Finite Group Databasebeta

← #14916571

Subgroups — #14916571

Order 2816.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13071778C212yesmaximal, complemented
3#13071772C212yesmaximal, complemented
4#13071697C212yesmaximal, complemented
5#13071661C212yesmaximal, complemented
6#13071567C211yesmaximal, characteristic, complemented
7#13071560C211yesmaximal, characteristic, complemented
8#13071548C211yesmaximal, characteristic, complemented
9#13071545C211yesmaximal, characteristic, complemented
10#13071541C211yesmaximal, characteristic, complemented
11#13071541C211yesmaximal, characteristic, complemented
12#13071512C211yesmaximal, characteristic, complemented
13#13071409C212yesmaximal, complemented
14#13071401C212yesmaximal, complemented
15#13071273C212yesmaximal, complemented
16#13071270C212yesmaximal, complemented
17#13071224C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071209C211yesmaximal, characteristic, complemented
20#13071205C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22C2×#10622600C211yesmaximal, characteristic, complemented
23D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic, complemented
30C2×#66992C2211yescharacteristic
31C2×#66990C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yes—
35C2×#66979C2211yescharacteristic, complemented
36C22×C4⋊Dic11C2211yescharacteristic
37#10623078C4116yescomplemented
38C2×#66949C2211yescharacteristic
39C2×#66947C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66945C2211yescharacteristic
42C2×#66945C2211yescharacteristic, complemented
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66937C2211yescharacteristic
45C2×#66936C2211yescharacteristic
46C2×#66935C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×#66931C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C2×#66925C2211yescharacteristic
51C11×#389C2212yescomplemented
52C11×#385C2212yes—
53C11×#385C2212yescomplemented
54C11×#384C2211yescharacteristic, complemented
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic, complemented
57C4×C11×C4⋊C4C2211yescharacteristic, complemented
58#10622833C2212yes—
59#10622826C2212yes—
60#10622826C2212yes—
61#10622826C2212yes—
62#10622826C2212yescomplemented
63#10622825C2211yescharacteristic
64#10622825C2211yescharacteristic, complemented
65C4×C22⋊Dic11C2212yes—
66C4×C22⋊Dic11C2212yescomplemented
67C2×C11⋊#95C2212yes—
68#10622603C2212yes—
69#10622603C2212yes—
70#10622603C2212yes—
71#10622603C2212yes—
72#10622603C2212yescomplemented
73#10622603C2212yescomplemented
74#10622601C2212yes—
75#10622601C2212yes—
76#10622600C2212yes—
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic
80#10622600C2211yescharacteristic
81#10622600C2212yes—
82#10622600C2211yescharacteristic
83#10622600C2211yescharacteristic
84#10622600C2211yescharacteristic, complemented
85#10622600C2211yescharacteristic, complemented
86#10622594C2212yescomplemented
87#10622591C2212yescomplemented
88#10622591C2212yescomplemented
89#10622591C2212yescomplemented
90#10622591C2212yescomplemented
91#10622590C2211yescharacteristic, complemented
92#10622589C2211yescharacteristic, complemented
93C4⋊C4×Dic11C2212yescomplemented
94C4⋊C4×Dic11C2211yescharacteristic, complemented
95C4⋊C4×Dic11C2211yescharacteristic, complemented
96#10622587C2212yescomplemented
97#10622570C2212yes—
98#10622570C2212yes—
99#10622569C2212yescomplemented
100#10622568C2212yes—
101#10622564C2212yescomplemented
102#10622559C2212yes—
103#10622558C2212yescomplemented
104C22⋊C4×Dic11C2212yes—
105C22⋊C4×Dic11C2212yes—
106#10622553C2212yes—
107#10622553C2212yes—
108C4×(C2×D11)⋊C4C2212yescomplemented
109#10622549C2211yescharacteristic, complemented
110C4×C4⋊Dic11C2211yescharacteristic, complemented
111#10622546C2212yescomplemented
112#10622282C2212yes—
113#10622282C2212yes—
114#10622281C2212yescomplemented
115#10622279C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118#10622277C2212yes—
119#10622266C2212yescomplemented
120#10622265C2212yescomplemented
121#10622262C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C2×#4339—42no—
