Finite Group Databasebeta

← #14916569

Subgroups — #14916569

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#13071776C212yesmaximal, complemented
3#13071774C212yesmaximal, complemented
4#13071693C212yesmaximal, complemented
5#13071667C212yesmaximal, complemented
6#13071566C211yesmaximal, characteristic, complemented
7#13071565C211yesmaximal, characteristic, complemented
8#13071542C211yesmaximal, characteristic, complemented
9#13071538C211yesmaximal, characteristic, complemented
10#13071538C211yesmaximal, characteristic, complemented
11C4⋊C4×D44C211yesmaximal, characteristic, complemented
12C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
13#13071412C212yesmaximal, complemented
14#13071408C212yesmaximal, complemented
15#13071278C212yesmaximal, complemented
16#13071272C212yesmaximal, complemented
17#13071226C211yesmaximal, characteristic, complemented
18#13071221C211yesmaximal, characteristic, complemented
19#13071209C211yesmaximal, characteristic, complemented
20#13071205C211yesmaximal, characteristic, complemented
21#13070995C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2352C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C2×#66979C2211yescharacteristic, complemented
36#10623078C4116yescomplemented
37C2×#66949C2211yescharacteristic
38C2×#66947C2211yescharacteristic
39C2×#66945C2211yescharacteristic, complemented
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic, complemented
43C2×#66937C2211yescharacteristic
44C2×#66936C2211yescharacteristic
45C2×#66935C2211yescharacteristic
46C2×C22⋊C4×D11C2212yes—
47C2×#66931C2211yescharacteristic
48C2×C4×D44C2212yes—
49C2×C4×D44C2211yescharacteristic
50C2×#66925C2211yescharacteristic
51C11×#388C2212yes—
52C11×#387C2212yescomplemented
53C11×#386C2212yes—
54C11×#382C2211yescharacteristic, complemented
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic, complemented
57C4×C11×C4⋊C4C2211yescharacteristic, complemented
58C4×C11×C22⋊C4C2212yescomplemented
59#10622834C2212yes—
60#10622826C2212yes—
61#10622826C2212yescomplemented
62#10622825C2211yescharacteristic
63#10622825C2211yescharacteristic, complemented
64#10622823C2212yescomplemented
65#10622602C2212yes—
66#10622601C2212yes—
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic, complemented
74#10622600C2211yescharacteristic, complemented
75#10622590C2211yescharacteristic, complemented
76#10622589C2211yescharacteristic, complemented
77C4⋊C4×Dic11C2212yescomplemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80#10622587C2212yescomplemented
81#10622585C2212yescomplemented
82#10622570C2212yes—
83#10622570C2212yes—
84#10622569C2212yes—
85#10622569C2212yes—
86#10622569C2212yescomplemented
87#10622568C2212yes—
88#10622564C2212yes—
89#10622564C2212yescomplemented
90#10622557C2212yes—
91#10622557C2212yes—
92#10622557C2212yescomplemented
93#10622556C2212yes—
94#10622555C2212yes—
95#10622553C2212yes—
96#10622553C2212yescomplemented
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2212yes—
99#10622548C2211yescharacteristic, complemented
100C4×C4⋊Dic11C2211yescharacteristic, complemented
101#10622546C2212yescomplemented
102C4×Dic11⋊C4C2212yescomplemented
103#10622541C2212yescomplemented
104#10622283C2212yes—
105#10622283C2212yes—
106#10622282C2212yes—
107#10622282C2212yescomplemented
108#10622281C2212yes—
109#10622281C2212yescomplemented
110#10622280C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113#10622279C2212yescomplemented
114#10622278C2212yes—
115#10622278C2212yes—
116D11×#95C2212yes—
117#10622268C2212yescomplemented
118#10622268C2212yescomplemented
119#10622267C2212yescomplemented
120#10622265C2212yescomplemented
121#10622265C2212yescomplemented
122#10622265C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C2×#4339—42no—
135C2×#4339—42no—
136C2×#4339C2×C418yescomplemented
137C22×D44C2311yescharacteristic
138C22×D44C2311yescharacteristic
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C4×D4×C11C2×C418yescomplemented
