Finite Group Databasebeta

← #14917767

Subgroups — #14917767

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
1#13071773C212yesmaximal, complemented
2#13071757C212yesmaximal, complemented
3#13071691C211yesmaximal, characteristic, complemented
4#13071691C211yesmaximal, characteristic, complemented
5#13071681C211yesmaximal, characteristic, complemented
6#13071681C211yesmaximal, characteristic, complemented
7#13071668C212yesmaximal, complemented
8#13071600C212yesmaximal, complemented
9#13071457C211yesmaximal, characteristic, complemented
10#13071446C211yesmaximal, characteristic, complemented
11D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
13#13071383C212yesmaximal, complemented
14#13071342C211yesmaximal, characteristic, complemented
15#13071329C211yesmaximal, characteristic, complemented
16#13071321C212yesmaximal, complemented
17#13071277C212yesmaximal, complemented
18#13071277C212yesmaximal, complemented
19#13071225C211yesmaximal, characteristic, complemented
20#127×Dic11C211yesmaximal, characteristic, complemented
21#124×Dic11C211yesmaximal, characteristic, complemented
22#13071114C211yesmaximal, characteristic, complemented
23C2×C11×#535C211yesmaximal, characteristic
24C22×C11×#41C2211yescharacteristic
25C23×D4×C11C2211yescharacteristic
26C11×#535C4116yescomplemented
27C2×C11×#127C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C2×C11×#124C2211yescharacteristic
30C2×C11×#124C2211yescharacteristic
31C2×C11×#121C2212yes—
32C2×C11×#121C2212yes—
33C2×C11×#120C2212yes—
34C2×C11×#120C2212yes—
35C2×C11×#117C2211yescharacteristic
36C22×C22⋊Dic11C2212yes—
37C22×C22⋊Dic11C2212yes—
38C2×Q8×Dic11C2211yescharacteristic, complemented
39C2×Q8×Dic11C2211yescharacteristic, complemented
40C2×D4×Dic11C2211yescharacteristic
41C2×D4×Dic11C2211yescharacteristic
42C2×D4×Dic11C2211yescharacteristic
43C2×D4×Dic11C2211yescharacteristic
44C2×D4×Dic11C2212yescomplemented
45C2×D4×Dic11C2212yescomplemented
46C2×D4×Dic11C2211yescharacteristic, complemented
47C2×D4×Dic11C2211yescharacteristic, complemented
48C2×D4×Dic11C2212yescomplemented
49C2×D4×Dic11C2212yescomplemented
50#10622860C2212yes—
51#10622860C2212yes—
52#10622843C2211yescharacteristic, complemented
53#10622843C2211yescharacteristic, complemented
54#10622834C2211yescharacteristic
55#10622834C2211yescharacteristic
56#10622834C2211yescharacteristic
57#10622834C2211yescharacteristic
58#10622834C2212yes—
59#10622834C2212yes—
60#10622834C2212yescomplemented
61#10622834C2212yescomplemented
62#10622834C2211yescharacteristic, complemented
63#10622834C2211yescharacteristic, complemented
64#10622834C2212yescomplemented
65#10622834C2212yescomplemented
66#10622833C2212yes—
67#10622833C2212yes—
68#10622833C2212yes—
69#10622833C2212yes—
70#10622833C2212yes—
71#10622833C2212yes—
72#10622833C2212yescomplemented
73#10622833C2212yescomplemented
74#10622833C2212yescomplemented
75#10622833C2212yescomplemented
76#10622833C2212yescomplemented
77#10622833C2212yescomplemented
78#10622833C2212yescomplemented
79#10622833C2212yescomplemented
80#10622825C2211yescharacteristic
81#10622825C2211yescharacteristic
82#10622825C2212yescomplemented
83#10622824C2212yescomplemented
84C4×C22⋊Dic11C2211yescharacteristic
85C4×C22⋊Dic11C2211yescharacteristic
86C4×C22⋊Dic11C2212yescomplemented
87C2×C11⋊#95C2212yescomplemented
88#10622594C2211yescharacteristic, complemented
89#10622594C2211yescharacteristic, complemented
90#10622594C2211yescharacteristic, complemented
91#10622594C2211yescharacteristic, complemented
92#10622594C2212yescomplemented
93#10622594C2212yescomplemented
94#10622564C2211yescharacteristic
