Finite Group Databasebeta

← D11×#2564 #14923985

Subgroups — D11×#2564 #14923985

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic
3#13073801C212yesmaximal, complemented
4#13073800C212yesmaximal, complemented
5#13073799C211yesmaximal, characteristic, complemented
6#13073798C211yesmaximal, characteristic, complemented
7#13073797C211yesmaximal, characteristic, complemented
8#13073796C211yesmaximal, characteristic, complemented
9#13073795C212yesmaximal, complemented
10#13073794C212yesmaximal, complemented
11#13073793C211yesmaximal, characteristic, complemented
12#13073792C211yesmaximal, characteristic, complemented
13#13073791C211yesmaximal, characteristic, complemented
14D11×#400C211yesmaximal, characteristic, complemented
15D11×#399C211yesmaximal, characteristic, complemented
16D11×#395C211yesmaximal, characteristic, complemented
17D11×#393C211yesmaximal, characteristic, complemented
18D11×#387C212yesmaximal, complemented
19D11×#386C212yesmaximal
20D11×#385C212yesmaximal, complemented
21D11×#380C212yesmaximal, complemented
22C2×D11×#95C211yesmaximal, characteristic, complemented
23C11×#2564C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2212yes—
27C23×C4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic, complemented
30C2×C4×D4×C11C2211yescharacteristic
31C2×#66999C2211yescharacteristic, complemented
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66977C2211yescharacteristic, complemented
36D11×C22⋊Q8—28no—
37C4×D4×D11—28no—
38C2×#66950C2211yescharacteristic, complemented
39C2×#66949C2212yescomplemented
40C2×#66946C2211yescharacteristic
41C2×C4⋊C4×D11C2212yes—
42C2×C4⋊C4×D11C2212yes—
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2212yes—
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2212yes—
53C2×#66931C2212yescomplemented
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C11×#400C2211yescharacteristic, complemented
57C11×#399C2211yescharacteristic, complemented
58C11×#395C2211yescharacteristic, complemented
59C11×#393C2211yescharacteristic, complemented
60C11×#387C2212yescomplemented
61C11×#386C2212yes—
62C11×#385C2212yescomplemented
63C11×#380C2212yescomplemented
64C2×C11×#95C2211yescharacteristic, complemented
65#10622844C2211yescharacteristic, complemented
66#10622842C2211yescharacteristic, complemented
67#10622833C2212yes—
68#10622826C2212yes—
69#10622825C2212yescomplemented
70#10622823C2212yescomplemented
71C2×C11⋊#95C2211yescharacteristic, complemented
72C2×C11⋊#95C2212yescomplemented
73#10622605C2212yescomplemented
74#10622605C2211yescharacteristic, complemented
75#10622602C2212yescomplemented
76#10622602C2212yescomplemented
77#10622600C2212yescomplemented
78#10622600C2212yescomplemented
79#10622599C2211yescharacteristic, complemented
80#10622595C2211yescharacteristic, complemented
81#10622594C2212yescomplemented
82#10622592C2211yescharacteristic, complemented
83#10622592C2212yescomplemented
84#10622591C2212yescomplemented
85#10622571C2212yes—
86#10622569C2212yes—
87#10622569C2212yes—
88#10622563C2212yescomplemented
89#10622562C2211yescharacteristic, complemented
90#10622562C2212yescomplemented
91#10622560C2211yescharacteristic, complemented
92#10622560C2212yescomplemented
93#10622559C2212yescomplemented
94#10622555C2212yescomplemented
95#10622555C2212yescomplemented
96#10622546C2212yescomplemented
97#10622290C2211yescharacteristic, complemented
98#10622286C2212yescomplemented
99#10622286C2211yescharacteristic, complemented
100#10622281C2212yescomplemented
101#10622281C2212yescomplemented
102#10622280C2212yescomplemented
103#10622280C2212yescomplemented
104#10622278C2212yes—
105#10622278C2212yes—
106D11×#95C2212yes—
107D11×#95C2211yescharacteristic
108D11×#95C2211yescharacteristic
109D11×#95C2212yes—
