Finite Group Databasebeta

← #14914481

Subgroups — #14914481

Order 2816.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2#13071634C211yesmaximal, characteristic, complemented
3#13071631C211yesmaximal, characteristic, complemented
4#13071626C211yesmaximal, characteristic, complemented
5#13071617C211yesmaximal, characteristic, complemented
6#13071598C212yesmaximal, complemented
7#13071592C212yesmaximal, complemented
8#13071550C212yesmaximal, complemented
9#13071522C212yesmaximal, complemented
10#13071508C211yesmaximal, characteristic, complemented
11#13071497C211yesmaximal, characteristic, complemented
12#13071454C211yesmaximal, characteristic, complemented
13#13071445C211yesmaximal, characteristic, complemented
14#13071412C212yesmaximal, complemented
15#13071400C212yesmaximal, complemented
16#13071248C212yesmaximal, complemented
17C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
18C4×#66983C211yesmaximal, characteristic, complemented
19#13071122C211yesmaximal, characteristic, complemented
20D11×#380C211yesmaximal, characteristic, complemented
21#13070976C212yesmaximal, complemented
22C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36#10623158C4116yescomplemented
37C2×#66948C2211yescharacteristic
38C2×#66947C2212yes—
39C2×#66946C2212yes—
40C2×#66946C2212yes—
41C2×#66946C2211yescharacteristic, complemented
42C2×#66945C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×#66935C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C4×D44C2212yes—
50C2×C4×D44C2211yescharacteristic, complemented
51C11×#391C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#387C2212yescomplemented
54C11×#385C2212yes—
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C4⋊C4C2212yescomplemented
58C4×C11×C22⋊C4C2212yes—
59#10622843C2211yescharacteristic, complemented
60#10622826C2212yes—
61#10622825C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622603C2212yes—
65#10622602C2212yes—
66#10622602C2212yescomplemented
67#10622601C2212yes—
68#10622601C2211yescharacteristic, complemented
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2212yescomplemented
72#10622598C2211yescharacteristic, complemented
73#10622594C2212yescomplemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76C4⋊C4×Dic11C2212yescomplemented
77C4⋊C4×Dic11C2212yescomplemented
78#10622586C2211yescharacteristic, complemented
79#10622585C2212yescomplemented
80#10622571C2212yes—
81#10622563C2212yes—
82#10622555C2212yes—
83C22⋊C4×Dic11C2212yes—
84#10622553C2212yes—
85#10622553C2212yescomplemented
86#10622553C2212yescomplemented
87#10622552C2212yes—
88#10622552C2211yescharacteristic, complemented
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2212yes—
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2211yescharacteristic
93C4×(C2×D11)⋊C4C2211yescharacteristic
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×(C2×D11)⋊C4C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×C4⋊Dic11C2211yescharacteristic, complemented
101#10622546C2212yescomplemented
102#10622545C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622282C2212yes—
106#10622282C2212yescomplemented
107#10622282C2212yescomplemented
108#10622281C2212yes—
109#10622281C2212yescomplemented
110#10622280C2212yes—
111#10622279C2212yes—
112#10622279C2212yescomplemented
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yes—
117#10622277C2212yescomplemented
118D11×#95C2212yes—
119D11×#95C2212yescomplemented
120#10622265C2212yescomplemented
121#10622264C2212yescomplemented
122#10622263C2212yescomplemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2312yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C2×#4343—42no—