95#10622564C2211yescharacteristic
96#10622564C2211yescharacteristic
97#10622564C2211yescharacteristic
98#10622564C2212yes—
99#10622564C2212yes—
100#10622564C2212yescomplemented
101#10622564C2212yescomplemented
102#10622564C2212yescomplemented
103#10622564C2212yescomplemented
104#10622564C2212yescomplemented
105#10622564C2212yescomplemented
106#10622564C2212yescomplemented
107#10622564C2212yescomplemented
108#10622563C2212yescomplemented
109#10622563C2212yescomplemented
110#10622563C2212yescomplemented
111#10622563C2212yescomplemented
112C22⋊C4×Dic11C2212yescomplemented
113C22⋊C4×Dic11C2212yescomplemented
114C22⋊C4×Dic11C2212yescomplemented
115C22⋊C4×Dic11C2212yescomplemented
116#10622549C2211yescharacteristic, complemented
117#10622548C2211yescharacteristic, complemented
118C4×C4⋊Dic11C2211yescharacteristic, complemented
119C4×C4⋊Dic11C2211yescharacteristic, complemented
120C4×C4⋊Dic11C2211yescharacteristic, complemented
121C4×C4⋊Dic11C2211yescharacteristic, complemented
122#10622545C2211yescharacteristic, complemented
123C42×Dic11C2211yescharacteristic, complemented
124C25×C11C2312yes—
125C2×C11×#41—42no—
126C2×C11×#41—42no—
127C2×C11×#41C2×C418yescomplemented
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11—42no—
130C22×D4×C11—42no—
131C22×D4×C11C2×C418yescomplemented
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C22×D4×C11C2312yes—
136C22×D4×C11C2312yes—
137C22×D4×C11C2312yes—
138C22×D4×C11C2312yes—
139C22×D4×C11C2312yes—
140C22×D4×C11C2312yes—
141C23×C4×C11C2311yescharacteristic
142C23×C4×C11C2312yes—
143C23×Dic11C2312yes—
144C23×Dic11C2312yes—
145C23×Dic11C2312yes—
146C23×Dic11C2312yes—
147C23×Dic11C2312yes—
148C23×Dic11C2312yes—
149C11×#127C2×C418yescomplemented
150C11×#127C2×C418yescomplemented
151C11×#124C2×C418yescomplemented
152C11×#124C2×C418yescomplemented
153C11×#121C2×C4116yescomplemented
154C11×#121C2×C4116yescomplemented
155C11×#120C2×C4116yescomplemented
156C11×#120C2×C4116yescomplemented
157C11×#117C2×C418yescomplemented
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11—44no—
169C2×C22⋊Dic11—44no—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2312yes—
193C2×C22⋊Dic11C2312yes—
194Q8×Dic11—42no—
195Q8×Dic11—42no—
196D4×Dic11—42no—
197D4×Dic11—42no—
198D4×Dic11—42no—
199D4×Dic11—42no—
200D4×Dic11—42no—
201D4×Dic11—42no—
202D4×Dic11—44no—
203D4×Dic11—44no—
204D4×Dic11—44no—
205D4×Dic11—44no—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252#34438—111nomaximal, Sylow
253C24×C11—42no—
254C24×C11—42no—
255C24×C11—42no—
256C24×C11—42no—
257C24×C11—42no—
258C24×C11—42no—
259C24×C11C22×C418yes—
260C24×C11C2411yescharacteristic
261C24×C11C2412yes—
262C24×C11C2412yes—
263C24×C11C2412yes—
264C11×#41—416no—
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11C22×C414yes—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—416no—
275C2×D4×C11—42no—
276C2×D4×C11—42no—
277C2×D4×C11—42no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C2×D4×C11—42no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C2×D4×C11C22×C414yes—
288C2×D4×C11C22×C414yes—
289C2×D4×C11C22×C414yes—
290C2×D4×C11C22×C418yes—
291C2×D4×C11C22×C418yes—
292C2×D4×C11C22×C418yes—
293C2×D4×C11C22×C418yes—
294C2×D4×C11C22×C418yes—
295C2×D4×C11C22×C418yes—
296C22×C4×C11—22no—
297C22×C4×C11—22no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11C22×C414yes—
301C22×C4×C11C22×C418yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2412yes—
308C22×C4×C11C2411yescharacteristic
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—24no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11—42no—
317C22×Dic11—42no—
318C22×Dic11—42no—
319C22×Dic11—42no—
