Finite Group Databasebeta

← #14917759

Subgroups — #14917759

Order 2816.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623336C211yesmaximal, characteristic
2#13071768C212yesmaximal, complemented
3#13071755C212yesmaximal, complemented
4#13071686C211yesmaximal, characteristic, complemented
5#13071686C211yesmaximal, characteristic, complemented
6#13071678C211yesmaximal, characteristic, complemented
7#13071678C211yesmaximal, characteristic, complemented
8#13071665C212yesmaximal, complemented
9#13071595C212yesmaximal, complemented
10#13071456C211yesmaximal, characteristic, complemented
11#13071444C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
13#13071377C212yesmaximal, complemented
14#13071340C211yesmaximal, characteristic, complemented
15#13071328C211yesmaximal, characteristic, complemented
16#13071318C212yesmaximal, complemented
17#13071274C212yesmaximal, complemented
18#13071271C212yesmaximal, complemented
19#13071223C211yesmaximal, characteristic, complemented
20#13071180C211yesmaximal, characteristic, complemented
21C4×#66989C211yesmaximal, characteristic, complemented
22#13071112C211yesmaximal, characteristic, complemented
23D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C2×#67006C2212yes—
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2212yes—
32#10623336C4116yescomplemented
33C2×#66993C2211yescharacteristic
34C2×#66993C2211yescharacteristic
35C2×#66991C2212yes—
36C2×#66991C2212yes—
37C2×#66989C2211yescharacteristic
38C2×#66989C2211yescharacteristic
39C2×D4×Dic11C2211yescharacteristic
40C2×D4×Dic11C2211yescharacteristic
41C2×C4×C22⋊D11C2212yescomplemented
42C2×C4×C22⋊D11C2212yescomplemented
43C2×#66979C2211yescharacteristic
44C2×#66946C2211yescharacteristic, complemented
45C2×#66946C2211yescharacteristic, complemented
46C2×(C22⋊D11)⋊C4C2212yescomplemented
47C2×(C22⋊D11)⋊C4C2212yescomplemented
48C2×C4×Dic22C2211yescharacteristic, complemented
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#386C2212yes—
53C11×#386C2212yes—
54C11×#380C2211yescharacteristic
55C11×#379C2212yes—
56C4×C11×C22⋊C4C2211yescharacteristic
57#10622860C2212yes—
58#10622834C2211yescharacteristic
59#10622834C2211yescharacteristic
60#10622833C2212yes—
61#10622833C2212yes—
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic
65#10622823C2212yescomplemented
66#10622823C2212yescomplemented
67C4×C22⋊Dic11C2211yescharacteristic
68C4×C22⋊Dic11C2212yescomplemented
69C4×C22⋊Dic11C2212yescomplemented
70#10622590C2211yescharacteristic, complemented
71#10622589C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2211yescharacteristic, complemented
73C4⋊C4×Dic11C2211yescharacteristic, complemented
74#10622587C2211yescharacteristic, complemented
75#10622587C2211yescharacteristic, complemented
76#10622571C2212yescomplemented
77#10622571C2212yescomplemented
78#10622570C2212yes—
79#10622570C2212yes—
80#10622570C2212yescomplemented
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622570C2212yescomplemented
84#10622569C2212yes—
85#10622569C2212yes—
86#10622569C2212yescomplemented
87#10622569C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622559C2212yescomplemented
91#10622559C2212yescomplemented
92#10622558C2211yescharacteristic
93#10622558C2211yescharacteristic
94#10622558C2212yes—
95#10622558C2212yescomplemented
96#10622558C2212yescomplemented
97#10622558C2212yescomplemented
98#10622558C2212yescomplemented
99#10622557C2211yescharacteristic
100#10622557C2211yescharacteristic
101#10622557C2212yes—
102#10622557C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105#10622557C2212yescomplemented
106C22⋊C4×Dic11C2212yescomplemented
107C22⋊C4×Dic11C2212yescomplemented
108#10622552C2211yescharacteristic, complemented
109#10622552C2211yescharacteristic, complemented
110#10622545C2211yescharacteristic, complemented
111C4×Dic11⋊C4C2211yescharacteristic, complemented
112C4×Dic11⋊C4C2211yescharacteristic, complemented
113C42×Dic11C2211yescharacteristic, complemented
114#10622280C2212yescomplemented
115#10622279C2212yescomplemented
116#10622277C2212yescomplemented
117D11×#95C2212yescomplemented