134C2×#4343—42no—
135C2×#4343C2×C418yescomplemented
136C22×D44C2312yes—
137C22×D44C2311yescharacteristic
138C22×D44C2312yes—
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C11×C22⋊Q8C2×C418yescomplemented
152C4×Q8×C11—42no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C42×C11—42no—
162C2×C42×C11C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169#66999C2×C418yescomplemented
170Q8×Dic11—42no—
171#66983C2×C418yescomplemented
172C4×C22⋊D11—44no—
173C2×(C2×D11)⋊C4—24no—
174C2×(C2×D11)⋊C4—24no—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×C4×Dic11—42no—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215#66948C2×C418yescomplemented
216#66947C2×C4116yescomplemented
217#66946—28no—
218#66946—42no—
219#66946C2×C4116yescomplemented
220#66945C2×C418yescomplemented
221C4⋊C4×D11—42no—
222C4⋊C4×D11—42no—
223#66935C2×C4116yescomplemented
224(C22⋊D11)⋊C4—44no—
225(C22⋊D11)⋊C4C2×C4116yescomplemented
226C22⋊C4×D11—44no—
227C4×D44—28no—
228C4×D44—42no—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253#34233—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C23×D11—22no—
256C23×D11—22no—
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11C22×C414yes—
262C23×D11C2411yescharacteristic
263C23×D11C2412yes—
264C23×D11C2411yescharacteristic
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11C22×C414yes—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—41no—
275C22×C4×C11—41no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2412yes—
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C2×C22⋊D11—24no—
288C2×C22⋊D11—24no—
289C2×C22⋊D11C22×C418yes—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—41no—
295C22×Dic11—41no—
296C22×Dic11—41no—
297C22×Dic11—41no—
298C22×Dic11C22×C414yes—
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2412yes—
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2412yes—
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2412yes—
305C22×Dic11C2411yescharacteristic
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308#4343—416no—
309C2×D44—24no—
310C2×D44—24no—
311C2×D44—22no—
312C2×D44—22no—
313C2×D44—42no—
314C2×D44—42no—
315C2×D44C22×C418yes—
316C2×D44C22×C414yes—
317C2×D44C22×C418yes—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—41no—
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—
339C2×C4×D11—42no—
340C2×C4×D11—416no—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×C4×D11C22×C418yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yes—
346C11×C4⋊C4—24no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—42no—
350C11×C4⋊C4C22×C414yes—
351C11×C4⋊C4C22×C418yes—
352C11×C22⋊C4—24no—
353C11×C22⋊C4C22×C418yes—
354C42×C11—24no—
355C42×C11—22no—
356C42×C11—22no—
357C42×C11—41no—
358C42×C11—41no—
359C42×C11—42no—
360C22⋊Dic11—24no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—22no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—22no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—22no—
368(C2×D11)⋊C4—22no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4C22×C418yes—
376(C2×D11)⋊C4C22×C418yes—
377(C2×D11)⋊C4C22×C418yes—
378(C2×D11)⋊C4C22×C418yes—
379(C2×D11)⋊C4#4114yescomplemented
380(C2×D11)⋊C4#4114yescomplemented
381C4⋊Dic11—24no—
382C4⋊Dic11—22no—
383C4⋊Dic11—22no—
384C4⋊Dic11—42no—
385C4⋊Dic11C22×C414yes—
386Dic11⋊C4—42no—
387Dic11⋊C4—42no—
388Dic11⋊C4—42no—
389Dic11⋊C4—42no—
390Dic11⋊C4C22×C418yes—
391C4×Dic11—24no—
392C4×Dic11—22no—
393C4×Dic11—22no—
394C4×Dic11—42no—
395C4×Dic11—41no—
396C4×Dic11—41no—
397C4×Dic11—42no—
398C4×Dic11—42no—
399C4×Dic11C22×C418yes—
400C2×#525—111no—
401#2361—111no—
