Finite Group Databasebeta

← D11×#3217 #15625032

Subgroups — D11×#3217 #15625032

Order 2816.

2834 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#127C211yesmaximal, characteristic, complemented
2D11×#529C211yesmaximal, characteristic, complemented
3#13079638C212yesmaximal, complemented
4#13079637C212yesmaximal, complemented
5#13079636C211yesmaximal, characteristic, complemented
6#13079635C212yesmaximal, complemented
7#13079634C211yesmaximal, characteristic, complemented
8#13079633C212yesmaximal, complemented
9#13079632C212yesmaximal, complemented
10#13079631C211yesmaximal, characteristic, complemented
11#13079630C212yesmaximal, complemented
12D11×#496C212yesmaximal, complemented
13D11×#490C212yesmaximal, complemented
14D11×#460C212yesmaximal, complemented
15D11×#459C212yesmaximal, complemented
16D11×#450C212yesmaximal, complemented
17D11×#447C212yesmaximal, complemented
18D11×#432C211yesmaximal, characteristic, complemented
19C11×#3217C211yesmaximal, characteristic, complemented
20C22×D4×D11—21no—
21C22×D4×D11—21no—
22C22×D4×D11C2212yes—
23C2×C11×#127C2211yescharacteristic, complemented
24C11×#529C2211yescharacteristic, complemented
25C2×#66993—21no—
26C2×#66993—21no—
27C2×#66993C2212yescomplemented
28C2×SD16×D11C2214yescomplemented
29C2×D8×D11C2214yescomplemented
30D11×#127—21no—
31D11×#127—21no—
32D11×#127—21no—
33D11×#127—21no—
34D11×#127C2212yes—
35D11×#127C2212yes—
36D11×#127C2212yescomplemented
37D11×#127C2212yescomplemented
38#10623237—21no—
39D11×#126—21no—
40#10623222C2211yescharacteristic, complemented
41D11×#125C2211yescharacteristic, complemented
42#10623211C2211yescharacteristic, complemented
43D11×#124C2211yescharacteristic, complemented
44D11×#123—21no—
45#10623180—21no—
46D11×C22⋊Q8C2211yescharacteristic
47#10623155C2211yescharacteristic, complemented
48D11×#121C2211yescharacteristic
49#10623131C2211yescharacteristic, complemented
50#10623111C2211yescharacteristic, complemented
51C4×Q8×D11C2211yescharacteristic, complemented
52#10623088C2211yescharacteristic, complemented
53C4×D4×D11—21no—
54C4×D4×D11C2211yescharacteristic, complemented
55#10623069—21no—
56#10623059—21no—
57D11×#117—21no—
58#10623010C2211yescharacteristic, complemented
59C2×#66927C2211yescharacteristic, complemented
60C2×C42×D11C2211yescharacteristic
61C11×#496C2212yescomplemented
62C11×#490C2212yescomplemented
63C11×#460C2212yescomplemented
64C11×#459C2212yescomplemented
65C11×#450C2212yescomplemented
66C11×#447C2212yescomplemented
67C11×#432C2211yescharacteristic, complemented
68#10622831C2212yescomplemented
69#10622830C2212yescomplemented
70#10622789C2214yescomplemented
71#10622782C2214yescomplemented
72#10622776C2214yescomplemented
73#10622769C2214yescomplemented
74#10622767C2214yescomplemented
75#10622763C2214yescomplemented
76#10622688C2212yescomplemented
77#10622687C2212yescomplemented
78#10622685C2212yescomplemented
79#10622684C2212yescomplemented
80#10622680C2212yescomplemented
81#10622671C2212yescomplemented
82#10622659C2212yescomplemented
83#10622649C2212yescomplemented
84#10622640C2212yescomplemented
85#10622628C2212yescomplemented
86#10622539C2211yescharacteristic, complemented
87#10622461C2212yescomplemented
88#10622456C2212yescomplemented
89#10622448C2212yescomplemented
90D11×C4⋊C8C2212yescomplemented
91#10622399C2214yescomplemented
92#10622389C2214yescomplemented
93#10622386C2214yescomplemented
94D11×#102C2214yescomplemented
