170C4—222no—
1171C4—224no—
1172C4—441no—
1173C4—441no—
1174C4—441no—
1175C4—442no—
1176C4—441no—
1177C4—442no—
1178C4#1062307614yes—
1179C2—44no—
1180C2—42no—
1181C2—442no—
1182C2—444no—
1183C2—442no—
1184C2C2×#1062307611yescharacteristic
1185C2C4×#6703711yescharacteristic
1186C2C4×#6704211yescharacteristic
1187C2#1308285111yescharacteristic
1188C2#1308288411yescharacteristic
1189C2#1308298211yescharacteristic
1190C2#1308299011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#121C2
socle, cosocleC23×C11C25
prime radicalC2×#10623138C2
hypercenterC4×#121D11
hypocenterC11#34411
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #13071791C2semidirect
3. #13071754C2semidirect
4. #13071678C2semidirect
5. #13071659C2semidirect
6. #13071656C2semidirect
7. #13071631C2semidirect
8. #13071628C2semidirect
9. #13071593C2semidirect
10. #13071508C2semidirect
11. #13071505C2semidirect
12. #13071437C2semidirect
13. D4×(C2×D11)⋊C4C2semidirect
14. #13071424C2semidirect
15. #13071423C2semidirect
16. #13071311C2semidirect
17. #13071305C2semidirect
18. #13071276C2semidirect
19. #13071269C2semidirect
20. #13071205C2semidirect
21. C4×#66983C2semidirect
22. #13071106C2semidirect
23. C4×C11×#121C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C22×C42×C11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
38. C2×#66979C22semidirect
39. #10623138C4semidirect
42. C2×#66946C22semidirect
44. C2×#66945C22semidirect
45. C2×C4⋊C4×D11C22semidirect
51. C11×#389C22semidirect
52. C11×#388C22semidirect
53. C11×#386C22semidirect
54. C11×#380C22semidirect
55. C4×C11×C4⋊C4C22semidirect
56. C4×C11×C22⋊C4C22semidirect
58. #10622834C22semidirect
59. #10622833C22semidirect
63. #10622826C22semidirect
64. #10622826C22semidirect
65. #10622826C22semidirect
66. #10622825C22semidirect
67. #10622823C22semidirect
69. #10622602C22semidirect
73. #10622598C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. #10622586C22semidirect
79. #10622571C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
85. #10622569C22semidirect
86. #10622569C22semidirect
87. #10622569C22semidirect
90. #10622564C22semidirect
91. #10622563C22semidirect
92. #10622558C22semidirect
93. #10622558C22semidirect
94. C22⋊C4×Dic11C22semidirect
96. #10622553C22semidirect
100. #10622552C22semidirect
103. C4×(C2×D11)⋊C4C22semidirect
104. C4×(C2×D11)⋊C4C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622542C22semidirect
110. #10622542C22semidirect
111. #10622541C22semidirect
113. #10622283C22semidirect
114. #10622283C22semidirect
116. #10622282C22semidirect
117. #10622281C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622264C22semidirect
122. #10622264C22semidirect
123. #10622259C22semidirect
139. C2×D4×D11C2×C4semidirect
142. C2×#4339C2×C4semidirect
152. C11×#121C2×C4semidirect
177. #66993C2×C4semidirect
178. #66991C2×C4semidirect
179. #66990C2×C4semidirect
181. #66983C2×C4semidirect
222. #66948C2×C4semidirect
226. #66945C2×C4semidirect
228. #66938C2×C4semidirect
229. #66935C2×C4semidirect
426. C4×#121D11semidirect
564. C2×C4×D4C2×D11semidirect
571. C22×C42C2×D11semidirect
589. #389C2×D11semidirect
601. #388C2×D11semidirect
619. #386C2×D11semidirect
629. #380C2×D11semidirect
637. C4×C4⋊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
#130717542
#130716782
#130716592
#130716562
#130716312
#130716282
#130715932
#130715082
#130715052
#130714372
D4×(C2×D11)⋊C42
#130714242
#130714232
#130713112
#130713052
#130712762
#130712692
#130712052
C4×#669832
#130711062
C4×C11×#1212
#3441111