Finite Group Databasebeta

← #14917763

Subgroups — #14917763

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×#10623361C211yesmaximal, characteristic
2#13071775C212yesmaximal, complemented
3#13071754C212yesmaximal, complemented
4#13071692C211yesmaximal, characteristic, complemented
5#13071692C211yesmaximal, characteristic, complemented
6#13071678C211yesmaximal, characteristic, complemented
7#13071678C211yesmaximal, characteristic, complemented
8#13071663C212yesmaximal, complemented
9#13071599C212yesmaximal, complemented
10#13071457C211yesmaximal, characteristic, complemented
11C22⋊C4×D44C211yesmaximal, characteristic, complemented
12#13071436C211yesmaximal, characteristic, complemented
13#13071378C212yesmaximal, complemented
14#13071338C211yesmaximal, characteristic, complemented
15#13071330C211yesmaximal, characteristic, complemented
16#13071319C212yesmaximal, complemented
17#13071272C212yesmaximal, complemented
18#13071272C212yesmaximal, complemented
19#13071223C211yesmaximal, characteristic, complemented
20C4×#66993C211yesmaximal, characteristic, complemented
21#13071159C211yesmaximal, characteristic, complemented
22#13071112C211yesmaximal, characteristic, complemented
23C11×#2339C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic, complemented
27C2×C4×D4×C11C2211yescharacteristic, complemented
28#10623361C4116yescomplemented
29C2×#67000C2211yescharacteristic
30C2×#67000C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C2×#66993C2211yescharacteristic
34C2×#66993C2211yescharacteristic
35C2×#66990C2212yes—
36C2×#66990C2212yes—
37C2×#66983C2212yes—
38C2×#66983C2212yes—
39C2×C4×C22⋊D11C2212yescomplemented
40C2×C4×C22⋊D11C2212yescomplemented
41C2×C4×C22⋊D11C2212yescomplemented
42C2×C4×C22⋊D11C2212yescomplemented
43C2×#66979C2211yescharacteristic
44C2×#66946C2211yescharacteristic
45C2×#66946C2211yescharacteristic
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C11×#391C2211yescharacteristic, complemented
51C11×#391C2211yescharacteristic, complemented
52C11×#386C2212yes—
53C11×#386C2212yes—
54C11×#381C2212yescomplemented
55C11×#380C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C2×C11×#95C2212yescomplemented
58#10622834C2212yes—
59#10622834C2212yes—
60#10622834C2211yescharacteristic, complemented
61#10622834C2211yescharacteristic, complemented
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64#10622826C2212yescomplemented
65#10622826C2212yescomplemented
66#10622825C2211yescharacteristic
67#10622825C2212yescomplemented
68C4×C22⋊Dic11C2211yescharacteristic
69C4×C22⋊Dic11C2212yescomplemented
70#10622601C2211yescharacteristic
71#10622601C2211yescharacteristic
72#10622590C2211yescharacteristic, complemented
73#10622589C2211yescharacteristic, complemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76#10622570C2212yescomplemented
77#10622570C2212yescomplemented
78#10622570C2212yescomplemented
79#10622570C2212yescomplemented
80#10622569C2212yescomplemented
81#10622569C2212yescomplemented
82#10622569C2212yescomplemented
83#10622569C2212yescomplemented
84#10622568C2212yes—
85#10622568C2212yes—
86#10622558C2211yescharacteristic
87#10622558C2211yescharacteristic
88#10622558C2212yes—
89#10622557C2211yescharacteristic
90#10622557C2211yescharacteristic
91#10622557C2212yes—
92#10622552C2211yescharacteristic
93#10622552C2211yescharacteristic
94#10622545C2211yescharacteristic, complemented
95C4×Dic11⋊C4C2211yescharacteristic, complemented
96C4×Dic11⋊C4C2211yescharacteristic, complemented
97C42×Dic11C2211yescharacteristic, complemented
98#10622283C2212yescomplemented
99#10622283C2212yescomplemented
100#10622283C2212yescomplemented
101#10622283C2212yescomplemented
102#10622282C2212yescomplemented
103#10622282C2212yescomplemented
104#10622282C2212yescomplemented
105#10622282C2212yescomplemented
106#10622281C2212yescomplemented
107#10622281C2212yescomplemented
108#10622281C2212yescomplemented
109#10622281C2212yescomplemented
110#10622279C2212yescomplemented
111#10622279C2212yescomplemented
112#10622279C2212yescomplemented
