Finite Group Databasebeta

← #14917757

Subgroups — #14917757

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#13071753C212yesmaximal, complemented
4#13071689C211yesmaximal, characteristic, complemented
5#13071686C211yesmaximal, characteristic, complemented
6#13071678C211yesmaximal, characteristic, complemented
7#13071677C211yesmaximal, characteristic, complemented
8#13071661C212yesmaximal, complemented
9#13071593C212yesmaximal, complemented
10#13071455C211yesmaximal, characteristic, complemented
11#13071441C211yesmaximal, characteristic, complemented
12#13071437C211yesmaximal, characteristic, complemented
13D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071375C212yesmaximal, complemented
15#13071342C211yesmaximal, characteristic, complemented
16#13071324C211yesmaximal, characteristic, complemented
17#13071314C212yesmaximal, complemented
18#13071275C212yesmaximal, complemented
19#13071270C212yesmaximal, complemented
20#13071224C211yesmaximal, characteristic, complemented
21C4×#66928C211yesmaximal, characteristic, complemented
22#13071113C211yesmaximal, characteristic, complemented
23C4×C11×#127C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C2×C11×#127C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yescomplemented
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11C2212yescomplemented
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yes—
33C2×#66992C2212yes—
34C2×#66990C2212yes—
35C2×#66990C2212yes—
36C2×#66989C2211yescharacteristic
37C2×D4×Dic11C2211yescharacteristic
38C2×D4×Dic11C2211yescharacteristic, complemented
39C2×C4×C22⋊D11C2212yescomplemented
40C22×(C2×D11)⋊C4C2212yes—
41#10623246C4116yescomplemented
42C2×#66946C2211yescharacteristic
43C2×#66940C2211yescharacteristic, complemented
44C2×(C22⋊D11)⋊C4C2212yescomplemented
45C2×C22⋊C4×D11C2212yes—
46C2×#66928C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#390C2211yescharacteristic
51C11×#390C2212yescomplemented
52C11×#390C2211yescharacteristic, complemented
53C11×#390C2212yescomplemented
54C11×#384C2211yescharacteristic, complemented
55C43×C11C2211yescharacteristic, complemented
56#10622834C2211yescharacteristic
57#10622834C2211yescharacteristic, complemented
58#10622833C2212yescomplemented
59#10622833C2212yescomplemented
60#10622833C2212yescomplemented
61#10622833C2212yescomplemented
62#10622826C2212yes—
63#10622826C2212yes—
64#10622826C2212yescomplemented
65#10622823C2212yescomplemented
66C4×C22⋊Dic11C2212yescomplemented
67C2×C11⋊#95C2212yescomplemented
68#10622603C2212yes—
69#10622603C2212yes—
70#10622603C2212yescomplemented
71#10622603C2212yescomplemented
72#10622602C2212yescomplemented
73#10622602C2212yescomplemented
74#10622601C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622600C2211yescharacteristic
77#10622591C2212yescomplemented
78#10622591C2212yescomplemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81#10622587C2211yescharacteristic, complemented
82#10622571C2212yes—
83#10622571C2212yes—
84#10622571C2212yescomplemented
85#10622570C2212yes—
86#10622570C2212yes—
87#10622570C2212yescomplemented
88#10622570C2212yescomplemented
89#10622569C2212yes—
90#10622569C2212yes—
91#10622569C2212yescomplemented
92#10622569C2212yescomplemented
93#10622568C2212yes—
94#10622568C2212yes—
95#10622559C2212yescomplemented
96#10622558C2212yescomplemented
97#10622558C2212yescomplemented
98#10622557C2212yescomplemented
99#10622557C2212yescomplemented
100#10622556C2212yescomplemented
101#10622555C2212yescomplemented
102C22⋊C4×Dic11C2212yescomplemented
103C22⋊C4×Dic11C2212yescomplemented
104#10622553C2211yescharacteristic
105#10622553C2211yescharacteristic
106#10622553C2211yescharacteristic
107#10622553C2211yescharacteristic
108#10622553C2212yescomplemented
109#10622553C2212yescomplemented
110#10622552C2211yescharacteristic
111C4×(C2×D11)⋊C4C2211yescharacteristic
112C4×(C2×D11)⋊C4C2211yescharacteristic
113C4×(C2×D11)⋊C4C2212yescomplemented
114C4×(C2×D11)⋊C4C2212yescomplemented
115#10622549C2211yescharacteristic, complemented