118#10622267C2211yescharacteristic, complemented
119#10622267C2211yescharacteristic, complemented
120#10622267C2212yescomplemented
121#10622266C2211yescharacteristic, complemented
122#10622266C2211yescharacteristic, complemented
123#10622266C2212yescomplemented
124C25×C11C2312yes—
125C22×D4×C11—42no—
126C22×D4×C11—42no—
127C22×D4×C11C2×C418yescomplemented
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C23×Dic11C2312yes—
140C23×Dic11C2312yes—
141C2×#4339—42no—
142C2×#4339—42no—
143C2×#4339C2×C418yescomplemented
144C22×D44C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×Dic22C2311yescharacteristic
149C4×D4×C11—42no—
150C4×D4×C11—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4—44no—
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165#67006C2×C4116yescomplemented
166#67006C2×C4116yescomplemented
167C2×C22⋊Dic11—44no—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183#66993C2×C418yescomplemented
184#66993C2×C418yescomplemented
185#66991C2×C4116yescomplemented
186#66991C2×C4116yescomplemented
187#66989C2×C418yescomplemented
188#66989C2×C418yescomplemented
189D4×Dic11—42no—
190D4×Dic11—42no—
191C4×C22⋊D11—44no—
192C4×C22⋊D11—44no—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199#66979C2×C418yescomplemented
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224#66946—42no—
225#66946—42no—
226(C22⋊D11)⋊C4—44no—
227(C22⋊D11)⋊C4—44no—
228C4×Dic22—42no—
229C4×Dic22—42no—
230C11×#95C2312yes—
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
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—
263C23×D11C2412yes—
264C2×D4×C11—22no—
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11—416no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C2×D4×C11C22×C414yes—
272C2×D4×C11C22×C414yes—
273C2×D4×C11C22×C418yes—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—24no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C22×C414yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11C22×C418yes—
302C2×C22⋊D11C22×C418yes—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C418yes—
306C22×Dic11—24no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11—42no—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323#4339—416no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44C22×C414yes—
327C2×C4×D11—24no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11C22×C418yes—
336C2×Dic22—22no—
337C2×Dic22—22no—
338C2×Dic22C22×C414yes—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—41no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—42no—
350C42×C11—22no—
351C42×C11—22no—
352C22⋊Dic11—24no—
353C22⋊Dic11—22no—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—42no—
359C22⋊Dic11—42no—
360C22⋊Dic11—41no—
361C22⋊Dic11C22×C414yes—
362C22⋊Dic11C22×C414yes—
363C22⋊Dic11C22×C418yes—
364C22⋊Dic11C22×C418yes—
365C22⋊Dic11C22×C418yes—
366C22⋊Dic11C22×C418yes—
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—
373C4⋊Dic11—22no—
374C4⋊Dic11—22no—
375C4⋊Dic11C22×C414yes—
376C4⋊Dic11C22×C414yes—
377Dic11⋊C4—22no—
378Dic11⋊C4—22no—
379Dic11⋊C4—42no—
380Dic11⋊C4—42no—
381Dic11⋊C4—42no—
382Dic11⋊C4—42no—
383Dic11⋊C4—41no—
384Dic11⋊C4—41no—
385C4×Dic11—22no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—42no—
390C4×Dic11—42no—
391C4×Dic11—41no—
392C4×Dic11—41no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11C22×C414yes—
396C4×Dic11C22×C414yes—
397C2×#535—111no—
398#2377—112no—
399#2375—112no—
400#2367—111no—
401#2367—111no—
402#2366—111no—
403#2366—111no—
404#2364—112no—
405#2358—112no—
406#2341—111no—
407#2339—111no—
408D4×C22⋊C4—111no—
409D4×C22⋊C4D1111yescharacteristic, complemented
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—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—21no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—22no—
433C23×C11—21no—
434C23×C11—22no—
435C23×C11—21no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—48no—
439C23×C11—48no—
440C23×C11—48no—
441C23×C11—84no—
442C23×C11—84no—
443C23×C11—84no—
444C23×C11—84no—
445C23×C11C23×C412yes—
446C23×C11C23×C414yes—