95D11×#102C2214yescomplemented
96#10622377C2214yescomplemented
97#10622377C2214yescomplemented
98#10622375C2214yescomplemented
99#10622345C2212yescomplemented
100#10622344C2212yescomplemented
101D11×C22⋊C8C2212yes—
102#10622332C2212yescomplemented
103#10622326C2212yescomplemented
104#10622325C2212yescomplemented
105#10622318C2212yescomplemented
106D11×#97C2212yescomplemented
107C24×D11—22no—
108C22×D4×C11—21no—
109C22×D4×C11—21no—
110C22×D4×C11C2312yes—
111C22×C22⋊D11—22no—
112C22×C22⋊D11—22no—
113C22×C22⋊D11—22no—
114C2×Q8×D11C2311yescharacteristic
115C2×D4×D11—21no—
116C2×D4×D11—22no—
117C2×D4×D11—22no—
118C2×D4×D11—22no—
119C2×D4×D11—22no—
120C2×D4×D11—22no—
121C2×D4×D11—22no—
122C2×D4×D11—22no—
123C2×D4×D11—22no—
124C2×D4×D11—22no—
125C2×D4×D11—22no—
126C2×D4×D11—48no—
127C2×D4×D11—48no—
128C2×D4×D11—48no—
129C2×D4×D11C2314yes—
130C2×D4×D11C2311yescharacteristic
131C2×D4×D11C2314yes—
132C22×D44—21no—
133C22×D44—21no—
134C22×D44C2312yes—
135C22×C4×D11—21no—
136C22×C4×D11D411yescharacteristic
137C22×C4×D11D411yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C2×C11×SD16C2314yescomplemented
140C2×C11×D8C2314yescomplemented
141C11×#127—21no—
142C11×#127—21no—
143C11×#127C2312yes—
144C11×#127C2312yes—
145C11×#126—21no—
146C11×#125C2311yescharacteristic, complemented
147C11×#124C2311yescharacteristic, complemented
148C11×#123—21no—
149C11×C22⋊Q8C2311yescharacteristic
150C11×#121C2311yescharacteristic
151C4×Q8×C11C2311yescharacteristic, complemented
152C4×D4×C11—21no—
153C4×D4×C11C2311yescharacteristic, complemented
154C11×#117—21no—
155C2×C42×C11C2311yescharacteristic
156#67000C2311yescharacteristic, complemented
157#66999C2311yescharacteristic
158Q8×Dic11C2311yescharacteristic, complemented
159C2×#4325C2314yescomplemented
160#66993—22no—
161#66993—22no—
162#66993—22no—
163#66993—22no—
164#66993—22no—
165#66993—22no—
166#66993—22no—
167#66993—22no—
168#66993—22no—
169#66993—22no—
170#66993C2314yes—
171#66993C2314yes—
172#66992—21no—
173#66991C2311yescharacteristic
174#66989C2311yescharacteristic, complemented
175#66988—21no—
176D4×Dic11—21no—
177D4×Dic11C2311yescharacteristic, complemented
178C2×#4324C2314yescomplemented
179C2×#4323C2314yescomplemented
180C2×#4323C2314yescomplemented
181#66983C2311yescharacteristic
182#66982—21no—
183C4×C22⋊D11—21no—
184C4×C22⋊D11—21no—
185C4×C22⋊D11—21no—
186#66979—21no—
187#66977C2311yescharacteristic
188C2×C4×Dic11D411yescharacteristic
189C2×C4×Dic11D411yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191SD16×D11—48no—
192D8×D11—48no—
193C2×D88C2314yescomplemented
194C2×#4314C2314yescomplemented
195C2×C8×D11C2314yes—
196#66951—21no—
197#66951—21no—
198#66951—21no—
199#66950C2311yescharacteristic
200#66949—21no—
201#66948C2311yescharacteristic
202#66947—21no—
203#66947—21no—
204#66946—21no—
205#66946C2311yescharacteristic, complemented
206#66945—21no—
207#66945—21no—
208C4⋊C4×D11—21no—
209C4⋊C4×D11—21no—
210C4⋊C4×D11—21no—
211C4⋊C4×D11—21no—
212C4⋊C4×D11C2311yescharacteristic
213C4⋊C4×D11C2311yescharacteristic
214#66943C2311yescharacteristic, complemented
215#66943C2311yescharacteristic, complemented
216#66942—21no—
217#66942—21no—
218#66940—21no—
219#66940C2311yescharacteristic, complemented
220#66939—21no—
221#66938—21no—
222#66938—21no—
223#66937—21no—
224#66936—21no—
225#66936—21no—
226(C22⋊D11)⋊C4—21no—
227(C22⋊D11)⋊C4—21no—
228(C22⋊D11)⋊C4—21no—
229C22⋊C4×D11—21no—
230C22⋊C4×D11—21no—