402#2361—111no—
403#2360—111no—
404#2360—111no—
405#2358—112no—
406#2358—112no—
407#2353—112no—
408#2349—112no—
409#2347—111no—
410#2346—111no—
411#2341—111no—
412#2339—111no—
413#2335—112no—
414#2335—112no—
415#2318—112no—
416C4×C22⋊Q8—111no—
417C4×C22⋊Q8D1111yescharacteristic, complemented
418C4×#121—111no—
419C4×#121—111no—
420C2×#380—111no—
421#2275—112no—
422C2×C4×C22⋊C4—111no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—21no—
426C23×C11—21no—
427C23×C11C23×C412yes—
428C23×C11H(5,𝔽2)12yes—
429C23×C112−1+412yes—
430C23×C11C2511yescharacteristic
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—21no—
435C22×D11—28no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—21no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—22no—
447C22×D11—21no—
448C22×D11—28no—
449C22×D11—44no—
450C22×D11—44no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11—44no—
454C22×D11C23×C412yes—
455C22×D11C23×C414yes—
456C22×D11C23×C412yes—
457C22×D11C2×#4112yes—
458C22×D11C2×#4112yes—
459Q8×C11—28no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—28no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—44no—
484C2×C4×C11—44no—
485C2×C4×C11C23×C414yes—
486C2×C4×C11C23×C414yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C412yes—
489C2×C4×C11C2×#4112yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11H(5,𝔽2)12yes—
492C2×C4×C11H(5,𝔽2)12yes—
493C22⋊D11—216no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—22no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—44no—
517C2×Dic11—44no—
518C2×Dic11—44no—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C414yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C2×#4112yes—
523C2×Dic11C2×#4112yes—
524D44—216no—
525D44—28no—
526D44—48no—
527C4×D11—28no—
528C4×D11—28no—
529C4×D11—44no—
530C4×D11—44no—
531C4×D11—48no—
532C4×D11—84no—
533C4×D11—84no—
534C4×D11—84no—
535C4×D11—84no—
536C22×#41—111no—
537C24×C4—111no—
538#525—1116no—
539C2×#123—112no—
540C2×C22⋊Q8—111no—
541C2×C22⋊Q8C2×D1111yescharacteristic
542C2×#121—111no—
543C2×#121—111no—
544C2×#120—112no—
545C2×C4×Q8—111no—
546C2×C4×Q8C2×D1111yescharacteristic, complemented
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—112no—
550C2×C4×D4—111no—
551C2×C4×D4—112no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—111no—
555C2×#117—111no—
556C22×C4⋊C4—111no—
557C22×C4⋊C4—111no—
558C22×C22⋊C4—111no—
559C22×C22⋊C4—111no—
560C22×C22⋊C4—112no—
561C22×C42—111no—
562C22×C42C2×D1111yescharacteristic
563#391—111no—
564#391C2×D1111yescharacteristic, complemented
565#390—112no—
566#390—111no—
567#390—112no—
568#390—111no—
569#389—112no—
570#389—111no—
571#389—111no—
572#389—111no—
573#389—112no—
574#389C2×D1111yescharacteristic, complemented
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#387—112no—
584#387—112no—
585#387—112no—
586#387C2×D1112yescomplemented
587#386—112no—
588#386—112no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#385—112no—
594#385—112no—
595#385—112no—
596#385—112no—
597#385—112no—
598#385C2×D1112yes—
599#383—112no—
600#382—112no—
601#381—112no—
602#380—111no—
603#380—112no—
604#380—111no—
605#380—111no—
606#380—112no—
607#380—112no—
608#380C2×D1111yescharacteristic
609C4×C4⋊C4—112no—
610C4×C4⋊C4—111no—
611C4×C4⋊C4—112no—
612C4×C4⋊C4—111no—
613C4×C4⋊C4—111no—
614C4×C4⋊C4C2×D1112yescomplemented
615C4×C4⋊C4C2×D1111yescharacteristic, complemented
616C4×C22⋊C4—112no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—111no—
622C4×C22⋊C4—111no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—111no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4C2×D1112yes—
631#376—112no—