137C2×#4339—42no—
138C2×#4339C2×C418yescomplemented
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×C4×D11—42no—
142C22×C4×D11—42no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C4×D4×C11—44no—
152C4×D4×C11C2×C418yescomplemented
153C2×C11×C4⋊C4—42no—
154C2×C11×C4⋊C4—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175#66992C2×C418yes—
176#66990C2×C418yescomplemented
177C4×C22⋊D11C2×C418yescomplemented
178C4×C22⋊D11C2×C418yescomplemented
179C2×(C2×D11)⋊C4—44no—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197#66979—42no—
198C2×C4⋊Dic11—42no—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220#66949C2×C418yescomplemented
221#66947C2×C418yescomplemented
222#66945—42no—
223#66945—42no—
224#66945—42no—
225C4⋊C4×D11—42no—
226#66937C2×C418yescomplemented
227#66936C2×C418yescomplemented
228#66935C2×C418yescomplemented
229(C22⋊D11)⋊C4—44no—
230#66931C2×C418yescomplemented
231C4×D44C2×C418yescomplemented
232#66925C2×C418yescomplemented
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34362—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C24×C11C2411yescharacteristic
256C23×D11—22no—
257C23×D11—22no—
258C23×D11—41no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11C22×C414yes—
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11C22×C414yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—24no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11C22×C414yes—
280C22×C4×C11C22×C414yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—22no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—41no—
293C2×C22⋊D11—41no—
294C2×C22⋊D11—41no—
295C2×C22⋊D11—41no—
296C2×C22⋊D11—41no—
297C2×C22⋊D11—41no—
298C2×C22⋊D11C22×C414yes—
299C2×C22⋊D11C22×C414yes—
300C2×C22⋊D11C22×C414yes—
301C2×C22⋊D11C22×C414yes—
302C22×Dic11—24no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C22×C414yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317#4339—416no—
318C2×D44—41no—
319C2×D44—41no—
320C2×D44—41no—
321C2×D44—41no—
322C2×D44C22×C414yes—
323C2×D44C22×C414yes—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—41no—
331C2×C4×D11—41no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—416no—
338C2×C4×D11C22×C414yes—
339C2×C4×D11C22×C414yes—
340C2×C4×D11C22×C414yes—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×Dic22—41no—
344C2×Dic22—41no—
345C2×Dic22C22×C414yes—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4—42no—
352C11×C4⋊C4—42no—
353C11×C4⋊C4—42no—
354C11×C4⋊C4C22×C414yes—
355C11×C22⋊C4—24no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4C22×C414yes—
358C11×C22⋊C4C22×C414yes—
359C42×C11—42no—
360C42×C11C22×C414yes—
361C22⋊Dic11—24no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11C22×C414yes—
365C22⋊Dic11C22×C414yes—
366(C2×D11)⋊C4—42no—
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—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C414yes—
379(C2×D11)⋊C4C22×C414yes—
380(C2×D11)⋊C4C22×C414yes—
381(C2×D11)⋊C4C22×C414yes—
382(C2×D11)⋊C4C22×C414yes—
383C4⋊Dic11—22no—
384C4⋊Dic11—22no—
385C4⋊Dic11—22no—
386C4⋊Dic11—22no—
387C4⋊Dic11—42no—
388C4⋊Dic11C22×C414yes—
389Dic11⋊C4—42no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4C22×C414yes—
393Dic11⋊C4C22×C414yes—
394Dic11⋊C4C22×C414yes—
395Dic11⋊C4C22×C414yes—
396C4×Dic11—42no—
397C4×Dic11—42no—
398C4×Dic11—42no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11C22×C414yes—
404C2×#525—111no—
405#2378—112no—
406#2377—112no—
407#2368—112no—
408#2364—112no—
409#2354—111no—
410#2354—111no—
411#2352—111no—
412#2352—111no—
413#2352—111no—
414#2352—111no—
415D4×C4⋊C4—111no—
416D4×C4⋊C4D1111yescharacteristic, complemented
417#2335—112no—
418#2335—112no—
419#2321—112no—
420#2321—112no—
421#2314—111no—
422#2314—111no—
423#2311—111no—
424#2311—111no—
425#2280—111no—
426C2×#380—111no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11C23×C412yes—
438C23×C11C23×C412yes—
439C23×C11H(5,𝔽2)12yes—
440C23×C112−1+412yes—
441C23×C11C2511yescharacteristic