231C22⋊C4×D11—21no—
232C22⋊C4×D11—21no—
233C22⋊C4×D11—21no—
234#66932—21no—
235#66932—21no—
236#66932—21no—
237#66931—21no—
238#66930—21no—
239#66930—21no—
240#66929—21no—
241#66928C2311yescharacteristic, complemented
242#66927—21no—
243#66927—21no—
244#66927C2312yes—
245#66927C2312yes—
246C4×D44—21no—
247C4×D44C2311yescharacteristic, complemented
248#66925—21no—
249#66925—21no—
250C42×D11—21no—
251C42×D11D411yescharacteristic
252C42×D11D411yescharacteristic
253C42×D11D411yescharacteristic
254C42×D11D411yescharacteristic
255C42×D11C2311yescharacteristic
256C42×D11C2311yescharacteristic
257C42×D11C2311yescharacteristic
258C42×D11C2311yescharacteristic
259#66923C2311yescharacteristic, complemented
260C4×Dic22—21no—
261C4×Dic22C2311yescharacteristic, complemented
262C11×C4⋊C8C2312yescomplemented
263C11×#102C2314yescomplemented
264C11×#102C2314yescomplemented
265C11×C22⋊C8C2312yes—
266C11×#97C2312yescomplemented
267#66896C2314yescomplemented
268#66896C2314yescomplemented
269C22⋊(C11⋊C8)C2312yes—
270#66885C2314yescomplemented
271#66885C2314yescomplemented
272(C2×D11)⋊C8C2314yes—
273#66879C2314yescomplemented
274Dic11⋊C8C2314yescomplemented
275#66873C2314yescomplemented
276#66873C2314yescomplemented
277C4⋊(C11⋊C8)C2312yescomplemented
278#66867C2312yescomplemented
279C2×#3217—111nomaximal, Sylow
280C24×C11—22no—
281C23×D11—22no—
282C23×D11—21no—
283C23×D11—24no—
284C23×D11—24no—
285C23×D11—48no—
286C23×D11—48no—
287C23×D11—48no—
288C23×D11C2×D411yescharacteristic
289C2×Q8×C11C2411yescharacteristic
290C2×D4×C11—21no—
291C2×D4×C11—22no—
292C2×D4×C11—22no—
293C2×D4×C11—22no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—44no—
297C2×D4×C11—44no—
298C2×D4×C11—44no—
299C2×D4×C11C2414yes—
300C2×D4×C11C2411yescharacteristic
301C22×C4×C11—21no—
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C2×C22⋊D11—21no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—21no—
313C2×C22⋊D11—21no—
314C2×C22⋊D11—48no—
315C2×C22⋊D11—48no—
316C2×C22⋊D11—48no—
317C22×Dic11—21no—
318C22×Dic11C2×D411yescharacteristic
319C22×Dic11C2×D411yescharacteristic
320C22×Dic11C2×D411yescharacteristic
321Q8×D11—24no—
322D4×D11—24no—
323D4×D11—28no—
324D4×D11—28no—
325D4×D11—44no—
326D4×D11—44no—
327D4×D11—48no—
328D4×D11—48no—
329D4×D11—48no—
330D4×D11—48no—
331D4×D11—48no—
332D4×D11—48no—
333D4×D11—48no—
334D4×D11—48no—
335D4×D11—48no—
336D4×D11—48no—
337D4×D11—44no—
338C2×D44—21no—
339C2×D44—22no—
340C2×D44—22no—
341C2×D44—22no—
342C2×D44—22no—
343C2×D44—22no—
344C2×D44—44no—
345C2×D44—44no—
346C2×D44—44no—
347C2×D44C2414yes—
348C2×D44C2411yescharacteristic
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—21no—
352C2×C4×D11—24no—
353C2×C4×D11—21no—
354C2×C4×D11—21no—
355C2×C4×D11—21no—
356C2×C4×D11—21no—
357C2×C4×D11—44no—
358C2×C4×D11C2×D411yescharacteristic
359C2×C4×D11C2×D411yescharacteristic
360C2×C4×D11C2×D411yescharacteristic
361C2×C4×D11C2×D411yescharacteristic
362C2×C4×D11C2×D411yescharacteristic
363C2×C4×D11C2×D411yescharacteristic
364C2×C4×D11C2×D411yescharacteristic
365C2×C4×D11C2×D411yescharacteristic
366C2×C4×D11C2×D411yescharacteristic
367C2×C4×D11C2×D411yescharacteristic
368C2×C4×D11C2411yescharacteristic
369C2×C4×D11C2411yescharacteristic
370C2×Dic22—21no—
371C2×Dic22C2411yescharacteristic
372C11×SD16—44no—
373C11×D8—44no—
374C2×C8×C11C2414yes—
375C11×C4⋊C4—21no—
376C11×C4⋊C4—21no—
377C11×C4⋊C4—21no—
378C11×C4⋊C4—21no—
379C11×C4⋊C4C2411yescharacteristic