110D11×#95C2212yes—
111D11×#95C2212yes—
112D11×#95C2212yes—
113D11×#95C2211yescharacteristic, complemented
114D11×#95C2211yescharacteristic, complemented
115D11×#95C2212yescomplemented
116#10622273C2212yescomplemented
117#10622272C2211yescharacteristic, complemented
118#10622271C2212yescomplemented
119#10622269C2211yescharacteristic, complemented
120#10622269C2212yescomplemented
121#10622268C2212yescomplemented
122#10622267C2212yescomplemented
123#10622266C2212yescomplemented
124#10622265C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C2×Q8×D11—24no—
138C2×Q8×D11—44no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11Q818yescomplemented
142C22×D44C2311yescharacteristic
143C22×C4×D11—28no—
144C22×C4×D11—24no—
145C22×C4×D11—28no—
146C22×C4×D11—44no—
147C22×C4×D11—44no—
148C22×C4×D11—44no—
149C22×C4×D11D418yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C22×Dic22C2312yes—
166C22×Dic22C2311yescharacteristic
167C11×C22⋊Q8—24no—
168C4×D4×C11—24no—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C42×C11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185#66999—24no—
186D4×Dic11—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—24no—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204#66977—24no—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217#66950—24no—
218#66949—28no—
219#66946—24no—
220C4⋊C4×D11—24no—
221C4⋊C4×D11—24no—
222C4⋊C4×D11—28no—
223C4⋊C4×D11—28no—
224C4⋊C4×D11—44no—
225(C22⋊D11)⋊C4—24no—
226(C22⋊D11)⋊C4—24no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11—28no—
229C22⋊C4×D11—24no—
230C22⋊C4×D11—28no—
231C22⋊C4×D11—44no—
232#66931—28no—
233C4×D44—24no—
234C42×D11—24no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2311yescharacteristic
240C11×#95C2312yes—
241C11×#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2312yes—
261C2×#2564—111nomaximal, Sylow
262C24×C11C2411yescharacteristic
263C24×C11C2411yescharacteristic
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—22no—
267C23×D11—24no—
268C23×D11—22no—
269C23×D11—24no—
270C23×D11C2×D414yes—
271C23×D11C2×Q814yes—
272C23×D11C2×Q814yes—
273C23×D11#4114yes—
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C2×Q8×C11—22no—
278C2×Q8×C11—42no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11C2×Q814yescomplemented
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11C2×D414yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11C2×Q814yescomplemented
303C2×C22⋊D11C2×Q814yescomplemented
304C22×Dic11—22no—
305C22×Dic11—24no—
306C22×Dic11—24no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C2×D414yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2412yes—
320Q8×D11—416no—
321D4×D11—232no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44C2×Q814yescomplemented
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—24no—
330C2×C4×D11—22no—
331C2×C4×D11—24no—
332C2×C4×D11—24no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—22no—
349C2×C4×D11—24no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—416no—
357C2×C4×D11—432no—
358C2×C4×D11—416no—
359C2×C4×D11C2×D414yes—
360C2×C4×D11C2×D414yes—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×Q814yes—
364C2×C4×D11#4118yes—
365C2×Dic22—24no—
366C2×Dic22—22no—
367C2×Dic22—42no—
368C2×Dic22—42no—
369C2×Dic22—42no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—24no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—24no—
374C11×C4⋊C4—42no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—42no—
380C42×C11—22no—
381C22⋊Dic11—22no—
382C22⋊Dic11—24no—
383C22⋊Dic11—24no—
384C22⋊Dic11—22no—
385C22⋊Dic11—42no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396C4⋊Dic11—22no—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—24no—
400C4⋊Dic11—42no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—22no—