320C22×Dic11—42no—
321C22×Dic11—42no—
322C22×Dic11—42no—
323C22×Dic11—42no—
324C22×Dic11—42no—
325C22×Dic11—42no—
326C22×Dic11—42no—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2412yes—
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2412yes—
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2412yes—
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C11×C4⋊C4C22×C414yes—
340C11×C4⋊C4C22×C414yes—
341C11×C22⋊C4C22×C414yes—
342C11×C22⋊C4C22×C414yes—
343C11×C22⋊C4C22×C418yes—
344C11×C22⋊C4C22×C418yes—
345C11×C22⋊C4C22×C418yes—
346C11×C22⋊C4C22×C418yes—
347C42×C11C22×C414yes—
348C42×C11C22×C414yes—
349C22⋊Dic11—24no—
350C22⋊Dic11—24no—
351C22⋊Dic11—24no—
352C22⋊Dic11—22no—
353C22⋊Dic11—22no—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—42no—
359C22⋊Dic11—42no—
360C22⋊Dic11—42no—
361C22⋊Dic11—42no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11—42no—
365C22⋊Dic11—42no—
366C22⋊Dic11—42no—
367C22⋊Dic11—42no—
368C22⋊Dic11—42no—
369C22⋊Dic11—42no—
370C22⋊Dic11—42no—
371C22⋊Dic11—41no—
372C22⋊Dic11—41no—
373C4⋊Dic11—22no—
374C4⋊Dic11—22no—
375C4⋊Dic11—22no—
376C4⋊Dic11—22no—
377C4⋊Dic11—22no—
378C4⋊Dic11—22no—
379C4⋊Dic11—41no—
380C4⋊Dic11—41no—
381C4⋊Dic11—42no—
382C4⋊Dic11—42no—
383C4⋊Dic11—42no—
384C4⋊Dic11—42no—
385C4×Dic11—22no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—41no—
392C4×Dic11—41no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11—42no—
396C4×Dic11—42no—
397C2×#535D1111yescharacteristic
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×#127—111no—
418C4×#124—111no—
419#2298—111no—
420C23×C11—21no—
421C23×C11—21no—
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×C11—22no—
433C23×C11—22no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—48no—
445C23×C11—48no—
446C23×C11—48no—
447C23×C11—84no—
448C23×C11—84no—
449C23×C11—84no—
450C23×C11—84no—
451C23×C11C23×C412yes—
452C23×C11C23×C414yes—
453C23×C11C23×C414yes—
454C23×C11C23×C414yes—
455C23×C11C2511yescharacteristic
456Q8×C11—28no—
457D4×C11—28no—
458D4×C11—28no—
459D4×C11—28no—
460D4×C11—48no—
461D4×C11—48no—
462D4×C11—48no—
463D4×C11—48no—
464D4×C11—48no—
465D4×C11—48no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
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—28no—
479C2×C4×C11—48no—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C414yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11H(5,𝔽2)12yes—
488C2×C4×C11H(5,𝔽2)12yes—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—84no—
524C2×Dic11—84no—
525C2×Dic11—84no—
526C2×Dic11—84no—
527C2×Dic11—84no—
528C2×Dic11—84no—
529C2×Dic11H(5,𝔽2)12yes—
530C2×Dic11H(5,𝔽2)12yes—
531C22×#41C2×D1111yescharacteristic
532C23×D4C2×D1111yescharacteristic
533#535Dic11116yescomplemented
534C2×#127C2×D1111yescharacteristic
535C2×#127C2×D1111yescharacteristic
536C2×#124C2×D1111yescharacteristic
537C2×#124C2×D1111yescharacteristic
538C2×#121C2×D1112yes—
539C2×#121C2×D1112yes—
540C2×#120C2×D1112yes—
541C2×#120C2×D1112yes—
542C2×C4×Q8—111no—
543C2×C4×Q8—111no—
544C2×C4×D4—112no—
545C2×C4×D4—111no—
546C2×C4×D4—111no—
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—112no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4—111no—
553C2×C4×D4—111no—
554C2×#117C2×D1111yescharacteristic
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391—111no—
559#390—112no—
560#390—111no—
561#390—111no—
562#390—112no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390—111no—
567#390—111no—
568#390—111no—
569#390—112no—
570#390—111no—
571#388—112no—
572#388—112no—
573#388—111no—
574#388—111no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