632C2×#95—111no—
633C2×#95—111no—
634C2×#95—112no—
635C2×#95—112no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—22no—
641C22×C11—22no—
642C22×C11#52014yes—
643C22×C11C24×C411yescharacteristic
644C22×C11C22×#4111yescharacteristic
645C22×C11C22×#4111yescharacteristic
646C22×C11C2×H(5,𝔽2)11yescharacteristic
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C22×C11C2×H(5,𝔽2)11yescharacteristic
649C22×C11C2×2−1+411yescharacteristic
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—24no—
658C2×D11—22no—
659C2×D11—24no—
660C2×D11—22no—
661C2×D11—24no—
662C2×D11—416no—
663C2×D11—41no—
664C2×D11—41no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11C4×#4114yes—
672C4×C11—24no—
673C4×C11—22no—
674C4×C11—24no—
675C4×C11—22no—
676C4×C11—22no—
677C4×C11—41no—
678C4×C11—42no—
679C4×C11—42no—
680C4×C11—41no—
681C4×C11#51814yes—
682Dic11—22no—
683Dic11—22no—
684Dic11—24no—
685Dic11—22no—
686Dic11—22no—
687Dic11—42no—
688Dic11—42no—
689Dic11—41no—
690Dic11—41no—
691C25—111no—
692C2×#41—118no—
693C2×#41—442no—
694C2×#41—442no—
695C22×Q8C22×D1111yescharacteristic
696C22×D4—112no—
697C22×D4—112no—
698C22×D4—111no—
699C22×D4—112no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—118no—
704C23×C4—111no—
705C23×C4—112no—
706C23×C4—111no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—112no—
711C23×C4—112no—
712C23×C4—112no—
713C23×C4—442no—
714C23×C4—442no—
715C23×C4C22×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718#123—1116no—
719C22⋊Q8—118no—
720C22⋊Q8C4×D1118yescomplemented
721#121—118no—
722#121—118no—
723#120—1116no—
724C4×Q8—42no—
725C4×Q8—442no—
726C4×D4—1116no—
727C4×D4—1116no—
728C4×D4—228no—
729C4×D4—228no—
730C4×D4—442no—
731C4×D4—442no—
732C4×D4—444no—
733C4×D4—444no—
734#117—118no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—112no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—442no—
746C2×C4⋊C4—442no—
747C2×C4⋊C4C22×D1111yescharacteristic
748C2×C4⋊C4C22×D1111yescharacteristic
749C2×C4⋊C4C22×D1112yes—
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1111yescharacteristic
752C2×C4⋊C4C22×D1112yes—
753C2×C22⋊C4—111no—
754C2×C22⋊C4—111no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—111no—
761C2×C22⋊C4—111no—
762C2×C22⋊C4—111no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—224no—
775C2×C22⋊C4—224no—
776C2×C22⋊C4—444no—
777C2×C22⋊C4C22×D1112yes—
778C2×C22⋊C4C22×D1112yes—
779C2×C42—42no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—111no—
788C2×C42—111no—
789C2×C42—442no—
790C2×C42C22×D1112yes—
791C2×C42C22×D1111yescharacteristic
792C2×C42C22×D1111yescharacteristic
793C2×C42C22×D1112yes—
794C2×C42C22×D1111yescharacteristic
795C2×C42C22×D1111yescharacteristic
796#95—111no—
797#95—112no—
798#95—111no—
799#95—111no—
800#95—111no—
801#95—111no—
802#95—111no—
803#95—111no—
804#95—111no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95C22×D1112yes—
816#95C22×D1112yes—
817#95C22×D1112yes—
818#95C22×D1112yes—
819#95C22×D1112yes—
820C2×C11—24no—
821C2×C11C2×C4×#4111yescharacteristic
822C2×C11C2×#51811yescharacteristic
823C2×C11C2×#52011yescharacteristic
824C2×C11#351911yescharacteristic
825C2×C11#351911yescharacteristic
826C2×C11#352011yescharacteristic
827C2×C11#352011yescharacteristic
828D11—24no—
829D11—44no—
830D11—42no—
831C24—111no—
832C24—111no—
833C24—112no—
834C24—114no—
835C24—222no—
836C24—222no—
837C24—222no—
838C24—222no—
839C24—441no—
840C24—441no—
841C24C23×D1111yescharacteristic
842#41—4416no—
843C2×Q8—22no—
844C2×Q8—22no—
845C2×Q8C2×C4×D1114yes—
846C2×D4—118no—
847C2×D4—118no—
848C2×D4—114no—
849C2×D4—118no—
850C2×D4—224no—
851C2×D4—224no—
852C2×D4—224no—