407Dic11⋊C4—24no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C22×C22⋊Q8—111no—
414C22×C4×D4—111no—
415#2564—111no—
416#2564—111no—
417#2564—111no—
418#2564—111no—
419#2564—112no—
420#2564—112no—
421#2564—112no—
422#2564—112no—
423#2564—111no—
424#2564—111no—
425#2564—111no—
426#2564D1111yescharacteristic, direct product factor
427C2×#400—111no—
428C2×#399—111no—
429C2×#395—111no—
430C2×#393—111no—
431C2×#387—112no—
432C2×#386—112no—
433C2×#385—112no—
434C2×#380—112no—
435C22×#95—111no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—21no—
441C23×C11—22no—
442C23×C11C22×D412yes—
443C23×C11C22×Q812yes—
444C23×C11C22×Q812yes—
445C23×C11C2×#4112yes—
446C23×C11C2511yescharacteristic
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—28no—
450C22×D11—28no—
451C22×D11—216no—
452C22×D11—216no—
453C22×D11—21no—
454C22×D11—22no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—28no—
458C22×D11—216no—
459C22×D11—44no—
460C22×D11—44no—
461C22×D11—48no—
462C22×D11C22⋊Q8116yes—
463C22×D11C22×D412yes—
464C22×D11C22×D412yes—
465C22×D11C22×Q812yes—
466C22×D11C22×Q812yes—
467C22×D11C22×Q812yes—
468C22×D11C2×#4112yes—
469C22×D11C2×#4112yes—
470C22×D11C2×#4114yes—
471C22×D11H(5,𝔽2)14yes—
472Q8×C11—44no—
473D4×C11—28no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
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—44no—
494C2×C4×C11—48no—
495C2×C4×C11—44no—
496C2×C4×C11C22×D412yes—
497C2×C4×C11C22×D412yes—
498C2×C4×C11C22×Q812yes—
499C2×C4×C11C2×#4114yes—
500C22⋊D11—28no—
501C22⋊D11—28no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—44no—
522C2×Dic11—48no—
523C2×Dic11—44no—
524C2×Dic11C22×D412yes—
525C2×Dic11C22×D412yes—
526C2×Dic11C22×Q812yes—
527C2×Dic11C2×#4114yes—
528D44—28no—
529C4×D11—28no—
530C4×D11—28no—
531C4×D11—28no—
532C4×D11—216no—
533C4×D11—44no—
534C4×D11—44no—
535C4×D11—48no—
536C4×D11—44no—
537C4×D11—48no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—48no—
541C4×D11—44no—
542C4×D11—48no—
543C4×D11—48no—
544Dic22—48no—
545Dic22—44no—
546C23×Q8—111no—
547C23×D4—111no—
548C24×C4—111no—
549C24×C4—112no—
550C24×C4—111no—
551C2×C22⋊Q8—111no—
552C2×C22⋊Q8—111no—
553C2×C22⋊Q8—112no—
554C2×C22⋊Q8—111no—
555C2×C22⋊Q8—112no—
556C2×C22⋊Q8—228no—
557C2×C22⋊Q8C2×D1111yescharacteristic, complemented
558C2×C4×D4—111no—
559C2×C4×D4—111no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—111no—
564C2×C4×D4—111no—
565C2×C4×D4—228no—
566C2×C4×D4C2×D1111yescharacteristic
567C22×C4⋊C4—111no—
568C22×C4⋊C4—111no—
569C22×C4⋊C4—112no—
570C22×C4⋊C4—112no—
571C22×C4⋊C4—112no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—112no—
574C22×C22⋊C4—111no—
575C22×C22⋊C4—112no—
576C22×C22⋊C4—112no—
577C22×C42—111no—
578#400—111no—
579#400—111no—
580#400—112no—
581#400—111no—
582#400—112no—
583#400C2×D1111yescharacteristic, complemented
584#399—112no—
585#399—111no—
586#399—112no—
587#399—111no—
588#399—111no—
589#399C2×D1111yescharacteristic, complemented
590#395—111no—
591#395—112no—
592#395—111no—
593#395—112no—
594#395—111no—
595#395C2×D1111yescharacteristic, complemented
596#393—111no—
597#393—112no—
598#393—111no—
599#393—112no—
600#393—111no—
601#393C2×D1111yescharacteristic, complemented
602#387—112no—
603#387—112no—
604#387—112no—
605#387—112no—
606#387—112no—
607#387—112no—
608#387—112no—
609#387C2×D1112yescomplemented
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386C2×D1112yes—
618#385—112no—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#385—112no—
625#385C2×D1112yescomplemented
626#380—112no—
627#380—112no—
628#380—112no—
629#380—112no—
630#380—112no—
631#380—112no—
632#380—112no—
633#380C2×D1112yescomplemented
634C2×#95—112no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—112no—