113#10622279C2212yescomplemented
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118#10622267C2211yescharacteristic, complemented
119#10622267C2211yescharacteristic, complemented
120#10622267C2212yescomplemented
121#10622266C2211yescharacteristic, complemented
122#10622266C2211yescharacteristic, complemented
123#10622266C2212yescomplemented
124C24×D11C2312yes—
125C2×C11×#41—42no—
126C2×C11×#41—42no—
127C2×C11×#41C2×C418yescomplemented
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×D44—42no—
140C22×D44—42no—
141C22×D44C2×C418yescomplemented
142C22×D44C2311yescharacteristic
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C4×D4×C11—42no—
150C4×D4×C11—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C22⋊Dic11C2311yescharacteristic
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169#67000C2×C418yescomplemented
170#67000C2×C418yescomplemented
171Q8×Dic11—42no—
172Q8×Dic11—42no—
173#66993C2×C418yescomplemented
174#66993C2×C418yescomplemented
175#66990C2×C4116yescomplemented
176#66990C2×C4116yescomplemented
177#66983C2×C4116yescomplemented
178#66983C2×C4116yescomplemented
179C4×C22⋊D11—44no—
180C4×C22⋊D11—44no—
181C4×C22⋊D11—44no—
182C4×C22⋊D11—44no—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199#66979C2×C418yescomplemented
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
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×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224#66946—42no—
225#66946—42no—
226C22⋊C4×D11—44no—
227C22⋊C4×D11—44no—
228C4×D44—42no—
229C4×D44—42no—
230C11×#95C2311yescharacteristic
231C11×#95C2312yes—
232C11×#95C2311yescharacteristic
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252#34438—111nomaximal, Sylow
253C24×C11C2411yescharacteristic
254C24×C11C2412yes—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11—42no—
261C23×D11C22×C418yes—
262C23×D11C2412yes—
263C23×D11C2412yes—
264C11×#41—416no—
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11C22×C414yes—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C22×C414yes—
273C2×D4×C11C22×C418yes—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
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×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11C22×C414yes—
285C22×C4×C11C22×C418yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C418yes—
306C2×C22⋊D11C22×C418yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C2×D44—22no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44—22no—
321C2×D44—42no—
322C2×D44—42no—
323C2×D44—416no—
324C2×D44C22×C414yes—
325C2×D44C22×C414yes—
326C2×D44C22×C418yes—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—41no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C42×C11—22no—
347C42×C11—22no—
348C22⋊Dic11—22no—
349C22⋊Dic11—24no—
350C22⋊Dic11—42no—
351C22⋊Dic11—42no—
352C22⋊Dic11—42no—
353C22⋊Dic11—42no—
354C22⋊Dic11—41no—
355C22⋊Dic11C22×C414yes—
356C22⋊Dic11C22×C414yes—
357(C2×D11)⋊C4—24no—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—42no—
360(C2×D11)⋊C4—42no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4C22×C418yes—
370(C2×D11)⋊C4C22×C418yes—
371(C2×D11)⋊C4C22×C418yes—
372(C2×D11)⋊C4C22×C418yes—
373C4⋊Dic11—22no—
374C4⋊Dic11—22no—
375C4⋊Dic11—42no—
376C4⋊Dic11—42no—
377C4⋊Dic11C22×C414yes—
378C4⋊Dic11C22×C414yes—
379Dic11⋊C4—22no—
380Dic11⋊C4—22no—
381Dic11⋊C4—41no—
382Dic11⋊C4—41no—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385C4×Dic11—22no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—41no—
390C4×Dic11—41no—
391C4×Dic11—42no—
392C4×Dic11—42no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11C22×C414yes—
396C4×Dic11C22×C414yes—
397C2×#535—111no—
398#2377—112no—
399#2375—112no—
400#2367—111no—
401#2367—111no—
402#2366—111no—
403#2366—111no—
404#2364—112no—
405#2358—112no—
406#2341—111no—
407#2339D1111yescharacteristic, complemented
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—21no—
421C23×C11—22no—
422C23×C11—21no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—21no—
427C23×C11—21no—
428C23×C11—22no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—22no—