152C11×#117—42no—
153C2×C11×C4⋊C4—42no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174#66992C2×C418yescomplemented
175#66990C2×C418yescomplemented
176C4×C22⋊D11—44no—
177C4×C22⋊D11C2×C418yescomplemented
178C4×C22⋊D11C2×C418yescomplemented
179C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194#66979—42no—
195#66979—42no—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
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×Dic11C2311yescharacteristic
219#66949C2×C418yescomplemented
220#66947C2×C418yescomplemented
221#66945—42no—
222C4⋊C4×D11—42no—
223C4⋊C4×D11—42no—
224C4⋊C4×D11—42no—
225#66937C2×C418yes—
226#66936C2×C418yescomplemented
227#66935C2×C418yescomplemented
228C22⋊C4×D11—44no—
229#66931C2×C418yescomplemented
230C4×D44—44no—
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—41no—
267C2×D4×C11—41no—
268C2×D4×C11C22×C414yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C22×C414yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C2×C22⋊D11—22no—
288C2×C22⋊D11—22no—
289C2×C22⋊D11—41no—
290C2×C22⋊D11—41no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11—41no—
293C2×C22⋊D11—41no—
294C2×C22⋊D11—41no—
295C2×C22⋊D11C22×C414yes—
296C2×C22⋊D11C22×C414yes—
297C2×C22⋊D11C22×C414yes—
298C2×C22⋊D11C22×C414yes—
299C22×Dic11—41no—
300C22×Dic11—41no—
301C22×Dic11C22×C414yes—
302C22×Dic11C2412yes—
303C22×Dic11C2412yes—
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311#4339—416no—
312C2×D44—22no—
313C2×D44—22no—
314C2×D44—41no—
315C2×D44—41no—
316C2×D44C22×C414yes—
317C2×D44C22×C414yes—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
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—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⋊C4C22×C414yes—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4C22×C414yes—
356C11×C22⋊C4C22×C414yes—
357C42×C11—42no—
358C42×C11—42no—
359C42×C11C22×C414yes—
360C22⋊Dic11—42no—
361C22⋊Dic11—42no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11C22×C414yes—
365C22⋊Dic11C22×C414yes—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—24no—
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)⋊C4C22×C414yes—
376(C2×D11)⋊C4C22×C414yes—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C414yes—
379(C2×D11)⋊C4C22×C414yes—
380(C2×D11)⋊C4C22×C414yes—
381C4⋊Dic11—22no—
382C4⋊Dic11—22no—
383C4⋊Dic11—22no—
384C4⋊Dic11—22no—
385C4⋊Dic11—42no—
386C4⋊Dic11—42no—
387C4⋊Dic11C22×C414yes—
388Dic11⋊C4—42no—
389Dic11⋊C4—42no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4—42no—
393Dic11⋊C4C22×C414yes—
394Dic11⋊C4C22×C414yes—
395Dic11⋊C4C22×C414yes—
396Dic11⋊C4C22×C414yes—
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#2352D1111yescharacteristic, complemented
415D4×C4⋊C4—111no—
416D4×C4⋊C4—111no—
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×C11—21no—
438C23×C11—21no—
439C23×C11C23×C412yes—
440C23×C11C23×C412yes—
441C23×C11C2511yescharacteristic
442C22×D11—21no—
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—28no—
459C22×D11—44no—
460C22×D11—44no—
461C22×D11—44no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11C23×C412yes—
466C22×D11C23×C412yes—
467C22×D11C23×C412yes—
468C22×D11H(5,𝔽2)12yes—
469C22×D112−1+412yes—
470D4×C11—44no—
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×C11C23×C412yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C22⋊D11—28no—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C22⋊D11—44no—
505C2×Dic11—21no—
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—22no—
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—44no—
528C2×Dic11C23×C412yes—
529C2×Dic11C23×C412yes—
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C412yes—
532C2×Dic11C23×C412yes—
533D44—28no—
534D44—44no—
535C4×D11—28no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—84no—
541C4×D11—84no—
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×D4—112no—
560C2×C4×D4C2×D1111yescharacteristic
561C2×#117—111no—
562C2×#117—111no—
563C2×#117—111no—
564C2×#117—111no—