116#10622546C2211yescharacteristic, complemented
117#10622546C2211yescharacteristic, complemented
118#10622546C2211yescharacteristic, complemented
119#10622546C2211yescharacteristic, complemented
120#10622545C2211yescharacteristic, complemented
121C4×Dic11⋊C4C2211yescharacteristic, complemented
122C4×Dic11⋊C4C2211yescharacteristic, complemented
123#10622542C2211yescharacteristic, complemented
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—44no—
151C4×D4×C11—42no—
152C4×D4×C11—42no—
153C4×D4×C11—44no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#66993C2×C418yescomplemented
180#66992C2×C4116yescomplemented
181#66992C2×C4116yescomplemented
182#66990C2×C4116yescomplemented
183#66990C2×C4116yescomplemented
184#66989C2×C418yescomplemented
185D4×Dic11—42no—
186D4×Dic11—42no—
187C4×C22⋊D11—44no—
188C2×(C2×D11)⋊C4—44no—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222#66946—42no—
223#66940—42no—
224(C22⋊D11)⋊C4—44no—
225C22⋊C4×D11—44no—
226#66928C2×C418yescomplemented
227C4×D44—42no—
228#66925C2×C418yescomplemented
229C4×Dic22—42no—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
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—24no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
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—42no—
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×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322#4341—416no—
323D4×D11—416no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44C22×C414yes—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—24no—
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—42no—
342C11×C4⋊C4—42no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C42×C11—22no—
350C42×C11—22no—
351C42×C11—22no—
352C42×C11—22no—
353C42×C11—41no—
354C42×C11—41no—
355C42×C11C22×C414yes—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—42no—
359C22⋊Dic11—42no—
360C22⋊Dic11—42no—
361C22⋊Dic11—42no—
362C22⋊Dic11C22×C418yes—
363C22⋊Dic11C22×C418yes—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—22no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—41no—
374(C2×D11)⋊C4—41no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4C22×C414yes—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C418yes—
379(C2×D11)⋊C4C22×C418yes—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382Dic11⋊C4—22no—
383Dic11⋊C4—22no—
384Dic11⋊C4—42no—
385Dic11⋊C4—42no—
386Dic11⋊C4—41no—
387Dic11⋊C4—41no—
388Dic11⋊C4C22×C414yes—
389Dic11⋊C4C22×C414yes—
390C4×Dic11—22no—
391C4×Dic11—22no—
392C4×Dic11—42no—
393C4×Dic11—42no—
394C4×Dic11—42no—
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#2366—111no—
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×#127D1111yescharacteristic, complemented
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—21no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
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—21no—
480C2×C4×C11—84no—
481C2×C4×C11—84no—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11H(5,𝔽2)12yes—
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—22no—
496C2×Dic11—22no—
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—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—48no—
520C2×Dic11—84no—
521C2×Dic11—84no—
522C2×Dic11C23×C412yes—
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C414yes—
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—111no—
546C2×C4×D4—112no—
547C2×C4×D4—111no—
548C2×C4×D4—112no—
549C2×C4×D4—111no—
550C2×C4×D4C2×D1111yescharacteristic
551C2×C4×D4C2×D1112yescomplemented
552C2×C4×D4C2×D1111yescharacteristic, complemented
553C2×C4×D4C2×D1112yescomplemented
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391—111no—
559#390—111no—
560#390—111no—
561#390—111no—
562#390—112no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390—111no—
567#390C2×D1111yescharacteristic
568#390C2×D1112yescomplemented
569#390C2×D1111yescharacteristic, complemented
570#390C2×D1112yescomplemented
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—111no—