853C2×D4—224no—
854C2×D4—222no—
855C2×D4—222no—
856C2×D4—442no—
857C2×D4—442no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—111no—
869C22×C4—112no—
870C22×C4—111no—
871C22×C4—114no—
872C22×C4—114no—
873C22×C4—114no—
874C22×C4—114no—
875C22×C4—118no—
876C22×C4—114no—
877C22×C4—111no—
878C22×C4—112no—
879C22×C4—111no—
880C22×C4—112no—
881C22×C4—224no—
882C22×C4—224no—
883C22×C4—224no—
884C22×C4—222no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—224no—
893C22×C4—4416no—
894C22×C4—441no—
895C22×C4—441no—
896C22×C4—441no—
897C22×C4—441no—
898C22×C4—442no—
899C22×C4—442no—
900C22×C4—442no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—441no—
909C22×C4—441no—
910C22×C4—441no—
911C22×C4—441no—
912C22×C4C2×C4×D1114yes—
913C22×C4C23×D1111yescharacteristic
914C22×C4C23×D1112yes—
915C22×C4C23×D1112yes—
916C22×C4C23×D1111yescharacteristic
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1112yes—
919C22×C4C23×D1112yes—
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C4⋊C4—22no—
924C4⋊C4—24no—
925C4⋊C4—22no—
926C4⋊C4—42no—
927C4⋊C4—114no—
928C4⋊C4—118no—
929C4⋊C4—224no—
930C4⋊C4—222no—
931C4⋊C4—222no—
932C4⋊C4—442no—
933C4⋊C4—442no—
934C4⋊C4—442no—
935C4⋊C4—442no—
936C4⋊C4—442no—
937C4⋊C4C2×C4×D1114yes—
938C4⋊C4C2×C4×D1118yes—
939C22⋊C4—24no—
940C22⋊C4—118no—
941C22⋊C4—118no—
942C22⋊C4—118no—
943C22⋊C4—118no—
944C22⋊C4—114no—
945C22⋊C4—114no—
946C22⋊C4—222no—
947C22⋊C4—222no—
948C22⋊C4—224no—
949C22⋊C4—222no—
950C22⋊C4—222no—
951C22⋊C4—224no—
952C22⋊C4—222no—
953C22⋊C4—222no—
954C22⋊C4—224no—
955C22⋊C4—442no—
956C22⋊C4—442no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4—442no—
961C22⋊C4C2×C4×D1118yes—
962C42—22no—
963C42—22no—
964C42—24no—
965C42—41no—
966C42—41no—
967C42—42no—
968C42—118no—
969C42—224no—
970C42—222no—
971C42—222no—
972C42—441no—
973C42—441no—
974C42—442no—
975C42—442no—
976C42—442no—
977C11#3423311yescharacteristic, complemented, Sylow
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—112no—
983C23—112no—
984C23—112no—
985C23—112no—
986C23—114no—
987C23—228no—
988C23—221no—
989C23—221no—
990C23—221no—
991C23—221no—
992C23—228no—
993C23—222no—
994C23—221no—
995C23—222no—
996C23—221no—
997C23—221no—
998C23—221no—
999C23—222no—
1000C23—222no—
1001C23—221no—
1002C23—222no—
1003C23—222no—
1004C23—221no—
1005C23—444no—
1006C23—444no—
1007C23—444no—
1008C23—444no—
1009C23—444no—
1010C23C22×C4×D1112yes—
1011C23#6704012yes—
1012C23#6704212yes—
1013C23C24×D1111yescharacteristic
1014Q8—28no—
1015D4—2216no—
1016D4—2216no—
1017D4—228no—
1018D4—448no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—44no—
1043C2×C4—44no—
1044C2×C4—112no—
1045C2×C4—114no—
1046C2×C4—112no—
1047C2×C4—112no—
1048C2×C4—112no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—222no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—222no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—228no—
1060C2×C4—228no—
1061C2×C4—222no—
1062C2×C4—221no—
1063C2×C4—222no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—221no—
1073C2×C4—444no—
1074C2×C4—444no—
1075C2×C4—448no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—444no—
1079C2×C4—884no—
1080C2×C4—884no—
1081C2×C4—884no—
1082C2×C4—884no—
1083C2×C4C22×C4×D1114yes—
1084C2×C4C22×C4×D1112yes—
1085C2×C4C22×C4×D1114yes—
1086C2×C4C22×C4×D1112yes—
1087C2×C4#6703712yes—
1088C2×C4#41×D1112yes—
1089C2×C4#41×D1112yes—
1090C2×C4#6704212yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—114no—
1098C22—222no—
1099C22—222no—
1100C22—222no—
1101C22—222no—
1102C22—222no—
1103C22—222no—
1104C22—224no—
1105C22—222no—
1106C22—222no—
1107C22—224no—
1108C22—224no—
1109C22—222no—