442C22×D11—28no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—44no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11C23×C412yes—
468C22×D11C23×C412yes—
469C22×D11C23×C412yes—
470D4×C11—28no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—28no—
480C2×C4×C11—28no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—84no—
494C2×C4×C11—84no—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11H(5,𝔽2)12yes—
502C22⋊D11—28no—
503C22⋊D11—44no—
504C22⋊D11—44no—
505C22⋊D11—44no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—44no—
529C2×Dic11—84no—
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C412yes—
532C2×Dic11C23×C412yes—
533C2×Dic11C23×C412yes—
534C2×Dic11C23×C412yes—
535D44—44no—
536D44—44no—
537C4×D11—28no—
538C4×D11—28no—
539C4×D11—28no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—84no—
543Dic22—44no—
544C22×#41—111no—
545C24×C4—111no—
546#525—1116no—
547C2×#123—111no—
548C2×#123—111no—
549C2×C22⋊Q8—111no—
550C2×C22⋊Q8—111no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#120—111no—
554C2×#120—111no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—112no—
558C2×C4×D4—111no—
559C2×C4×D4C2×D1112yes—
560C2×C4×D4C2×D1111yescharacteristic
561C2×#117—111no—
562C2×#117—111no—
563C2×#117—111no—
564C2×#117—111no—
565C2×#117—111no—
566C22×C4⋊C4—111no—
567C22×C4⋊C4—111no—
568C22×C4⋊C4C2×D1111yescharacteristic
569C22×C4⋊C4C2×D1111yescharacteristic, complemented
570C22×C22⋊C4—112no—
571#391—112no—
572#391—112no—
573#390—112no—
574#390—112no—
575#390—112no—
576#390—112no—
577#389—112no—
578#389C2×D1112yescomplemented
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388—112no—
590#388—112no—
591#387—112no—
592#387—112no—
593#387—112no—
594#387—112no—
595#387—112no—
596#387—112no—
597#387—112no—
598#387—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#385—112no—
608#385—112no—
609#385C2×D1112yes—
610#385C2×D1112yescomplemented
611#384—111no—
612#384C2×D1111yescharacteristic, complemented
613#382—111no—
614#382—111no—
615#381—112no—
616#380—111no—
617#380—111no—
618#380—111no—
619#380—111no—
620#380—111no—
621#380—111no—
622#380—111no—
623#380—111no—
624#380—112no—
625#380—111no—
626#380—111no—
627#380—112no—
628#380C2×D1111yescharacteristic
629#380C2×D1111yescharacteristic, complemented
630#379—112no—
631C4×C4⋊C4—111no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—112no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—112no—
636C4×C4⋊C4C2×D1111yescharacteristic, complemented
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C2×#95—112no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11#52014yes—
658C22×C11C24×C411yescharacteristic
659C22×C11C2×H(5,𝔽2)11yescharacteristic
660C22×C11C2×H(5,𝔽2)11yescharacteristic
661C22×C11C2×H(5,𝔽2)11yescharacteristic
662C22×C11C2×2−1+411yescharacteristic
663C22×C11#58511yescharacteristic
664C22×C11#58511yescharacteristic
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—416no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—41no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—41no—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—22no—
690C4×C11—22no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11—42no—
695C4×C11#51814yes—
696Dic11—22no—
697Dic11—22no—
698Dic11—22no—
699Dic11—22no—
700Dic11—22no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C2×#41—118no—
707C2×#41—442no—
708C2×#41—442no—
709C22×Q8—111no—
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4C22×D1111yescharacteristic
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—118no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—442no—
727C23×C4—442no—
728C23×C4C22×D1111yescharacteristic
729C23×C4C22×D1111yescharacteristic
730C23×C4C22×D1112yes—
731C23×C4C22×D1112yes—
732#123—118no—
733#123—118no—
734C22⋊Q8—118no—
735C22⋊Q8—118no—
736#121—118no—
737#121—118no—
738#120—118no—
739#120—118no—
740C4×D4—44no—
741C4×D4—118no—
742C4×D4—118no—
743C4×D4—118no—
744C4×D4—444no—
745C4×D4C4×D1118yescomplemented
746#117—118no—
747#117—442no—
748#117—442no—
749#117—442no—
750#117—442no—