580#388—111no—
581#388—112no—
582#388—111no—
583#388—111no—
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#386—112no—
604#386—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#384C2×D1111yescharacteristic, complemented
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⋊C4—111no—
620C4×C4⋊C4—111no—
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—
630C43C2×D1111yescharacteristic, complemented
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—42no—
661C2×D11—41no—
662C2×D11—41no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—41no—
666C2×D11—816no—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—42no—
672C4×C11—42no—
673C4×C11—41no—
674C4×C11—41no—
675C4×C11#51814yes—
676Dic11—24no—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—41no—
681Dic11—42no—
682Dic11—41no—
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—44no—
722C4×D4—42no—
723C4×D4—42no—
724C4×D4—44no—
725C4×D4—442no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—442no—
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—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4C22×D1111yescharacteristic
743C2×C4⋊C4C22×D1111yescharacteristic
744C2×C4⋊C4C22×D1112yes—
745C2×C4⋊C4C22×D1112yes—
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—111no—
753C2×C22⋊C4—111no—
754C2×C22⋊C4—112no—
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—112no—
782C2×C42—112no—
783C2×C42—112no—
784C2×C42—112no—
785C2×C42C22×D1111yescharacteristic
786C2×C42C22×D1111yescharacteristic
787C2×C42C22×D1111yescharacteristic
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1111yescharacteristic
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—111no—
803#95—112no—
804#95—111no—
805#95—111no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—111no—
813#95—111no—
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—24no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—111no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—112no—
878C22×C4—118no—
879C22×C4—114no—
880C22×C4—112no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—111no—
884C22×C4—112no—
885C22×C4—111no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—224no—
889C22×C4—442no—
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×D1112yes—
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1112yes—
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—114no—
916C4⋊C4—114no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—222no—
920C4⋊C4—222no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—441no—
924C4⋊C4—441no—
925C22⋊C4—24no—
926C22⋊C4—24no—
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—222no—
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—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—22no—
958C42—22no—
959C42—41no—
960C42—41no—
961C42—114no—
962C42—222no—
963C42—222no—
964C42—442no—
965C42—442no—
966C42—442no—
967C42—442no—
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—221no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—221no—
990C23—222no—
991C23—221no—
992C23—222no—
993C23—221no—
994C23—221no—
995C23—222no—
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—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—112no—
1039C2×C4—112no—
1040C2×C4—114no—
1041C2×C4—112no—
1042C2×C4—221no—
1043C2×C4—221no—
1044C2×C4—222no—
1045C2×C4—221no—
1046C2×C4—222no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—228no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—221no—
1060C2×C4—221no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—222no—
1066C2×C4—221no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—448no—
1070C2×C4—884no—
1071C2×C4—884no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4C22×C4×D1112yes—
1075C2×C4C22×C4×D1112yes—
1076C2×C4C22×C4×D1112yes—
1077C2×C4#6703712yes—
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—224no—
1099C22—222no—
1100C22—222no—
1101C22—442no—
1102C22—441no—
1103C22—442no—
1104C22—441no—
1105C22—441no—
1106C22—442no—
1107C22—441no—