432C23×C11C23×C412yes—
433C23×C11C23×C414yes—
434C23×C11C2511yescharacteristic
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
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×C414yes—
455C22×D11C23×C414yes—
456Q8×C11—28no—
457D4×C11—28no—
458D4×C11—48no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—28no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—22no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—48no—
482C2×C4×C11—84no—
483C2×C4×C11—84no—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C414yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C2×C4×C11H(5,𝔽2)12yes—
489C2×C4×C11H(5,𝔽2)12yes—
490C22⋊D11—48no—
491C22⋊D11—48no—
492C22⋊D11—48no—
493C22⋊D11—48no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C412yes—
523C2×Dic11H(5,𝔽2)12yes—
524D44—28no—
525D44—28no—
526D44—48no—
527C4×D11—84no—
528C4×D11—84no—
529C4×D11—84no—
530C4×D11—84no—
531C22×#41C2×D1111yescharacteristic
532C23×D4—111no—
533#535—1116no—
534C2×#127—111no—
535C2×#127—111no—
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—112no—
545C2×C4×D4—112no—
546C2×C4×D4—112no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4C2×D1111yescharacteristic, complemented
553C2×C4×D4C2×D1111yescharacteristic, complemented
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391C2×D1111yescharacteristic, complemented
558#391C2×D1111yescharacteristic, complemented
559#390—111no—
560#390—112no—
561#390—112no—
562#390—111no—
563#390—111no—
564#390—111no—
565#390—112no—
566#390—112no—
567#390—112no—
568#390—112no—
569#390—111no—
570#390—111no—
571#388—112no—
572#388—112no—
573#388—111no—
574#388—111no—
575#388—111no—
576#388—111no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#387—112no—
586#387—112no—
587#387—111no—
588#387—111no—
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×D1112yes—
604#386C2×D1112yes—
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#384—111no—
610#382—111no—
611#381C2×D1112yescomplemented
612#380—111no—
613#380—112no—
614#380C2×D1111yescharacteristic
615#379—112no—
616#379—112no—
617C4×C4⋊C4—111no—
618C4×C4⋊C4—111no—
619C4×C4⋊C4—111no—
620C4×C4⋊C4—111no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—111no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4C2×D1111yescharacteristic
628#376—111no—
629C2×#95C2×D1112yescomplemented
630C43—111no—
631C22×C11—22no—
632C22×C11—24no—
633C22×C11—22no—
634C22×C11—22no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—42no—
638C22×C11—41no—
639C22×C11—41no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—41no—
643C22×C11—41no—
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—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—816no—
667C4×C11—22no—
668C4×C11—24no—
669C4×C11—22no—
670C4×C11—42no—
671C4×C11—41no—
672C4×C11—41no—
673C4×C11—42no—
674C4×C11—41no—
675C4×C11#51814yes—
676Dic11—22no—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—41no—
682Dic11—42no—
683Dic11—42no—
684Dic11—41no—
685Dic11—41no—
686C25—112no—
687C2×#41—42no—
688C2×#41—42no—
689C2×#41C4×D1118yescomplemented
690C22×Q8C22×D1111yescharacteristic
691C22×D4—112no—
692C22×D4—112no—
693C22×D4—112no—
694C22×D4—112no—
695C22×D4—118no—
696C22×D4—111no—
697C22×D4—111no—
698C22×D4—112no—
699C22×D4—442no—
700C22×D4—442no—
701C22×D4C22×D1111yescharacteristic
702C22×D4C22×D1112yes—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1112yes—
709C23×C4C22×D1112yes—
710C23×C4C22×D1112yes—
711#127—118no—
712#127—118no—
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—442no—
724C4×D4—442no—
725C4×D4—444no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—444no—
729C4×D4—444no—
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—111no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4C22×D1111yescharacteristic
745C2×C4⋊C4C22×D1111yescharacteristic
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—111no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—111no—
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—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—444no—