565C2×#117C2×D1111yescharacteristic
566C22×C4⋊C4—111no—
567C22×C4⋊C4—111no—
568C22×C4⋊C4—111no—
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#389—112no—
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#388C2×D1112yes—
591#387—112no—
592#387—112no—
593#387—112no—
594#387—112no—
595#387—112no—
596#387—112no—
597#387—112no—
598#387C2×D1112yescomplemented
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386C2×D1112yes—
607#385—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#384—111no—
612#384—111no—
613#382—111no—
614#382C2×D1111yescharacteristic, complemented
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—111no—
625#380—111no—
626#380—112no—
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⋊C4C2×D1112yescomplemented
643C2×#95—112no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—41no—
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—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—416no—
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#52014yes—
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—112no—
727C23×C4—442no—
728C23×C4—442no—
729C23×C4C22×D1111yescharacteristic
730C23×C4C22×D1111yescharacteristic
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—118no—
741C4×D4—118no—
742C4×D4—118no—
743C4×D4—444no—
744C4×D4—444no—
745C4×D4C4×D1118yescomplemented
746#117—42no—
747#117—118no—
748#117—442no—
749#117—442no—
750#117—442no—
751C2×C4⋊C4—42no—
752C2×C4⋊C4—111no—
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—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—442no—
769C2×C4⋊C4—442no—
770C2×C4⋊C4—442no—
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1111yescharacteristic
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1111yescharacteristic
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—444no—
799C2×C22⋊C4C22×D1112yes—
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×C42C22×D1112yes—
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#95C22×D1112yes—
830#95C22×D1112yes—
831#95C22×D1112yes—
832#95C22×D1112yes—
833#95C22×D1112yes—
834C2×C11—42no—
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—24no—
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—41no—
863C2×D4—41no—
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—222no—
873C2×D4—222no—
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—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—111no—
891C22×C4—111no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—114no—
896C22×C4—114no—
897C22×C4—114no—
898C22×C4—114no—
899C22×C4—114no—
900C22×C4—114no—
901C22×C4—112no—
902C22×C4—112no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—4416no—
914C22×C4—441no—
915C22×C4—441no—
916C22×C4—441no—
917C22×C4—441no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—441no—
926C22×C4—441no—
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—114no—
944C4⋊C4—114no—
945C4⋊C4—114no—
946C4⋊C4—114no—
947C4⋊C4—114no—
948C4⋊C4—222no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4C2×C4×D1114yes—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—114no—
964C22⋊C4—114no—
965C22⋊C4—114no—
966C22⋊C4—114no—
967C22⋊C4—114no—
968C22⋊C4—114no—
969C22⋊C4—114no—
970C22⋊C4—114no—
971C22⋊C4—224no—
972C22⋊C4—224no—
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—42no—
988C42—114no—
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—21no—
1008C23—21no—
1009C23—112no—
1010C23—112no—
1011C23—112no—
1012C23—112no—
1013C23—112no—
1014C23—228no—
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—221no—
1030C23—221no—
1031C23—444no—
1032C23—444no—
1033C23—444no—
1034C23—444no—
1035C23—444no—
1036C23—444no—
1037C23C22×C4×D1112yes—
1038C23C22×C4×D1112yes—
1039C23C24×D1111yescharacteristic
1040Q8—444no—
1041D4—44no—
1042D4—228no—
1043D4—228no—
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—112no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—112no—
1075C2×C4—112no—
1076C2×C4—221no—