639C2×#95—111no—
640C2×#95—112no—
641C2×#95—111no—
642C2×#95—112no—
643C2×#95—112no—
644C2×#95—112no—
645C2×#95—112no—
646C2×#95C2×D1111yescharacteristic, complemented
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—22no—
652C22×C11—24no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—42no—
656C22×C11C2×C22⋊Q814yes—
657C22×C11C23×D411yescharacteristic
658C22×C11C23×Q811yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11C22×#4112yes—
661C22×C11C2×H(5,𝔽2)12yes—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—232no—
667C2×D11—22no—
668C2×D11—24no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11—42no—
672C2×D11—416no—
673C2×D11C2×C22⋊Q814yes—
674C2×D11C2×C22⋊Q814yes—
675C2×D11#53214yes—
676C2×D11#53414yes—
677C2×D11#55118yes—
678C2×D11#55418yes—
679C4×C11—22no—
680C4×C11—22no—
681C4×C11—22no—
682C4×C11—24no—
683C4×C11—41no—
684C4×C11—42no—
685C4×C11—41no—
686C4×C11—42no—
687C4×C11—42no—
688Dic11—22no—
689Dic11—22no—
690Dic11—22no—
691Dic11—24no—
692Dic11—41no—
693Dic11—42no—
694Dic11—42no—
695Dic11—41no—
696Dic11—42no—
697C25—111no—
698C25—111no—
699C22×Q8—112no—
700C22×Q8—111no—
701C22×Q8—224no—
702C22×Q8—444no—
703C22×Q8C22×D1111yescharacteristic
704C22×D4—111no—
705C22×D4—111no—
706C22×D4—118no—
707C22×D4—111no—
708C22×D4—224no—
709C22×D4—224no—
710C22×D4C22×D1111yescharacteristic
711C23×C4—111no—
712C23×C4—111no—
713C23×C4—112no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—118no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—112no—
720C23×C4—111no—
721C23×C4—112no—
722C23×C4—112no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—112no—
726C23×C4—112no—
727C23×C4—112no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—224no—
731C23×C4—228no—
732C23×C4—228no—
733C23×C4—444no—
734C23×C4—444no—
735C23×C4—444no—
736C23×C4C22×D1112yes—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739C22⋊Q8—24no—
740C22⋊Q8—228no—
741C22⋊Q8—228no—
742C22⋊Q8—224no—
743C22⋊Q8—224no—
744C22⋊Q8—224no—
745C4×D4—24no—
746C4×D4—224no—
747C4×D4—224no—
748C4×D4—224no—
749C4×D4—224no—
750C4×D4—224no—
751C4×D4—224no—
752C4×D4—224no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
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—224no—
768C2×C4⋊C4—224no—
769C2×C4⋊C4—228no—
770C2×C4⋊C4—228no—
771C2×C4⋊C4—444no—
772C2×C4⋊C4C22×D1111yescharacteristic
773C2×C4⋊C4C22×D1112yes—
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1112yes—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
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—224no—
793C2×C22⋊C4—228no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—228no—
796C2×C22⋊C4—444no—
797C2×C22⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4C22×D1111yescharacteristic
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—224no—
806C2×C42C22×D1111yescharacteristic
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—111no—
812#95—111no—
813#95—112no—
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#95C22×D1112yes—
827#95C22×D1111yescharacteristic
828#95C22×D1111yescharacteristic
829#95C22×D1112yes—
830#95C22×D1112yes—
831#95C22×D1112yes—
832#95C22×D1112yes—
833C2×C11—24no—
834C2×C11—42no—
835C2×C11C22×C22⋊Q811yescharacteristic
836C2×C11C2×#53211yescharacteristic
837C2×C11C2×#53411yescharacteristic
838C2×C11C2×#55112yes—
839C2×C11C2×#55412yes—
840D11—24no—
841D11—42no—
842D11#256418yesdirect product factor
843C24—111no—
844C24—114no—
845C24—114no—
846C24—114no—
847C24—111no—
848C24—114no—
849C24—111no—
850C24—224no—
851C24—224no—
852C24—222no—
853C24—224no—
854C24—224no—
855C24—222no—
856C24C23×D1111yescharacteristic
857C24C23×D1111yescharacteristic
858C2×Q8—22no—
859C2×Q8—42no—
860C2×Q8—224no—
861C2×Q8—222no—
862C2×Q8—442no—
863C2×Q8—442no—
864C2×Q8—442no—