772C2×C22⋊C4—444no—
773C2×C22⋊C4C22×D1111yescharacteristic
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1111yescharacteristic
778C2×C42—111no—
779C2×C42—111no—
780C2×C42—111no—
781C2×C42—111no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—111no—
789C2×C42—111no—
790C2×C42C22×D1111yescharacteristic
791C2×C42C22×D1111yescharacteristic
792#95—111no—
793#95—111no—
794#95—111no—
795#95—111no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—112no—
800#95—111no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—111no—
806#95—111no—
807#95C22×D1111yescharacteristic
808#95C22×D1112yes—
809#95C22×D1112yes—
810#95C22×D1112yes—
811#95C22×D1112yes—
812#95C22×D1112yes—
813#95C22×D1111yescharacteristic
814C2×C11—42no—
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—44no—
825C24—112no—
826C24—112no—
827C24—118no—
828C24—442no—
829C24—442no—
830C24—442no—
831C24—442no—
832C24—442no—
833C24—442no—
834C24C23×D1111yescharacteristic
835C24C23×D1112yes—
836#41—416no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8C2×C4×D1114yes—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—118no—
845C2×D4—118no—
846C2×D4—118no—
847C2×D4—118no—
848C2×D4—114no—
849C2×D4—114no—
850C2×D4—118no—
851C2×D4—222no—
852C2×D4—222no—
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×D4—442no—
865C2×D4—442no—
866C2×D4C2×C4×D1114yes—
867C2×D4C2×C4×D1118yes—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
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—111no—
884C22×C4—112no—
885C22×C4—111no—
886C22×C4—111no—
887C22×C4—112no—
888C22×C4—224no—
889C22×C4—224no—
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×C4C2×C4×D1114yes—
901C22×C4C2×C4×D1118yes—
902C22×C4C23×D1112yes—
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1112yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1112yes—
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—114no—
914C4⋊C4—114no—
915C4⋊C4—222no—
916C4⋊C4—222no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—442no—
920C4⋊C4—442no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—441no—
924C4⋊C4—441no—
925C22⋊C4—22no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—41no—
930C22⋊C4—114no—
931C22⋊C4—114no—
932C22⋊C4—118no—
933C22⋊C4—118no—
934C22⋊C4—118no—
935C22⋊C4—118no—
936C22⋊C4—224no—
937C22⋊C4—222no—
938C22⋊C4—224no—
939C22⋊C4—224no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C22⋊C4—442no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4—441no—
954C22⋊C4—442no—
955C42—22no—
956C42—22no—
957C42—114no—
958C42—114no—
959C42—222no—
960C42—222no—
961C42—222no—
962C42—222no—
963C42—442no—
964C42—442no—
965C42—442no—
966C42—442no—
967C42—441no—
968C42—441no—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—22no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—22no—
976C23—21no—
977C23—22no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—21no—
982C23—114no—
983C23—114no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—448no—
997C23—448no—
998C23—448no—
999C23—884no—
1000C23—884no—
1001C23—884no—
1002C23—884no—
1003C23C22×C4×D1112yes—
1004C23C22×C4×D1114yes—
1005C23C24×D1111yescharacteristic
1006Q8—28no—
1007D4—28no—
1008D4—48no—
1009D4—228no—
1010D4—228no—
1011D4—448no—
1012D4—448no—
1013D4—448no—
1014D4—448no—
1015D4—448no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—28no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—48no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4—112no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—112no—
1045C2×C4—112no—
1046C2×C4—221no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—222no—
1071C2×C4—884no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4—884no—
1075C2×C4C22×C4×D1114yes—
1076C2×C4C22×C4×D1112yes—
1077C2×C4C22×C4×D1112yes—
1078C2×C4#6703712yes—
1079C2×C4#6703712yes—
1080C2×C4#6704212yes—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—22no—
1085C22—24no—
1086C22—22no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—42no—
1091C22—41no—
1092C22—42no—