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—228no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—222no—
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—444no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—884no—
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—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—114no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—222no—
1133C22—222no—
1134C22—222no—
1135C22—222no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—4416no—
1142C22—441no—
1143C22—441no—
1144C22—441no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22C23×C4×D1111yescharacteristic
1151C22C2×#6703711yescharacteristic
1152C22C2×#6704211yescharacteristic
1153C22#1062345311yescharacteristic
1154C22#1062345311yescharacteristic
1155C22D11×H(5,𝔽2)11yescharacteristic
1156C22D11×2−1+411yescharacteristic
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—42no—
1176C2—42no—
1177C2—224no—
1178C2—442no—
1179C2—442no—
1180C2C2×#1062307611yescharacteristic
1181C2D11×#52011yescharacteristic
1182C2#1308181711yescharacteristic
1183C2#1308290711yescharacteristic
1184C2#1308291211yescharacteristic
1185C2#1308293011yescharacteristic
1186C2#1308293511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2352C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2352D11
hypocenterC11#34362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13071776C2semidirect
3. #13071774C2semidirect
4. #13071693C2semidirect
5. #13071667C2semidirect
6. #13071566C2semidirect
7. #13071565C2semidirect
8. #13071542C2semidirect
9. #13071538C2semidirect
10. #13071538C2semidirect
11. C4⋊C4×D44C2semidirect
12. C4⋊C4×C22⋊D11C2semidirect
13. #13071412C2semidirect
14. #13071408C2semidirect
15. #13071278C2semidirect
16. #13071272C2semidirect
17. #13071226C2semidirect
18. #13071221C2semidirect
19. #13071209C2semidirect
20. #13071205C2semidirect
21. #13070995C2semidirect
22. D11×#380C2semidirect
23. C11×#2352C2semidirect
28. C22×C11×C4⋊C4C22semidirect
35. C2×#66979C22semidirect
36. #10623078C4semidirect
39. C2×#66945C22semidirect
42. C2×C4⋊C4×D11C22semidirect
52. C11×#387C22semidirect
54. C11×#382C22semidirect
56. C11×#380C22semidirect
57. C4×C11×C4⋊C4C22semidirect
58. C4×C11×C22⋊C4C22semidirect
61. #10622826C22semidirect
63. #10622825C22semidirect
64. #10622823C22semidirect
73. #10622600C22semidirect
74. #10622600C22semidirect
75. #10622590C22semidirect
76. #10622589C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. #10622587C22semidirect
81. #10622585C22semidirect
86. #10622569C22semidirect
89. #10622564C22semidirect
92. #10622557C22semidirect
96. #10622553C22semidirect
99. #10622548C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. #10622546C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. #10622541C22semidirect
107. #10622282C22semidirect
109. #10622281C22semidirect
113. #10622279C22semidirect
117. #10622268C22semidirect
118. #10622268C22semidirect
119. #10622267C22semidirect
120. #10622265C22semidirect
121. #10622265C22semidirect
122. #10622265C22semidirect
123. #10622259C22semidirect
136. C2×#4339C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
151. C4×D4×C11C2×C4semidirect
174. #66992C2×C4semidirect
175. #66990C2×C4semidirect
177. C4×C22⋊D11C2×C4semidirect
178. C4×C22⋊D11C2×C4semidirect
219. #66949C2×C4semidirect
220. #66947C2×C4semidirect
226. #66936C2×C4semidirect
227. #66935C2×C4semidirect
229. #66931C2×C4semidirect
231. C4×D44C2×C4semidirect
232. #66925C2×C4semidirect
414. #2352D11semidirect
569. C22×C4⋊C4C2×D11semidirect
598. #387C2×D11semidirect
614. #382C2×D11semidirect
629. #380C2×D11semidirect
636. C4×C4⋊C4C2×D11semidirect
642. C4×C22⋊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
#130717762
#130717742
#130716932
#130716672
#130715662
#130715652
#130715422
#130715382
C4⋊C4×D442
C4⋊C4×C22⋊D112
#130714122
#130714082
#130712782
#130712722
#130712262
#130712212
#130712092
#130712052
#130709952
D11×#3802
C11×#23522
#3436211