1108C22—442no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6703711yescharacteristic
1113C22C2×#6703711yescharacteristic
1114C22C2×#6704211yescharacteristic
1115C22#1062345311yescharacteristic
1116C22#1062345311yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—42no—
1122C4—42no—
1123C4—41no—
1124C4—41no—
1125C4—222no—
1126C4—224no—
1127C4—222no—
1128C4—222no—
1129C4—442no—
1130C4—441no—
1131C4—441no—
1132C4—441no—
1133C4—441no—
1134C4—442no—
1135C4#1062307614yes—
1136C2—44no—
1137C2—44no—
1138C2—442no—
1139C2—444no—
1140C2C2×#1062307611yescharacteristic
1141C2C4×#6703711yescharacteristic
1142C2C4×#6703711yescharacteristic
1143C2#1308294911yescharacteristic
1144C2#1308298811yescharacteristic
1145C2#1308313911yescharacteristic
1146C2#1308320811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#127C2
socle, cosocleC23×C11C25
prime radicalC2×#10623246C2
hypercenterC4×#127D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
2. #13071767C2semidirect
3. #13071753C2semidirect
4. #13071689C2semidirect
5. #13071686C2semidirect
6. #13071678C2semidirect
7. #13071677C2semidirect
8. #13071661C2semidirect
9. #13071593C2semidirect
10. #13071455C2semidirect
11. #13071441C2semidirect
12. #13071437C2semidirect
13. D4×(C2×D11)⋊C4C2semidirect
14. #13071375C2semidirect
15. #13071342C2semidirect
16. #13071324C2semidirect
17. #13071314C2semidirect
18. #13071275C2semidirect
19. #13071270C2semidirect
20. #13071224C2semidirect
21. C4×#66928C2semidirect
22. #13071113C2semidirect
23. C4×C11×#127C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C4×D4×C11C22semidirect
30. C2×C4×D4×C11C22semidirect
38. C2×D4×Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
41. #10623246C4semidirect
43. C2×#66940C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
49. C2×C4×Dic22C22semidirect
51. C11×#390C22semidirect
52. C11×#390C22semidirect
53. C11×#390C22semidirect
54. C11×#384C22semidirect
55. C43×C11C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
59. #10622833C22semidirect
60. #10622833C22semidirect
61. #10622833C22semidirect
64. #10622826C22semidirect
65. #10622823C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. C2×C11⋊#95C22semidirect
70. #10622603C22semidirect
71. #10622603C22semidirect
72. #10622602C22semidirect
73. #10622602C22semidirect
77. #10622591C22semidirect
78. #10622591C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622587C22semidirect
84. #10622571C22semidirect
87. #10622570C22semidirect
88. #10622570C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
95. #10622559C22semidirect
96. #10622558C22semidirect
97. #10622558C22semidirect
98. #10622557C22semidirect
99. #10622557C22semidirect
100. #10622556C22semidirect
101. #10622555C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. C22⋊C4×Dic11C22semidirect
108. #10622553C22semidirect
109. #10622553C22semidirect
113. C4×(C2×D11)⋊C4C22semidirect
114. C4×(C2×D11)⋊C4C22semidirect
115. #10622549C22semidirect
116. #10622546C22semidirect
117. #10622546C22semidirect
118. #10622546C22semidirect
119. #10622546C22semidirect
120. #10622545C22semidirect
121. C4×Dic11⋊C4C22semidirect
122. C4×Dic11⋊C4C22semidirect
123. #10622542C22semidirect
140. C2×#4341C2×C4semidirect
143. C2×D4×D11C2×C4semidirect
149. C11×#127C2×C4semidirect
179. #66993C2×C4semidirect
180. #66992C2×C4semidirect
181. #66992C2×C4semidirect
182. #66990C2×C4semidirect
183. #66990C2×C4semidirect
184. #66989C2×C4semidirect
226. #66928C2×C4semidirect
228. #66925C2×C4semidirect
417. C4×#127D11semidirect
551. C2×C4×D4C2×D11semidirect
552. C2×C4×D4C2×D11semidirect
553. C2×C4×D4C2×D11semidirect
568. #390C2×D11semidirect
569. #390C2×D11semidirect
570. #390C2×D11semidirect
609. #384C2×D11semidirect
630. C43C2×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
#130717532
#130716892
#130716862
#130716782
#130716772
#130716612
#130715932
#130714552
#130714412
#130714372
D4×(C2×D11)⋊C42
#130713752
#130713422
#130713242
#130713142
#130712752
#130712702
#130712242
C4×#669282
#130711132
C4×C11×#1272
#3443811