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#384—111no—
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—111no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4—112no—
628#376—111no—
629C2×#95—112no—
630C43—111no—
631C22×C11—22no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—24no—
637C22×C11—24no—
638C22×C11—24no—
639C22×C11—24no—
640C22×C11—24no—
641C22×C11—22no—
642C22×C11—22no—
643C22×C11—41no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—41no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—41no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—816no—
660C22×C11C24×C411yescharacteristic
661C22×C11C2×H(5,𝔽2)11yescharacteristic
662C22×C11C2×H(5,𝔽2)11yescharacteristic
663C22×C11C2×H(5,𝔽2)11yescharacteristic
664C22×C11C2×H(5,𝔽2)11yescharacteristic
665C22×C11#58511yescharacteristic
666C22×C11#58511yescharacteristic
667C4×C11—22no—
668C4×C11—24no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—22no—
672C4×C11—22no—
673C4×C11#51814yes—
674Dic11—22no—
675Dic11—22no—
676Dic11—42no—
677Dic11—41no—
678Dic11—42no—
679Dic11—41no—
680Dic11—42no—
681Dic11—41no—
682Dic11—41no—
683Dic11—42no—
684Dic11—41no—
685Dic11—41no—
686C25C22×D1112yes—
687C2×#41—42no—
688C2×#41—42no—
689C2×#41C2×Dic1118yescomplemented
690C22×Q8C22×D1111yescharacteristic
691C22×D4—42no—
692C22×D4—42no—
693C22×D4C2×Dic1118yescomplemented
694C22×D4C22×D1111yescharacteristic
695C22×D4C22×D1111yescharacteristic
696C22×D4C22×D1111yescharacteristic
697C22×D4C22×D1112yes—
698C22×D4C22×D1112yes—
699C22×D4C22×D1112yes—
700C22×D4C22×D1112yes—
701C22×D4C22×D1112yes—
702C22×D4C22×D1112yes—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4C22×D1111yescharacteristic
710C23×C4C22×D1112yes—
711#127C2×Dic1118yescomplemented
712#127C2×Dic1118yescomplemented
713#124C2×Dic1118yescomplemented
714#124C2×Dic1118yescomplemented
715#121C2×Dic11116yescomplemented
716#121C2×Dic11116yescomplemented
717#120C2×Dic11116yescomplemented
718#120C2×Dic11116yescomplemented
719C4×Q8—442no—
720C4×Q8—442no—
721C4×D4—444no—
722C4×D4—442no—
723C4×D4—442no—
724C4×D4—442no—
725C4×D4—442no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—444no—
729C4×D4—444no—
730C4×D4—444no—
731#117C2×Dic1118yescomplemented
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4C22×D1111yescharacteristic
745C2×C4⋊C4C22×D1111yescharacteristic
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—444no—
771C2×C22⋊C4—444no—
772C2×C22⋊C4C22×D1111yescharacteristic
773C2×C22⋊C4C22×D1111yescharacteristic
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—111no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—111no—
789C2×C42—111no—
790C2×C42C22×D1111yescharacteristic
791C2×C42C22×D1111yescharacteristic
792#95—111no—
793#95—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×C11—44no—
817C2×C11—42no—
818C2×C11C2×#51811yescharacteristic
819C2×C11C4×H(5,𝔽2)11yescharacteristic
820C2×C11C4×H(5,𝔽2)11yescharacteristic
821C2×C11#354311yescharacteristic
822C2×C11#354611yescharacteristic
823C2×C11#355811yescharacteristic
824C2×C11#356211yescharacteristic
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24C22×Dic1118yes—
832C24C23×D1111yescharacteristic
833C24C23×D1112yes—
834C24C23×D1112yes—
835C24C23×D1112yes—
836#41—416no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8C22×Dic1114yes—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—416no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4C22×Dic1114yes—
860C2×D4C22×Dic1114yes—
861C2×D4C22×Dic1114yes—
862C2×D4C22×Dic1118yes—
863C2×D4C22×Dic1118yes—
864C2×D4C22×Dic1118yes—
865C2×D4C22×Dic1118yes—
866C2×D4C22×Dic1118yes—