865C2×Q8—4416no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—114no—
869C2×D4—114no—
870C2×D4—114no—
871C2×D4—222no—
872C2×D4—222no—
873C2×D4—2232no—
874C2×D4—222no—
875C2×D4—222no—
876C2×D4—222no—
877C2×D4—222no—
878C2×D4Q8×D1114yescomplemented
879C22×C4—24no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—111no—
886C22×C4—112no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—114no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—114no—
893C22×C4—118no—
894C22×C4—114no—
895C22×C4—114no—
896C22×C4—112no—
897C22×C4—111no—
898C22×C4—112no—
899C22×C4—112no—
900C22×C4—111no—
901C22×C4—222no—
902C22×C4—224no—
903C22×C4—222no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—224no—
911C22×C4—222no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—224no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—4416no—
936C22×C4—4432no—
937C22×C4—4416no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4D4×D1114yes—
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1112yes—
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1112yes—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—42no—
956C4⋊C4—222no—
957C4⋊C4—222no—
958C4⋊C4—224no—
959C4⋊C4—224no—
960C4⋊C4—224no—
961C4⋊C4—224no—
962C4⋊C4—224no—
963C4⋊C4—222no—
964C4⋊C4—224no—
965C4⋊C4—222no—
966C4⋊C4—224no—
967C4⋊C4—442no—
968C4⋊C4—442no—
969C4⋊C4—442no—
970C22⋊C4—22no—
971C22⋊C4—24no—
972C22⋊C4—22no—
973C22⋊C4—24no—
974C22⋊C4—42no—
975C22⋊C4—222no—
976C22⋊C4—224no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—224no—
983C22⋊C4—222no—
984C22⋊C4—224no—
985C22⋊C4—222no—
986C22⋊C4—224no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C42—22no—
991C42—222no—
992C42—222no—
993C42—222no—
994C11C2×#256411yescharacteristic, complemented, Sylow
995C23—22no—
996C23—22no—
997C23—21no—
998C23—22no—
999C23—21no—
1000C23—22no—
1001C23—112no—
1002C23—112no—
1003C23—114no—
1004C23—112no—
1005C23—114no—
1006C23—1116no—
1007C23—112no—
1008C23—112no—
1009C23—112no—
1010C23—112no—
1011C23—228no—
1012C23—2216no—
1013C23—2216no—
1014C23—228no—
1015C23—228no—
1016C23—2216no—
1017C23—222no—
1018C23—222no—
1019C23—221no—
1020C23—222no—
1021C23—221no—
1022C23—222no—
1023C23—444no—
1024C23—444no—
1025C23—448no—
1026C23C2×D4×D1112yes—
1027C23C2×Q8×D1112yes—
1028C23C2×Q8×D1112yes—
1029C23#41×D1112yes—
1030C23C24×D1111yescharacteristic
1031Q8—44no—
1032Q8—444no—
1033Q8—448no—
1034D4—28no—
1035D4—228no—
1036D4—228no—
1037D4—228no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—44no—
1058C2×C4—48no—
1059C2×C4—44no—
1060C2×C4—112no—
1061C2×C4—112no—
1062C2×C4—112no—
1063C2×C4—114no—
1064C2×C4—228no—
1065C2×C4—228no—
1066C2×C4—2216no—
1067C2×C4—228no—
1068C2×C4—221no—
1069C2×C4—222no—
1070C2×C4—221no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—221no—
1075C2×C4—222no—
1076C2×C4—221no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—444no—
1088C2×C4—444no—
1089C2×C4—448no—
1090C2×C4—444no—
1091C2×C4—448no—
1092C2×C4—444no—
1093C2×C4—444no—
1094C2×C4—448no—
1095C2×C4—448no—
1096C2×C4—444no—
1097C2×C4—448no—
1098C2×C4—444no—
1099C2×C4—448no—
1100C2×C4—444no—
1101C2×C4C2×D4×D1112yes—
1102C2×C4C2×D4×D1112yes—
1103C2×C4C2×Q8×D1112yes—
1104C2×C4#41×D1114yes—
1105C22—24no—
1106C22—22no—
1107C22—22no—
1108C22—24no—
1109C22—24no—
1110C22—22no—
1111C22—41no—
1112C22—41no—
1113C22—42no—
1114C22—118no—
1115C22—114no—
1116C22—114no—
1117C22—114no—
1118C22—118no—
1119C22—114no—
1120C22—2232no—
1121C22—224no—
1122C22—222no—
1123C22—222no—
1124C22—224no—
1125C22—224no—
1126C22—222no—
1127C22—4416no—
1128C22—441no—
1129C22—441no—
1130C22—442no—
1131C22D11×C22⋊Q814yes—
1132C22C22×D4×D1111yescharacteristic
1133C22C22×Q8×D1111yescharacteristic
1134C22C2×#41×D1112yes—
1135C22C2×#41×D1111yescharacteristic