447C23×C11C23×C414yes—
448C23×C11C2511yescharacteristic
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11C23×C414yes—
456D4×C11—28no—
457D4×C11—28no—
458D4×C11—48no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—28no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—84no—
480C2×C4×C11—84no—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C412yes—
483C2×C4×C11H(5,𝔽2)12yes—
484C2×C4×C11H(5,𝔽2)12yes—
485C2×C4×C11H(5,𝔽2)12yes—
486C22⋊D11—48no—
487C22⋊D11—48no—
488C22⋊D11—48no—
489C22⋊D11—48no—
490C22⋊D11—48no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—84no—
519C2×Dic11—84no—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C412yes—
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C414yes—
525C2×Dic11H(5,𝔽2)12yes—
526D44—28no—
527C4×D11—48no—
528C4×D11—84no—
529C4×D11—84no—
530Dic22—28no—
531C22×#41—111no—
532C23×D4C2×D1111yescharacteristic
533#535—1116no—
534C2×#127—111no—
535C2×#127—111no—
536C2×#124—111no—
537C2×#124—111no—
538C2×#121—112no—
539C2×#121—112no—
540C2×#120—112no—
541C2×#120—112no—
542C2×C4×Q8—111no—
543C2×C4×Q8—111no—
544C2×C4×D4—111no—
545C2×C4×D4—111no—
546C2×C4×D4—112no—
547C2×C4×D4—112no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—112no—
551C2×C4×D4—112no—
552C2×C4×D4C2×D1111yescharacteristic
553C2×C4×D4C2×D1111yescharacteristic
554C2×#117—111no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4C2×D1112yes—
557#391—111no—
558#391—111no—
559#390—111no—
560#390—111no—
561#390—112no—
562#390—112no—
563#390—112no—
564#390—112no—
565#390—112no—
566#390—112no—
567#390—111no—
568#390—111no—
569#390C2×D1111yescharacteristic
570#390C2×D1111yescharacteristic
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#386C2×D1112yes—
604#386C2×D1112yes—
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—112no—
614#380C2×D1111yescharacteristic
615#379—112no—
616#379C2×D1112yes—
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—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4C2×D1111yescharacteristic
628#376—111no—
629C2×#95—112no—
630C43—111no—
631C22×C11—22no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—22no—
635C22×C11—22no—
636C22×C11—24no—
637C22×C11—24no—
638C22×C11—24no—
639C22×C11—24no—
640C22×C11—42no—
641C22×C11—41no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—41no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—41no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—41no—
652C22×C11—816no—
653C22×C11C24×C411yescharacteristic
654C22×C11C2×H(5,𝔽2)11yescharacteristic
655C22×C11C2×H(5,𝔽2)11yescharacteristic
656C22×C11C2×H(5,𝔽2)11yescharacteristic
657C22×C11C2×H(5,𝔽2)11yescharacteristic
658C22×C11#58511yescharacteristic
659C22×C11#58511yescharacteristic
660C2×D11—24no—
661C2×D11—24no—
662C2×D11—24no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—41no—
670C4×C11—42no—
671C4×C11—41no—
672C4×C11—42no—
673C4×C11—41no—
674C4×C11#51814yes—
675Dic11—24no—
676Dic11—22no—
677Dic11—22no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—42no—
682Dic11—42no—
683Dic11—41no—
684Dic11—41no—
685Dic11—41no—
686C25C22×D1112yes—
687C2×#41—118no—
688C2×#41—442no—
689C2×#41—442no—
690C22×Q8—111no—
691C22×D4—42no—
692C22×D4—42no—
693C22×D4—112no—
694C22×D4—112no—
695C22×D4—112no—
696C22×D4—112no—
697C22×D4—112no—
698C22×D4—111no—
699C22×D4C4×D1118yescomplemented
700C22×D4C22×D1111yescharacteristic
701C22×D4C22×D1111yescharacteristic
702C22×D4C22×D1112yes—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4C22×D1111yescharacteristic
709C23×C4C22×D1112yes—
710C23×C4C22×D1112yes—
711#127—118no—
712#127—118no—
713#124—118no—
714#124—118no—
715#121—1116no—
716#121—1116no—
717#120—1116no—
718#120—1116no—
719C4×Q8—442no—
720C4×Q8—442no—
721C4×D4—42no—
722C4×D4—42no—
723C4×D4—444no—
724C4×D4—444no—
725C4×D4—442no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—442no—
729C4×D4—444no—
730C4×D4—444no—
731#117—118no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4C22×D1111yescharacteristic
745C2×C4⋊C4C22×D1111yescharacteristic