867C2×D4C22×Dic1118yes—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—111no—
873C22×C4—111no—
874C22×C4—111no—
875C22×C4—111no—
876C22×C4—112no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—112no—
880C22×C4—111no—
881C22×C4—112no—
882C22×C4—111no—
883C22×C4—112no—
884C22×C4—224no—
885C22×C4—224no—
886C22×C4—224no—
887C22×C4—442no—
888C22×C4—442no—
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×C4C22×Dic1114yes—
903C22×C4C22×Dic1118yes—
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1112yes—
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—222no—
912C4⋊C4—222no—
913C4⋊C4—222no—
914C4⋊C4—222no—
915C4⋊C4—222no—
916C4⋊C4—222no—
917C4⋊C4—442no—
918C4⋊C4—442no—
919C4⋊C4—442no—
920C4⋊C4—442no—
921C4⋊C4—441no—
922C4⋊C4—441no—
923C4⋊C4C22×Dic1114yes—
924C4⋊C4C22×Dic1114yes—
925C22⋊C4—222no—
926C22⋊C4—222no—
927C22⋊C4—224no—
928C22⋊C4—224no—
929C22⋊C4—224no—
930C22⋊C4—442no—
931C22⋊C4—442no—
932C22⋊C4—442no—
933C22⋊C4—442no—
934C22⋊C4—442no—
935C22⋊C4—442no—
936C22⋊C4—442no—
937C22⋊C4—442no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—441no—
946C22⋊C4—441no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C22⋊C4C22×Dic1114yes—
950C22⋊C4C22×Dic1114yes—
951C22⋊C4C22×Dic1118yes—
952C22⋊C4C22×Dic1118yes—
953C22⋊C4C22×Dic1118yes—
954C22⋊C4C22×Dic1118yes—
955C42—222no—
956C42—222no—
957C42—222no—
958C42—222no—
959C42—222no—
960C42—222no—
961C42—442no—
962C42—442no—
963C42—442no—
964C42—442no—
965C42—441no—
966C42—441no—
967C42C22×Dic1114yes—
968C42C22×Dic1114yes—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—48no—
995C23—48no—
996C23—48no—
997C23—84no—
998C23—84no—
999C23—84no—
1000C23—84no—
1001C23C23×Dic1112yes—
1002C23C23×Dic1114yes—
1003C23C23×Dic1114yes—
1004C23C23×Dic1114yes—
1005C23C24×D1111yescharacteristic
1006Q8—28no—
1007D4—28no—
1008D4—28no—
1009D4—28no—
1010D4—48no—
1011D4—48no—
1012D4—48no—
1013D4—48no—
1014D4—48no—
1015D4—48no—
1016C2×C4—22no—
1017C2×C4—22no—
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—21no—
1027C2×C4—21no—
1028C2×C4—28no—
1029C2×C4—48no—
1030C2×C4—112no—
1031C2×C4—112no—
1032C2×C4—221no—
1033C2×C4—221no—
1034C2×C4—221no—
1035C2×C4—221no—
1036C2×C4—221no—
1037C2×C4—221no—
1038C2×C4—221no—
1039C2×C4—221no—
1040C2×C4—221no—
1041C2×C4—221no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—221no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
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—221no—
1062C2×C4—222no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—884no—
1067C2×C4—884no—
1068C2×C4—884no—
1069C2×C4—884no—
1070C2×C4—884no—
1071C2×C4—884no—
1072C2×C4#6703712yes—
1073C2×C4#6703712yes—
1074C2×C4C23×Dic1112yes—
1075C2×C4C23×Dic1112yes—
1076C2×C4C23×Dic1112yes—
1077C2×C4C23×Dic1112yes—
1078C2×C4C23×Dic1114yes—
1079C2×C4C23×Dic1112yes—
1080C2×C4C23×Dic1112yes—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—22no—
1092C22—22no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—41no—
1097C22—41no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—41no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—41no—
1108C22—42no—
1109C22—816no—
1110C22C2×#6703711yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22D11×H(5,𝔽2)11yescharacteristic
1113C22D11×H(5,𝔽2)11yescharacteristic
1114C22#1062345511yescharacteristic
1115C22#1062345511yescharacteristic
1116C22C24×Dic1111yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—222no—
1124C4—222no—
1125C4—441no—
1126C4—442no—
1127C4—442no—
1128C4—441no—
1129C4—441no—
1130C4—441no—
1131C4—442no—
1132C4—441no—
1133C4—441no—
1134C4—442no—
1135C4#1062332914yes—
1136C2—42no—
1137C2—44no—
1138C2—44no—
1139C2—44no—