751C2×C4⋊C4—42no—
752C2×C4⋊C4—42no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—442no—
767C2×C4⋊C4—442no—
768C2×C4⋊C4C22×D1111yescharacteristic
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1111yescharacteristic
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1112yes—
773C2×C4⋊C4C22×D1112yes—
774C2×C4⋊C4C22×D1112yes—
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—444no—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C22⋊C4C22×D1111yescharacteristic
804C2×C42—111no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42C22×D1112yes—
813C2×C42C22×D1111yescharacteristic
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95C22×D1112yes—
832#95C22×D1112yes—
833#95C22×D1112yes—
834C2×C11—24no—
835C2×C11—42no—
836C2×C11C2×#51811yescharacteristic
837C2×C11C2×#52011yescharacteristic
838C2×C11#342811yescharacteristic
839C2×C11#354111yescharacteristic
840C2×C11#354111yescharacteristic
841C2×C11#354211yescharacteristic
842C2×C11#354211yescharacteristic
843D11—42no—
844D11—42no—
845D11—42no—
846C24—111no—
847C24—111no—
848C24—111no—
849C24—114no—
850C24—222no—
851C24—222no—
852C24—441no—
853C24—441no—
854C24—441no—
855C24—441no—
856C24C23×D1111yescharacteristic
857C24C23×D1111yescharacteristic
858#41—4416no—
859C2×Q8—114no—
860C2×Q8—441no—
861C2×Q8—441no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—114no—
865C2×D4—114no—
866C2×D4—114no—
867C2×D4—114no—
868C2×D4—114no—
869C2×D4—114no—
870C2×D4—222no—
871C2×D4—222no—
872C2×D4—441no—
873C2×D4—441no—
874C2×D4—441no—
875C2×D4—441no—
876C2×D4—441no—
877C2×D4—441no—
878C2×D4—441no—
879C2×D4—441no—
880C2×D4—441no—
881C2×D4—441no—
882C2×D4C2×C4×D1114yes—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—114no—
899C22×C4—114no—
900C22×C4—114no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—114no—
904C22×C4—112no—
905C22×C4—112no—
906C22×C4—112no—
907C22×C4—112no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—224no—
915C22×C4—4416no—
916C22×C4—441no—
917C22×C4—441no—
918C22×C4—441no—
919C22×C4—441no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—441no—
924C22×C4—441no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4C2×C4×D1114yes—
928C22×C4C2×C4×D1114yes—
929C22×C4C23×D1112yes—
930C22×C4C23×D1112yes—
931C22×C4C23×D1112yes—
932C22×C4C23×D1112yes—
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1111yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—114no—
947C4⋊C4—114no—
948C4⋊C4—114no—
949C4⋊C4—114no—
950C4⋊C4—114no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4C2×C4×D1114yes—
960C22⋊C4—24no—
961C22⋊C4—42no—
962C22⋊C4—114no—
963C22⋊C4—114no—
964C22⋊C4—114no—
965C22⋊C4—114no—
966C22⋊C4—114no—
967C22⋊C4—114no—
968C22⋊C4—114no—
969C22⋊C4—114no—
970C22⋊C4—224no—
971C22⋊C4—442no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4C2×C4×D1114yes—
985C22⋊C4C2×C4×D1114yes—
986C42—42no—
987C42—114no—
988C42—442no—
989C42—442no—
990C42—442no—
991C42—442no—
992C42—442no—
993C42—442no—
994C42—442no—
995C42C2×C4×D1114yes—
996C11#3436211yescharacteristic, complemented, Sylow
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—112no—
1008C23—112no—
1009C23—112no—
1010C23—228no—
1011C23—221no—
1012C23—221no—
1013C23—221no—
1014C23—221no—
1015C23—221no—
1016C23—221no—
1017C23—221no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—221no—
1023C23—221no—
1024C23—221no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—444no—
1030C23—444no—
1031C23—444no—
1032C23—444no—
1033C23—444no—
1034C23—444no—
1035C23C22×C4×D1112yes—
1036C23C22×C4×D1112yes—
1037C23#6703712yes—
1038C23#6704012yes—
1039C23C24×D1111yescharacteristic
1040Q8—444no—
1041D4—28no—
1042D4—228no—
1043D4—444no—
1044D4—444no—
1045D4—444no—
1046D4—444no—
1047D4—444no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—84no—
1071C2×C4—84no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—112no—
1075C2×C4—112no—
1076C2×C4—112no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4—884no—
1106C2×C4—884no—
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1112yes—