1093C22—42no—
1094C22—41no—
1095C22—224no—
1096C22—224no—
1097C22—224no—
1098C22—224no—
1099C22—224no—
1100C22—224no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6703711yescharacteristic
1113C22C2×#6704211yescharacteristic
1114C22#1062345311yescharacteristic
1115C22D11×H(5,𝔽2)11yescharacteristic
1116C22#1062345711yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—24no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—42no—
1125C4—222no—
1126C4—222no—
1127C4—222no—
1128C4—222no—
1129C4—222no—
1130C4—441no—
1131C4—442no—
1132C4—441no—
1133C4—442no—
1134C4—441no—
1135C4#1062301714yes—
1136C2—42no—
1137C2—44no—
1138C2—444no—
1139C2—444no—
1140C2C2×#1062301711yescharacteristic
1141C2#1308182211yescharacteristic
1142C2C4×#6704211yescharacteristic
1143C2#1308294811yescharacteristic
1144C2#1308298911yescharacteristic
1145C2#1308312511yescharacteristic
1146C2#1308320911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2339C2
socle, cosocleC23×C11C25
prime radicalC2×#10623361C2
hypercenter#2339D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #13071775C2semidirect
3. #13071754C2semidirect
4. #13071692C2semidirect
5. #13071692C2semidirect
6. #13071678C2semidirect
7. #13071678C2semidirect
8. #13071663C2semidirect
9. #13071599C2semidirect
10. #13071457C2semidirect
11. C22⋊C4×D44C2semidirect
12. #13071436C2semidirect
13. #13071378C2semidirect
14. #13071338C2semidirect
15. #13071330C2semidirect
16. #13071319C2semidirect
17. #13071272C2semidirect
18. #13071272C2semidirect
19. #13071223C2semidirect
20. C4×#66993C2semidirect
21. #13071159C2semidirect
22. #13071112C2semidirect
23. C11×#2339C2semidirect
26. C2×C4×D4×C11C22semidirect
27. C2×C4×D4×C11C22semidirect
28. #10623361C4semidirect
31. C2×Q8×Dic11C22semidirect
32. C2×Q8×Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
40. C2×C4×C22⋊D11C22semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
50. C11×#391C22semidirect
51. C11×#391C22semidirect
54. C11×#381C22semidirect
57. C2×C11×#95C22semidirect
60. #10622834C22semidirect
61. #10622834C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
64. #10622826C22semidirect
65. #10622826C22semidirect
67. #10622825C22semidirect
69. C4×C22⋊Dic11C22semidirect
72. #10622590C22semidirect
73. #10622589C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. #10622570C22semidirect
77. #10622570C22semidirect
78. #10622570C22semidirect
79. #10622570C22semidirect
80. #10622569C22semidirect
81. #10622569C22semidirect
82. #10622569C22semidirect
83. #10622569C22semidirect
94. #10622545C22semidirect
95. C4×Dic11⋊C4C22semidirect
96. C4×Dic11⋊C4C22semidirect
97. C42×Dic11C22semidirect
98. #10622283C22semidirect
99. #10622283C22semidirect
100. #10622283C22semidirect
101. #10622283C22semidirect
102. #10622282C22semidirect
103. #10622282C22semidirect
104. #10622282C22semidirect
105. #10622282C22semidirect
106. #10622281C22semidirect
107. #10622281C22semidirect
108. #10622281C22semidirect
109. #10622281C22semidirect
110. #10622279C22semidirect
111. #10622279C22semidirect
112. #10622279C22semidirect
113. #10622279C22semidirect
118. #10622267C22semidirect
119. #10622267C22semidirect
120. #10622267C22semidirect
121. #10622266C22semidirect
122. #10622266C22semidirect
123. #10622266C22semidirect
127. C2×C11×#41C2×C4semidirect
141. C22×D44C2×C4semidirect
169. #67000C2×C4semidirect
170. #67000C2×C4semidirect
173. #66993C2×C4semidirect
174. #66993C2×C4semidirect
175. #66990C2×C4semidirect
176. #66990C2×C4semidirect
177. #66983C2×C4semidirect
178. #66983C2×C4semidirect
199. #66979C2×C4semidirect
407. #2339D11semidirect
552. C2×C4×D4C2×D11semidirect
553. C2×C4×D4C2×D11semidirect
557. #391C2×D11semidirect
558. #391C2×D11semidirect
611. #381C2×D11semidirect
629. C2×#95C2×D11semidirect
689. C2×#41C4×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×#106233612
#130717752
#130717542
#130716922
#130716782
#130716632
#130715992
#130714572
C22⋊C4×D442
#130714362
#130713782
#130713382
#130713302
#130713192
#130712722
#130712232
C4×#669932
#130711592
#130711122
C11×#23392
#3443811