1140C2C2×#1062332911yescharacteristic
1141C2H(5,𝔽2)×Dic1111yescharacteristic
1142C2H(5,𝔽2)×Dic1111yescharacteristic
1143C2#1308294211yescharacteristic
1144C2#1308297711yescharacteristic
1145C2#1308313411yescharacteristic
1146C2#1308320011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#535C2
socle, cosocleC23×C11C25
hypercenterC2×#535D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. #13071773C2semidirect
2. #13071757C2semidirect
3. #13071691C2semidirect
4. #13071691C2semidirect
5. #13071681C2semidirect
6. #13071681C2semidirect
7. #13071668C2semidirect
8. #13071600C2semidirect
9. #13071457C2semidirect
10. #13071446C2semidirect
11. D4×C22⋊Dic11C2semidirect
12. D4×C22⋊Dic11C2semidirect
13. #13071383C2semidirect
14. #13071342C2semidirect
15. #13071329C2semidirect
16. #13071321C2semidirect
17. #13071277C2semidirect
18. #13071277C2semidirect
19. #13071225C2semidirect
20. #127×Dic11C2semidirect
21. #124×Dic11C2semidirect
22. #13071114C2semidirect
26. C11×#535C4semidirect
38. C2×Q8×Dic11C22semidirect
39. C2×Q8×Dic11C22semidirect
44. C2×D4×Dic11C22semidirect
45. C2×D4×Dic11C22semidirect
46. C2×D4×Dic11C22semidirect
47. C2×D4×Dic11C22semidirect
48. C2×D4×Dic11C22semidirect
49. C2×D4×Dic11C22semidirect
52. #10622843C22semidirect
53. #10622843C22semidirect
60. #10622834C22semidirect
61. #10622834C22semidirect
62. #10622834C22semidirect
63. #10622834C22semidirect
64. #10622834C22semidirect
65. #10622834C22semidirect
72. #10622833C22semidirect
73. #10622833C22semidirect
74. #10622833C22semidirect
75. #10622833C22semidirect
76. #10622833C22semidirect
77. #10622833C22semidirect
78. #10622833C22semidirect
79. #10622833C22semidirect
82. #10622825C22semidirect
83. #10622824C22semidirect
86. C4×C22⋊Dic11C22semidirect
87. C2×C11⋊#95C22semidirect
88. #10622594C22semidirect
89. #10622594C22semidirect
90. #10622594C22semidirect
91. #10622594C22semidirect
92. #10622594C22semidirect
93. #10622594C22semidirect
100. #10622564C22semidirect
101. #10622564C22semidirect
102. #10622564C22semidirect
103. #10622564C22semidirect
104. #10622564C22semidirect
105. #10622564C22semidirect
106. #10622564C22semidirect
107. #10622564C22semidirect
108. #10622563C22semidirect
109. #10622563C22semidirect
110. #10622563C22semidirect
111. #10622563C22semidirect
112. C22⋊C4×Dic11C22semidirect
113. C22⋊C4×Dic11C22semidirect
114. C22⋊C4×Dic11C22semidirect
115. C22⋊C4×Dic11C22semidirect
116. #10622549C22semidirect
117. #10622548C22semidirect
118. C4×C4⋊Dic11C22semidirect
119. C4×C4⋊Dic11C22semidirect
120. C4×C4⋊Dic11C22semidirect
121. C4×C4⋊Dic11C22semidirect
122. #10622545C22semidirect
123. C42×Dic11C22semidirect
127. C2×C11×#41C2×C4semidirect
131. C22×D4×C11C2×C4semidirect
149. C11×#127C2×C4semidirect
150. C11×#127C2×C4semidirect
151. C11×#124C2×C4semidirect
152. C11×#124C2×C4semidirect
153. C11×#121C2×C4semidirect
154. C11×#121C2×C4semidirect
155. C11×#120C2×C4semidirect
156. C11×#120C2×C4semidirect
157. C11×#117C2×C4semidirect
533. #535Dic11semidirect
689. C2×#41C2×Dic11semidirect
693. C22×D4C2×Dic11semidirect
711. #127C2×Dic11semidirect
712. #127C2×Dic11semidirect
713. #124C2×Dic11semidirect
714. #124C2×Dic11semidirect
715. #121C2×Dic11semidirect
716. #121C2×Dic11semidirect
717. #120C2×Dic11semidirect
718. #120C2×Dic11semidirect
731. #117C2×Dic11semidirect
969. C11#34438semidirect

Maximal subgroups

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

subgroupindex
#130717732
#130717572
#130716912
#130716812
#130716682
#130716002
#130714572
#130714462
D4×C22⋊Dic112
#130713832
#130713422
#130713292
#130713212
#130712772
#130712252
#127×Dic112
#124×Dic112
#130711142
C2×C11×#5352
#3443811