746C2×C22⋊C4—44no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—111no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—111no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—444no—
769C2×C22⋊C4C22×D1111yescharacteristic
770C2×C22⋊C4C22×D1112yes—
771C2×C22⋊C4C22×D1112yes—
772C2×C22⋊C4C22×D1112yes—
773C2×C22⋊C4C22×D1112yes—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1111yescharacteristic
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—111no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—111no—
800#95—111no—
801#95—112no—
802#95—111no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—111no—
810#95—111no—
811#95C22×D1112yes—
812#95C22×D1111yescharacteristic
813#95C22×D1111yescharacteristic
814C2×C11—44no—
815C2×C11—44no—
816C2×C11—42no—
817C2×C11C2×#51811yescharacteristic
818C2×C11C4×H(5,𝔽2)11yescharacteristic
819C2×C11C4×H(5,𝔽2)11yescharacteristic
820C2×C11#354311yescharacteristic
821C2×C11#354611yescharacteristic
822C2×C11#355811yescharacteristic
823C2×C11#356211yescharacteristic
824D11—44no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—112no—
832C24C2×C4×D1118yes—
833C24C23×D1111yescharacteristic
834C24C23×D1112yes—
835C24C23×D1112yes—
836#41—4416no—
837C2×Q8—114no—
838C2×Q8—222no—
839C2×Q8—222no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—416no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—118no—
848C2×D4—118no—
849C2×D4—118no—
850C2×D4—118no—
851C2×D4—118no—
852C2×D4—114no—
853C2×D4—222no—
854C2×D4—222no—
855C2×D4—442no—
856C2×D4—442no—
857C2×D4—442no—
858C2×D4—442no—
859C2×D4—442no—
860C2×D4—442no—
861C2×D4—442no—
862C2×D4—442no—
863C2×D4—442no—
864C2×D4—442no—
865C2×D4C2×C4×D1114yes—
866C2×D4C2×C4×D1114yes—
867C2×D4C2×C4×D1118yes—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—111no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—111no—
880C22×C4—111no—
881C22×C4—112no—
882C22×C4—118no—
883C22×C4—111no—
884C22×C4—111no—
885C22×C4—111no—
886C22×C4—112no—
887C22×C4—112no—
888C22×C4—224no—
889C22×C4—224no—
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×C4C2×C4×D1114yes—
903C22×C4C23×D1112yes—
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1112yes—
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—114no—
914C4⋊C4—114no—
915C4⋊C4—222no—
916C4⋊C4—222no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—442no—
920C4⋊C4—442no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4—441no—
924C4⋊C4—441no—
925C22⋊C4—22no—
926C22⋊C4—24no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—41no—
933C22⋊C4—42no—
934C22⋊C4—114no—
935C22⋊C4—114no—
936C22⋊C4—118no—
937C22⋊C4—118no—
938C22⋊C4—118no—
939C22⋊C4—118no—
940C22⋊C4—222no—
941C22⋊C4—224no—
942C22⋊C4—224no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C22⋊C4—442no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—441no—
955C42—22no—
956C42—22no—
957C42—114no—
958C42—114no—
959C42—222no—
960C42—222no—
961C42—222no—
962C42—222no—
963C42—442no—
964C42—442no—
965C42—442no—
966C42—442no—
967C42—441no—
968C42—441no—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—21no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—21no—
984C23—22no—
985C23—22no—
986C23—21no—
987C23—22no—
988C23—48no—
989C23—48no—
990C23—48no—
991C23—84no—
992C23—84no—
993C23—84no—
994C23—84no—
995C23—114no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23C22×C4×D1112yes—
1003C23C22×C4×D1114yes—
1004C23C22×C4×D1114yes—
1005C23C24×D1111yescharacteristic
1006Q8—228no—
1007D4—28no—
1008D4—28no—
1009D4—48no—
1010D4—228no—
1011D4—448no—
1012D4—448no—
1013D4—448no—
1014D4—448no—
1015D4—448no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—28no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—112no—
1039C2×C4—112no—
1040C2×C4—112no—
1041C2×C4—112no—
1042C2×C4—114no—
1043C2×C4—112no—
1044C2×C4—221no—
1045C2×C4—221no—
1046C2×C4—221no—
1047C2×C4—221no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—222no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—448no—
1072C2×C4—884no—
1073C2×C4—884no—
1074C2×C4—884no—
1075C2×C4—884no—
1076C2×C4C22×C4×D1112yes—
1077C2×C4C22×C4×D1112yes—
1078C2×C4#6703712yes—
1079C2×C4#6703712yes—