380C11×C4⋊C4C2411yescharacteristic
381C11×C22⋊C4—21no—
382C11×C22⋊C4—21no—
383C11×C22⋊C4—21no—
384C11×C22⋊C4—21no—
385C11×C22⋊C4—21no—
386C42×C11—21no—
387C42×C11C2×D411yescharacteristic
388C42×C11C2×D411yescharacteristic
389C42×C11C2411yescharacteristic
390C42×C11C2411yescharacteristic
391C22⋊Dic11—21no—
392C22⋊Dic11—21no—
393C22⋊Dic11—21no—
394C22⋊Dic11—21no—
395C22⋊Dic11—21no—
396#4325—44no—
397#4324—44no—
398#4323—44no—
399#4323—44no—
400(C2×D11)⋊C4—21no—
401(C2×D11)⋊C4—21no—
402(C2×D11)⋊C4—21no—
403(C2×D11)⋊C4—21no—
404(C2×D11)⋊C4—21no—
405(C2×D11)⋊C4—21no—
406(C2×D11)⋊C4—21no—
407(C2×D11)⋊C4—21no—
408(C2×D11)⋊C4—21no—
409(C2×D11)⋊C4—21no—
410C4⋊Dic11—21no—
411C4⋊Dic11—21no—
412C4⋊Dic11—21no—
413C4⋊Dic11—21no—
414C4⋊Dic11C2411yescharacteristic
415C4⋊Dic11C2411yescharacteristic
416Dic11⋊C4—21no—
417Dic11⋊C4—21no—
418Dic11⋊C4—21no—
419Dic11⋊C4—21no—
420Dic11⋊C4—21no—
421Dic11⋊C4—21no—
422Dic11⋊C4—21no—
423Dic11⋊C4—21no—
424Dic11⋊C4—21no—
425Dic11⋊C4—21no—
426C4×Dic11—21no—
427C4×Dic11—21no—
428C4×Dic11—21no—
429C4×Dic11C2×D411yescharacteristic
430C4×Dic11C2×D411yescharacteristic
431C4×Dic11C2×D411yescharacteristic
432C4×Dic11C2×D411yescharacteristic
433C4×Dic11C2×D411yescharacteristic
434C4×Dic11C2×D411yescharacteristic
435C4×Dic11C2×D411yescharacteristic
436C4×Dic11C2×D411yescharacteristic
437C4×Dic11C2×D411yescharacteristic
438C4×Dic11C2×D411yescharacteristic
439C4×Dic11C2411yescharacteristic
440C4×Dic11C2411yescharacteristic
441C2×C11⋊C8C2414yes—
442D88—44no—
443#4314—44no—
444C8×D11—28no—
445C22×#127—111no—
446C2×#529—111no—
447#3217—112no—
448#3217—112no—
449#3217—112no—
450#3217—112no—
451#3217—112no—
452#3217—112no—
453#3217—111no—
454#3217—111no—
455#3217—111no—
456#3217D1111yescharacteristic, direct product factor
457C2×#496—112no—
458C2×#490—112no—
459C2×#460—112no—
460C2×#459—112no—
461C2×#450—112no—
462C2×#447—112no—
463C2×#432—111no—
464C23×C11—21no—
465C23×C11—24no—
466C23×C11—44no—
467C23×C11—44no—
468C23×C11—44no—
469C23×C11C22×D411yescharacteristic
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—21no—
473C22×D11—24no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—44no—
477C22×D11—44no—
478C22×D11—44no—
479C22×D11—48no—
480C22×D11—42no—
481C22×D11—42no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—42no—
486C22×D11—832no—
487C22×D11AGL(1,ℤ/8)14yes—
488C22×D11C22×D411yescharacteristic
489C22×D11C22×D411yescharacteristic
490Q8×C11—22no—
491D4×C11—22no—
492D4×C11—24no—
493D4×C11—24no—
494D4×C11—44no—
495D4×C11—44no—
496D4×C11—44no—
497D4×C11—44no—
498D4×C11—42no—
499D4×C11—44no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—42no—
507C2×C4×C11C22×D411yescharacteristic
508C2×C4×C11C22×D411yescharacteristic
509C2×C4×C11C22×D411yescharacteristic
510C2×C4×C11C22×D411yescharacteristic
511C2×C4×C11C22×D411yescharacteristic
512C2×C4×C11C2511yescharacteristic
513C22⋊D11—48no—
514C22⋊D11—48no—
515C22⋊D11—48no—
516C22⋊D11—48no—
517C22⋊D11—42no—
518C22⋊D11—42no—
519C22⋊D11—48no—
520C22⋊D11—42no—
521C22⋊D11—48no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—42no—
529C2×Dic11C22×D411yescharacteristic
530C2×Dic11C22×D411yescharacteristic
531C2×Dic11C22×D411yescharacteristic
532C2×Dic11C22×D411yescharacteristic
533C2×Dic11C22×D411yescharacteristic
534C2×Dic11C22×D411yescharacteristic
535D44—24no—
536D44—22no—
537D44—24no—
538D44—44no—
539D44—44no—
540D44—44no—
541D44—44no—
542D44—42no—