1110C22—4416no—
1111C22—442no—
1112C22—441no—
1113C22—442no—
1114C22—441no—
1115C22—441no—
1116C22—442no—
1117C22—441no—
1118C22—442no—
1119C22#1062310514yes—
1120C22C23×C4×D1111yescharacteristic
1121C22C2×#6703711yescharacteristic
1122C22C2×#6704011yescharacteristic
1123C22C2×#41×D1111yescharacteristic
1124C22C2×#41×D1111yescharacteristic
1125C22C2×#6704211yescharacteristic
1126C22C2×#6704211yescharacteristic
1127C4—22no—
1128C4—22no—
1129C4—24no—
1130C4—22no—
1131C4—24no—
1132C4—41no—
1133C4—42no—
1134C4—42no—
1135C4—41no—
1136C4—222no—
1137C4—222no—
1138C4—222no—
1139C4—222no—
1140C4—224no—
1141C4—442no—
1142C4—441no—
1143C4—442no—
1144C4—441no—
1145C4#1062307614yes—
1146C2—24no—
1147C2—224no—
1148C2—442no—
1149C2—444no—
1150C2C4×#41×D1111yescharacteristic
1151C2C2×#1062307611yescharacteristic
1152C2C2×#1062310511yescharacteristic
1153C2#1308263611yescharacteristic
1154C2#1308265011yescharacteristic
1155C2#1308265911yescharacteristic
1156C2#1308266011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenterC4×C22⋊Q8D11
hypocenterC11#34233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13071634C2semidirect
3. #13071631C2semidirect
4. #13071626C2semidirect
5. #13071617C2semidirect
6. #13071598C2semidirect
7. #13071592C2semidirect
8. #13071550C2semidirect
9. #13071522C2semidirect
10. #13071508C2semidirect
11. #13071497C2semidirect
12. #13071454C2semidirect
13. #13071445C2semidirect
14. #13071412C2semidirect
15. #13071400C2semidirect
16. #13071248C2semidirect
17. C22⋊Q8×Dic11C2semidirect
18. C4×#66983C2semidirect
19. #13071122C2semidirect
20. D11×#380C2semidirect
21. #13070976C2semidirect
22. C2×C4×(C2×D11)⋊C4C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
36. #10623158C4semidirect
41. C2×#66946C22semidirect
50. C2×C4×D44C22semidirect
51. C11×#391C22semidirect
52. C11×#389C22semidirect
53. C11×#387C22semidirect
56. C4×C11×C4⋊C4C22semidirect
57. C4×C11×C4⋊C4C22semidirect
59. #10622843C22semidirect
66. #10622602C22semidirect
68. #10622601C22semidirect
71. #10622600C22semidirect
72. #10622598C22semidirect
73. #10622594C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. #10622586C22semidirect
79. #10622585C22semidirect
85. #10622553C22semidirect
86. #10622553C22semidirect
88. #10622552C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. #10622546C22semidirect
102. #10622545C22semidirect
103. #10622541C22semidirect
106. #10622282C22semidirect
107. #10622282C22semidirect
109. #10622281C22semidirect
112. #10622279C22semidirect
117. #10622277C22semidirect
119. D11×#95C22semidirect
120. #10622265C22semidirect
121. #10622264C22semidirect
122. #10622263C22semidirect
123. #10622260C22semidirect
135. C2×#4343C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
151. C11×C22⋊Q8C2×C4semidirect
169. #66999C2×C4semidirect
171. #66983C2×C4semidirect
215. #66948C2×C4semidirect
216. #66947C2×C4semidirect
219. #66946C2×C4semidirect
220. #66945C2×C4semidirect
223. #66935C2×C4semidirect
225. (C22⋊D11)⋊C4C2×C4semidirect
379. (C2×D11)⋊C4#41semidirect
380. (C2×D11)⋊C4#41semidirect
417. C4×C22⋊Q8D11semidirect
546. C2×C4×Q8C2×D11semidirect
564. #391C2×D11semidirect
574. #389C2×D11semidirect
586. #387C2×D11semidirect
614. C4×C4⋊C4C2×D11semidirect
615. C4×C4⋊C4C2×D11semidirect
720. C22⋊Q8C4×D11semidirect
977. C11#34233semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
#130716342
#130716312
#130716262
#130716172
#130715982
#130715922
#130715502
#130715222
#130715082
#130714972
#130714542
#130714452
#130714122
#130714002
#130712482
C22⋊Q8×Dic112
C4×#669832
#130711222
D11×#3802
#130709762
C2×C4×(C2×D11)⋊C42
C4×C11×C22⋊Q82
#3423311