1110C2×C4C22×C4×D1112yes—
1111C2×C4C22×C4×D1112yes—
1112C2×C4#6703712yes—
1113C2×C4#6704212yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—222no—
1128C22—222no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—222no—
1133C22—222no—
1134C22—222no—
1135C22—222no—
1136C22—4416no—
1137C22—441no—
1138C22—441no—
1139C22—441no—
1140C22—441no—
1141C22—441no—
1142C22—441no—
1143C22—441no—
1144C22—441no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22#1062303514yes—
1150C22C23×C4×D1111yescharacteristic
1151C22C2×#6703711yescharacteristic
1152C22C2×#6703711yescharacteristic
1153C22C2×#6704011yescharacteristic
1154C22C2×#6704211yescharacteristic
1155C22#1062345511yescharacteristic
1156C22#1062345711yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—222no—
1166C4—222no—
1167C4—222no—
1168C4—222no—
1169C4—222no—
1170C4—442no—
1171C4—442no—
1172C4—442no—
1173C4—442no—
1174C4#1062307614yes—
1175C2—24no—
1176C2—42no—
1177C2—442no—
1178C2—442no—
1179C2—442no—
1180C2C2×#1062307611yescharacteristic
1181C2C2×#1062303511yescharacteristic
1182C2#1308181611yescharacteristic
1183C2#1308291011yescharacteristic
1184C2#1308291411yescharacteristic
1185C2#1308293311yescharacteristic
1186C2#1308293711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenterD4×C4⋊C4D11
hypocenterC11#34362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071778C2semidirect
3. #13071772C2semidirect
4. #13071697C2semidirect
5. #13071661C2semidirect
6. #13071567C2semidirect
7. #13071560C2semidirect
8. #13071548C2semidirect
9. #13071545C2semidirect
10. #13071541C2semidirect
11. #13071541C2semidirect
12. #13071512C2semidirect
13. #13071409C2semidirect
14. #13071401C2semidirect
15. #13071273C2semidirect
16. #13071270C2semidirect
17. #13071224C2semidirect
18. #13071221C2semidirect
19. #13071209C2semidirect
20. #13071205C2semidirect
21. #13070998C2semidirect
22. C2×#10622600C2semidirect
23. D4×C11×C4⋊C4C2semidirect
29. C22×C11×C4⋊C4C22semidirect
35. C2×#66979C22semidirect
37. #10623078C4semidirect
42. C2×#66945C22semidirect
43. C2×C4⋊C4×D11C22semidirect
51. C11×#389C22semidirect
53. C11×#385C22semidirect
54. C11×#384C22semidirect
56. C11×#380C22semidirect
57. C4×C11×C4⋊C4C22semidirect
62. #10622826C22semidirect
64. #10622825C22semidirect
66. C4×C22⋊Dic11C22semidirect
72. #10622603C22semidirect
73. #10622603C22semidirect
84. #10622600C22semidirect
85. #10622600C22semidirect
86. #10622594C22semidirect
87. #10622591C22semidirect
88. #10622591C22semidirect
89. #10622591C22semidirect
90. #10622591C22semidirect
91. #10622590C22semidirect
92. #10622589C22semidirect
93. C4⋊C4×Dic11C22semidirect
94. C4⋊C4×Dic11C22semidirect
95. C4⋊C4×Dic11C22semidirect
96. #10622587C22semidirect
99. #10622569C22semidirect
101. #10622564C22semidirect
103. #10622558C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. #10622549C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. #10622546C22semidirect
114. #10622281C22semidirect
119. #10622266C22semidirect
120. #10622265C22semidirect
121. #10622262C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
138. C2×#4339C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
152. C4×D4×C11C2×C4semidirect
176. #66990C2×C4semidirect
177. C4×C22⋊D11C2×C4semidirect
178. C4×C22⋊D11C2×C4semidirect
220. #66949C2×C4semidirect
221. #66947C2×C4semidirect
226. #66937C2×C4semidirect
227. #66936C2×C4semidirect
228. #66935C2×C4semidirect
230. #66931C2×C4semidirect
231. C4×D44C2×C4semidirect
232. #66925C2×C4semidirect
416. D4×C4⋊C4D11semidirect
569. C22×C4⋊C4C2×D11semidirect
578. #389C2×D11semidirect
610. #385C2×D11semidirect
612. #384C2×D11semidirect
629. #380C2×D11semidirect
636. C4×C4⋊C4C2×D11semidirect
745. C4×D4C4×D11semidirect
996. C11#34362semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
#130717782
#130717722
#130716972
#130716612
#130715672
#130715602
#130715482
#130715452
#130715412
#130715122
#130714092
#130714012
#130712732
#130712702
#130712242
#130712212
#130712092
#130712052
#130709982
C2×#106226002
D4×C11×C4⋊C42
#3436211