1136C22D11×H(5,𝔽2)12yes—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—24no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—42no—
1145C4—42no—
1146C4—222no—
1147C4—222no—
1148C4—222no—
1149C4—224no—
1150C4—441no—
1151C4—442no—
1152C4—441no—
1153C4—442no—
1154C4—442no—
1155C2—24no—
1156C2—42no—
1157C2—118no—
1158C2—224no—
1159C2—442no—
1160C2C2×D11×C22⋊Q811yescharacteristic
1161C2D11×#53211yescharacteristic
1162C2D11×#53411yescharacteristic
1163C2D11×#55112yes—
1164C2D11×#55412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2564C2
prime radicalC22×D4×D11C22
hypercenter#2564D11
hypocenterC11C2×#2564
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2564

Complements

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

NH ≅ G/Ntype
1. C2×D11×C22⋊Q8C2semidirect
3. #13073801C2semidirect
4. #13073800C2semidirect
5. #13073799C2semidirect
6. #13073798C2semidirect
7. #13073797C2semidirect
8. #13073796C2semidirect
9. #13073795C2semidirect
10. #13073794C2semidirect
11. #13073793C2semidirect
12. #13073792C2semidirect
13. #13073791C2semidirect
14. D11×#400C2semidirect
15. D11×#399C2semidirect
16. D11×#395C2semidirect
17. D11×#393C2semidirect
18. D11×#387C2semidirect
20. D11×#385C2semidirect
21. D11×#380C2semidirect
22. C2×D11×#95C2semidirect
23. C11×#2564C2semidirect
29. C2×C11×C22⋊Q8C22semidirect
31. C2×#66999C22semidirect
35. C2×#66977C22semidirect
38. C2×#66950C22semidirect
39. C2×#66949C22semidirect
53. C2×#66931C22semidirect
56. C11×#400C22semidirect
57. C11×#399C22semidirect
58. C11×#395C22semidirect
59. C11×#393C22semidirect
60. C11×#387C22semidirect
62. C11×#385C22semidirect
63. C11×#380C22semidirect
64. C2×C11×#95C22semidirect
65. #10622844C22semidirect
66. #10622842C22semidirect
69. #10622825C22semidirect
70. #10622823C22semidirect
71. C2×C11⋊#95C22semidirect
72. C2×C11⋊#95C22semidirect
73. #10622605C22semidirect
74. #10622605C22semidirect
75. #10622602C22semidirect
76. #10622602C22semidirect
77. #10622600C22semidirect
78. #10622600C22semidirect
79. #10622599C22semidirect
80. #10622595C22semidirect
81. #10622594C22semidirect
82. #10622592C22semidirect
83. #10622592C22semidirect
84. #10622591C22semidirect
88. #10622563C22semidirect
89. #10622562C22semidirect
90. #10622562C22semidirect
91. #10622560C22semidirect
92. #10622560C22semidirect
93. #10622559C22semidirect
94. #10622555C22semidirect
95. #10622555C22semidirect
96. #10622546C22semidirect
97. #10622290C22semidirect
98. #10622286C22semidirect
99. #10622286C22semidirect
100. #10622281C22semidirect
101. #10622281C22semidirect
102. #10622280C22semidirect
103. #10622280C22semidirect
113. D11×#95C22semidirect
114. D11×#95C22semidirect
115. D11×#95C22semidirect
116. #10622273C22semidirect
117. #10622272C22semidirect
118. #10622271C22semidirect
119. #10622269C22semidirect
120. #10622269C22semidirect
121. #10622268C22semidirect
122. #10622267C22semidirect
123. #10622266C22semidirect
124. #10622265C22semidirect
141. C2×D4×D11Q8semidirect
281. C2×D4×C11C2×Q8semidirect
302. C2×C22⋊D11C2×Q8semidirect
303. C2×C22⋊D11C2×Q8semidirect
324. C2×D44C2×Q8semidirect
426. #2564D11direct (N × H)
557. C2×C22⋊Q8C2×D11semidirect
583. #400C2×D11semidirect
589. #399C2×D11semidirect
595. #395C2×D11semidirect
601. #393C2×D11semidirect
609. #387C2×D11semidirect
625. #385C2×D11semidirect
633. #380C2×D11semidirect
646. C2×#95C2×D11semidirect
842. D11#2564direct (N × H)
878. C2×D4Q8×D11semidirect
994. C11C2×#2564semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×C4×D4×D112
#130738012
#130738002
#130737992
#130737982
#130737972
#130737962
#130737952
#130737942
#130737932
#130737922
#130737912
D11×#4002
D11×#3992
D11×#3952
D11×#3932
D11×#3872
D11×#3862
D11×#3852
D11×#3802
C2×D11×#952
C11×#25642
C2×#256411