543D44—44no—
544C4×D11—22no—
545C4×D11—22no—
546C4×D11—22no—
547C4×D11—22no—
548C4×D11—22no—
549C4×D11—22no—
550C4×D11—22no—
551C4×D11—22no—
552C4×D11—22no—
553C4×D11—22no—
554C4×D11—42no—
555C4×D11—42no—
556C4×D11—42no—
557C4×D11—42no—
558C4×D11—42no—
559C4×D11AGL(1,ℤ/8)14yes—
560C4×D11H(5,𝔽2)14yes—
561Dic22—22no—
562Dic22—42no—
563C8×C11—24no—
564C11⋊C8—24no—
565C23×D4—112no—
566C23×D4—221no—
567C23×D4—221no—
568C22×SD16—114no—
569C22×D8—114no—
570C2×#127—112no—
571C2×#127—112no—
572C2×#127—112no—
573C2×#127—112no—
574C2×#127—112no—
575C2×#127—111no—
576C2×#127—221no—
577C2×#127—221no—
578C2×#127—221no—
579C2×#127—221no—
580C2×#127—221no—
581C2×#127—221no—
582C2×#127C2×D1111yescharacteristic, complemented
583#529—111no—
584#529—111no—
585#529—111no—
586#529—111no—
587#529—111no—
588#529—111no—
589#529—111no—
590#529—221no—
591#529—221no—
592#529—221no—
593#529—221no—
594#529C2×D1111yescharacteristic, complemented
595C2×#126—221no—
596C2×#125—111no—
597C2×#124—111no—
598C2×#123—221no—
599C2×C22⋊Q8—111no—
600C2×#121—111no—
601C2×C4×Q8—111no—
602C2×C4×D4—111no—
603C2×C4×D4—221no—
604C2×#117—221no—
605C22×C42—111no—
606#496—114no—
607#496—114no—
608#496—112no—
609#496—112no—
610#496—112no—
611#496C2×D1112yescomplemented
612#490—112no—
613#490—112no—
614#490—114no—
615#490—114no—
616#490—112no—
617#490C2×D1112yescomplemented
618#460—114no—
619#460—112no—
620#460—112no—
621#460—112no—
622#460—114no—
623#460C2×D1112yescomplemented
624#459—114no—
625#459—112no—
626#459—112no—
627#459—112no—
628#459—114no—
629#459C2×D1112yescomplemented
630#450—112no—
631#450—114no—
632#450—112no—
633#450—114no—
634#450—112no—
635#450C2×D1112yescomplemented
636#447—112no—
637#447—114no—
638#447—112no—
639#447—114no—
640#447—112no—
641#447C2×D1112yescomplemented
642#432—111no—
643#432—112no—
644#432—112no—
645#432—112no—
646#432C2×D1111yescharacteristic, complemented
647C2×C4⋊C8—112no—
648C2×#102—114no—
649C2×#102—114no—
650C2×C22⋊C8—112no—
651C2×#97—112no—
652C22×C11—21no—
653C22×C11—21no—
654C22×C11—44no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—44no—
658C22×C11—44no—
659C22×C11—41no—
660C22×C11—88no—
661C22×C11C2×AGL(1,ℤ/8)12yes—
662C22×C11C23×D411yescharacteristic
663C2×D11—21no—
664C2×D11—21no—
665C2×D11—28no—
666C2×D11—44no—
667C2×D11—41no—
668C2×D11—44no—
669C2×D11—44no—
670C2×D11—41no—
671C2×D11—41no—
672C2×D11—816no—
673C2×D11—88no—
674C2×D11—84no—
675C2×D11—816no—
676C2×D11#53512yes—
677C2×D11C2×AGL(1,ℤ/8)12yes—
678C2×D11C2×AGL(1,ℤ/8)12yes—
679C2×D11C2×AGL(1,ℤ/8)12yes—
680C4×C11—21no—
681C4×C11—21no—
682C4×C11—21no—
683C4×C11—21no—
684C4×C11—41no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11C2×AGL(1,ℤ/8)12yes—
688C4×C11C2×H(5,𝔽2)12yes—
689Dic11—21no—
690Dic11—21no—
691Dic11—21no—
692Dic11—21no—
693Dic11—41no—
694Dic11—41no—
695Dic11—41no—
696Dic11#53512yes—
697Dic11C2×AGL(1,ℤ/8)12yes—
698C25—222no—
699C22×Q8—111no—
700C22×D4—21no—
701C22×D4—21no—
702C22×D4—111no—
703C22×D4—114no—
704C22×D4—114no—
705C22×D4—112no—
706C22×D4—222no—
707C22×D4—222no—
708C22×D4—222no—
709C22×D4—222no—
710C22×D4—222no—
711C22×D4—222no—
712C22×D4—222no—
713C22×D4—222no—
714C22×D4—222no—
715C22×D4—222no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—221no—
720C22×D4—221no—
721C22×D4—221no—
722C22×D4—448no—
723C22×D4—448no—
724C22×D4—448no—
725C22×D4C22×D1112yes—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—221no—
730C2×SD16—114no—