1080C2×C4#6703712yes—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—22no—
1087C22—24no—
1088C22—24no—
1089C22—22no—
1090C22—41no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—42no—
1099C22—42no—
1100C22—41no—
1101C22—42no—
1102C22—816no—
1103C22—224no—
1104C22—224no—
1105C22—224no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6703711yescharacteristic
1112C22C2×#6703711yescharacteristic
1113C22C2×#6703711yescharacteristic
1114C22#1062345311yescharacteristic
1115C22D11×H(5,𝔽2)11yescharacteristic
1116C22#1062345511yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—41no—
1120C4—41no—
1121C4—42no—
1122C4—41no—
1123C4—42no—
1124C4—222no—
1125C4—224no—
1126C4—222no—
1127C4—222no—
1128C4—222no—
1129C4—222no—
1130C4—441no—
1131C4—442no—
1132C4—441no—
1133C4—442no—
1134C4—441no—
1135C4#1062301714yes—
1136C2—42no—
1137C2—44no—
1138C2—44no—
1139C2—444no—
1140C2C2×#1062301711yescharacteristic
1141C2#1308182011yescharacteristic
1142C2C4×#6703711yescharacteristic
1143C2#1308294711yescharacteristic
1144C2#1308298311yescharacteristic
1145C2#1308313011yescharacteristic
1146C2#1308319411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×#10623336C2
hypercenterD4×C22⋊C4D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071768C2semidirect
3. #13071755C2semidirect
4. #13071686C2semidirect
5. #13071686C2semidirect
6. #13071678C2semidirect
7. #13071678C2semidirect
8. #13071665C2semidirect
9. #13071595C2semidirect
10. #13071456C2semidirect
11. #13071444C2semidirect
12. D4×C22⋊Dic11C2semidirect
13. #13071377C2semidirect
14. #13071340C2semidirect
15. #13071328C2semidirect
16. #13071318C2semidirect
17. #13071274C2semidirect
18. #13071271C2semidirect
19. #13071223C2semidirect
20. #13071180C2semidirect
21. C4×#66989C2semidirect
22. #13071112C2semidirect
23. D4×C11×C22⋊C4C2semidirect
32. #10623336C4semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
44. C2×#66946C22semidirect
45. C2×#66946C22semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×(C22⋊D11)⋊C4C22semidirect
48. C2×C4×Dic22C22semidirect
49. C2×C4×Dic22C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
65. #10622823C22semidirect
66. #10622823C22semidirect
68. C4×C22⋊Dic11C22semidirect
69. C4×C22⋊Dic11C22semidirect
70. #10622590C22semidirect
71. #10622589C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. C4⋊C4×Dic11C22semidirect
74. #10622587C22semidirect
75. #10622587C22semidirect
76. #10622571C22semidirect
77. #10622571C22semidirect
80. #10622570C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622570C22semidirect
86. #10622569C22semidirect
87. #10622569C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622559C22semidirect
91. #10622559C22semidirect
95. #10622558C22semidirect
96. #10622558C22semidirect
97. #10622558C22semidirect
98. #10622558C22semidirect
102. #10622557C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
105. #10622557C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. #10622552C22semidirect
109. #10622552C22semidirect
110. #10622545C22semidirect
111. C4×Dic11⋊C4C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. C42×Dic11C22semidirect
114. #10622280C22semidirect
115. #10622279C22semidirect
116. #10622277C22semidirect
117. D11×#95C22semidirect
118. #10622267C22semidirect
119. #10622267C22semidirect
120. #10622267C22semidirect
121. #10622266C22semidirect
122. #10622266C22semidirect
123. #10622266C22semidirect
127. C22×D4×C11C2×C4semidirect
143. C2×#4339C2×C4semidirect
165. #67006C2×C4semidirect
166. #67006C2×C4semidirect
183. #66993C2×C4semidirect
184. #66993C2×C4semidirect
185. #66991C2×C4semidirect
186. #66991C2×C4semidirect
187. #66989C2×C4semidirect
188. #66989C2×C4semidirect
199. #66979C2×C4semidirect
409. D4×C22⋊C4D11semidirect
699. C22×D4C4×D11semidirect
969. C11#34438semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
#130717682
#130717552
#130716862
#130716782
#130716652
#130715952
#130714562
#130714442
D4×C22⋊Dic112
#130713772
#130713402
#130713282
#130713182
#130712742
#130712712
#130712232
#130711802
C4×#669892
#130711122
D4×C11×C22⋊C42
#3443811