731C2×SD16—114no—
732C2×SD16—114no—
733C2×SD16—448no—
734C2×SD16C22×D1114yescomplemented
735C2×D8—114no—
736C2×D8—114no—
737C2×D8—114no—
738C2×D8—448no—
739C2×D8C22×D1114yescomplemented
740C22×C8—114no—
741#127—21no—
742#127—21no—
743#127—114no—
744#127—114no—
745#127—112no—
746#127—112no—
747#127—222no—
748#127—222no—
749#127—222no—
750#127—222no—
751#127—222no—
752#127—222no—
753#127—222no—
754#127—222no—
755#127—222no—
756#127—222no—
757#127—221no—
758#127—221no—
759#127C22×D1112yes—
760#127C22×D1112yes—
761#126—21no—
762#126—221no—
763#126—221no—
764#126—221no—
765#126—221no—
766#126—221no—
767#126—221no—
768#126—221no—
769#125—111no—
770#125—111no—
771#125—111no—
772#125—221no—
773#125—221no—
774#125C22×D1111yescharacteristic, complemented
775#124—111no—
776#124—111no—
777#124—111no—
778#124—221no—
779#124—221no—
780#124C22×D1111yescharacteristic, complemented
781#123—21no—
782#123—221no—
783#123—221no—
784#123—221no—
785#123—221no—
786#123—221no—
787#123—221no—
788#123—221no—
789C22⋊Q8—111no—
790C22⋊Q8—111no—
791C22⋊Q8—111no—
792C22⋊Q8—221no—
793C22⋊Q8—221no—
794C22⋊Q8C22×D1111yescharacteristic
795#121—111no—
796#121—111no—
797#121—111no—
798#121—221no—
799#121—221no—
800#121C22×D1111yescharacteristic
801C4×Q8—111no—
802C4×Q8—111no—
803C4×Q8—111no—
804C4×Q8—221no—
805C4×Q8—221no—
806C4×Q8C22×D1111yescharacteristic, complemented
807C4×D4—21no—
808C4×D4—111no—
809C4×D4—111no—
810C4×D4—111no—
811C4×D4—221no—
812C4×D4—221no—
813C4×D4—221no—
814C4×D4—221no—
815C4×D4—221no—
816C4×D4—221no—
817C4×D4—221no—
818C4×D4—221no—
819C4×D4—221no—
820C4×D4C22×D1111yescharacteristic, complemented
821#117—21no—
822#117—221no—
823#117—221no—
824#117—221no—
825#117—221no—
826#117—221no—
827#117—221no—
828#117—221no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—221no—
832C2×C4⋊C4—221no—
833C2×C4⋊C4—221no—
834C2×C4⋊C4—221no—
835C2×C22⋊C4—221no—
836C2×C22⋊C4—221no—
837C2×C22⋊C4—221no—
838C2×C22⋊C4—221no—
839C2×C22⋊C4—221no—
840C2×C42—111no—
841C2×C42—111no—
842C2×C42—111no—
843C2×C42—111no—
844C2×C42—111no—
845C2×C42—111no—
846C2×C42—111no—
847C2×C42—111no—
848C2×C42—111no—
849C2×C42—111no—
850C2×C42—111no—
851C2×C42—221no—
852C2×C42C22×D1111yescharacteristic
853C4⋊C8—114no—
854C4⋊C8—112no—
855C4⋊C8C22×D1112yescomplemented
856#102—114no—
857#102—114no—
858#102—114no—
859#102—114no—
860#102—114no—
861#102—114no—
862#102C22×D1114yescomplemented
863#102C22×D1114yescomplemented
864C22⋊C8—112no—
865C22⋊C8—114no—
866C22⋊C8C22×D1112yes—
867#97—114no—
868#97—112no—
869#97C22×D1112yescomplemented
870C2×C11—22no—
871C2×C11—84no—
872C2×C11—81no—
873C2×C11C2×#53511yescharacteristic
874C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
875C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
876D11—22no—
877D11—81no—
878D11—84no—
879D11#321714yesdirect product factor
880C24—22no—
881C24—111no—
882C24—221no—
883C24—224no—
884C24—224no—
885C24—222no—
886C24—448no—
887C24—448no—
888C24—448no—
889C2×Q8—111no—
890C2×Q8—221no—
891C2×Q8—224no—
892C2×Q8C23×D1111yescharacteristic
893C2×D4—21no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—114no—
903C2×D4—111no—
904C2×D4—221no—
905C2×D4—224no—
906C2×D4—228no—
907C2×D4—228no—
908C2×D4—221no—
909C2×D4—224no—
910C2×D4—224no—
911C2×D4—224no—
912C2×D4—224no—
913C2×D4—224no—
914C2×D4—224no—
915C2×D4—221no—
916C2×D4—221no—
917C2×D4—222no—
918C2×D4—222no—
919C2×D4—222no—
920C2×D4—222no—
921C2×D4—222no—
922C2×D4—444no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—448no—
926C2×D4—444no—
927C2×D4—444no—
928C2×D4—448no—
929C2×D4—448no—
930C2×D4—448no—
931C2×D4—448no—
932C2×D4—448no—
933C2×D4—448no—
934C2×D4—448no—
935C2×D4—448no—
936C2×D4—448no—
937C2×D4—448no—
938C2×D4—448no—
939C2×D4—448no—
940C2×D4—444no—
941C2×D4C23×D1114yes—
942C2×D4C23×D1111yescharacteristic
943C22×C4—21no—
944C22×C4—111no—
945C22×C4—111no—
946C22×C4—111no—
947C22×C4—111no—
948C22×C4—111no—
949C22×C4—111no—
950C22×C4—111no—
951C22×C4—111no—
952C22×C4—111no—
953C22×C4—111no—
954C22×C4—111no—
955C22×C4—111no—
956C22×C4—111no—
957C22×C4—111no—
958C22×C4—111no—
959C22×C4—224no—
960C22×C4—224no—
961C22×C4—221no—
962C22×C4—224no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—444no—
969C22×C4D4×D1111yescharacteristic
970C22×C4D4×D1111yescharacteristic
971C22×C4C23×D1111yescharacteristic
972SD16—44no—
973SD16—444no—
974SD16—444no—
975SD16—444no—
976D8—44no—
977D8—444no—
978D8—444no—
979D8—444no—
980C2×C8—114no—
981C2×C8—228no—
982C2×C8C23×D1114yes—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—111no—
988C4⋊C4—111no—
989C4⋊C4—221no—
990C4⋊C4—221no—
991C4⋊C4—221no—
992C4⋊C4—221no—
993C4⋊C4—221no—
994C4⋊C4—221no—
995C4⋊C4—221no—
996C4⋊C4—221no—
997C4⋊C4—221no—
998C4⋊C4—221no—
999C4⋊C4—221no—
1000C4⋊C4—221no—
1001C4⋊C4—221no—
1002C4⋊C4—221no—
1003C4⋊C4C23×D1111yescharacteristic
1004C4⋊C4C23×D1111yescharacteristic
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—221no—
1011C22⋊C4—221no—
1012C22⋊C4—221no—
1013C22⋊C4—221no—
1014C22⋊C4—221no—
1015C22⋊C4—221no—
1016C22⋊C4—221no—
1017C22⋊C4—221no—
1018C22⋊C4—221no—
1019C22⋊C4—221no—
1020C22⋊C4—221no—
1021C22⋊C4—221no—
1022C22⋊C4—221no—
1023C22⋊C4—221no—
1024C22⋊C4—221no—
1025C42—21no—
1026C42—111no—
1027C42—111no—
1028C42—111no—
1029C42—111no—
1030C42—111no—
1031C42—111no—
1032C42—111no—
1033C42—111no—
1034C42—111no—
1035C42—111no—
1036C42—111no—
1037C42—111no—
1038C42—221no—
1039C42—221no—
1040C42—221no—
1041C42D4×D1111yescharacteristic
1042C42D4×D1111yescharacteristic
1043C42C23×D1111yescharacteristic
1044C42C23×D1111yescharacteristic
1045C11C2×#321711yescharacteristic, complemented, Sylow
1046C23—21no—
1047C23—24no—
1048C23—44no—
1049C23—44no—
1050C23—44no—
1051C23—111no—
1052C23—114no—
1053C23—111no—
1054C23—222no—
1055C23—222no—
1056C23—221no—
1057C23—224no—
1058C23—444no—
1059C23—444no—
1060C23—442no—
1061C23—448no—
1062C23—442no—
1063C23—448no—
1064C23—448no—
1065C23—448no—
1066C23—442no—
1067C23—448no—
1068C23—448no—
1069C23—444no—
1070C23—8832no—
1071C23C2×D4×D1111yescharacteristic
1072Q8—22no—
1073Q8—222no—
1074Q8—442no—
1075D4—22no—
1076D4—24no—
1077D4—24no—
1078D4—44no—
1079D4—44no—
1080D4—44no—
1081D4—44no—
1082D4—42no—
1083D4—44no—
1084D4—222no—
1085D4—224no—
1086D4—224no—
1087D4—444no—
1088D4—444no—
1089D4—444no—
1090D4—444no—
1091D4—442no—
1092D4—448no—
1093D4—442no—
1094D4—448no—
1095D4—448no—
1096D4—448no—
1097D4—448no—
1098D4—448no—
1099D4—442no—
1100D4—442no—
1101D4—444no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—42no—
1109C2×C4—111no—
1110C2×C4—111no—
1111C2×C4—114no—
1112C2×C4—114no—
1113C2×C4—111no—
1114C2×C4—111no—
1115C2×C4—111no—
1116C2×C4—111no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—442no—
1134C2×C4—442no—
1135C2×C4—442no—
1136C2×C4—442no—
1137C2×C4—442no—
1138C2×C4—442no—
1139C2×C4C2×D4×D1111yescharacteristic
1140C2×C4C2×D4×D1111yescharacteristic
1141C2×C4C2×D4×D1111yescharacteristic
1142C2×C4C2×D4×D1111yescharacteristic
1143C2×C4C2×D4×D1111yescharacteristic
1144C2×C4C24×D1111yescharacteristic
1145C8—24no—
1146C8—224no—
1147C22—21no—
1148C22—21no—
1149C22—44no—
1150C22—41no—
1151C22—41no—
1152C22—44no—
1153C22—44no—
1154C22—41no—
1155C22—88no—
1156C22—112no—
1157C22—112no—
1158C22—112no—
1159C22—112no—
1160C22—228no—
1161C22—221no—
1162C22—221no—
1163C22—444no—
1164C22—441no—
1165C22—441no—
1166C22—444no—
1167C22—444no—
1168C22—441no—
1169C22—888no—
1170C22—8816no—
1171C22—884no—
1172C22—8816no—
1173C22D11×AGL(1,ℤ/8)12yes—
1174C22C22×D4×D1111yescharacteristic
1175C4—21no—
1176C4—21no—
1177C4—21no—
1178C4—21no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—112no—
1183C4—112no—
1184C4—221no—
1185C4—221no—
1186C4—221no—
1187C4—221no—
1188C4—441no—
1189C4—441no—
1190C4—441no—
1191C4D11×AGL(1,ℤ/8)12yes—
1192C4D11×H(5,𝔽2)12yes—
1193C2—22no—
1194C2—84no—
1195C2—81no—
1196C2—114no—
1197C2—222no—
1198C2—884no—
1199C2—881no—
1200C2D11×#53511yescharacteristic
1201C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1202C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3217C2
socleC22×C11C23×D4
hypercenter#3217D11
hypocenterC11C2×#3217
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. C2×D11×#127C2semidirect
2. D11×#529C2semidirect
3. #13079638C2semidirect
4. #13079637C2semidirect
5. #13079636C2semidirect
6. #13079635C2semidirect
7. #13079634C2semidirect
8. #13079633C2semidirect
9. #13079632C2semidirect
10. #13079631C2semidirect
11. #13079630C2semidirect
12. D11×#496C2semidirect
13. D11×#490C2semidirect
14. D11×#460C2semidirect
15. D11×#459C2semidirect
16. D11×#450C2semidirect
17. D11×#447C2semidirect
18. D11×#432C2semidirect
19. C11×#3217C2semidirect
23. C2×C11×#127C22semidirect
24. C11×#529C22semidirect
27. C2×#66993C22semidirect
28. C2×SD16×D11C22semidirect
29. C2×D8×D11C22semidirect
36. D11×#127C22semidirect
37. D11×#127C22semidirect
40. #10623222C22semidirect
41. D11×#125C22semidirect
42. #10623211C22semidirect
43. D11×#124C22semidirect
47. #10623155C22semidirect
49. #10623131C22semidirect
50. #10623111C22semidirect
51. C4×Q8×D11C22semidirect
52. #10623088C22semidirect
54. C4×D4×D11C22semidirect
58. #10623010C22semidirect
59. C2×#66927C22semidirect
61. C11×#496C22semidirect
62. C11×#490C22semidirect
63. C11×#460C22semidirect
64. C11×#459C22semidirect
65. C11×#450C22semidirect
66. C11×#447C22semidirect
67. C11×#432C22semidirect
68. #10622831C22semidirect
69. #10622830C22semidirect
70. #10622789C22semidirect
71. #10622782C22semidirect
72. #10622776C22semidirect
73. #10622769C22semidirect
74. #10622767C22semidirect
75. #10622763C22semidirect
76. #10622688C22semidirect
77. #10622687C22semidirect
78. #10622685C22semidirect
79. #10622684C22semidirect
80. #10622680C22semidirect
81. #10622671C22semidirect
82. #10622659C22semidirect
83. #10622649C22semidirect
84. #10622640C22semidirect
85. #10622628C22semidirect
86. #10622539C22semidirect
87. #10622461C22semidirect
88. #10622456C22semidirect
89. #10622448C22semidirect
90. D11×C4⋊C8C22semidirect
91. #10622399C22semidirect
92. #10622389C22semidirect
93. #10622386C22semidirect
94. D11×#102C22semidirect
95. D11×#102C22semidirect
96. #10622377C22semidirect
97. #10622377C22semidirect
98. #10622375C22semidirect
99. #10622345C22semidirect
100. #10622344C22semidirect
102. #10622332C22semidirect
103. #10622326C22semidirect
104. #10622325C22semidirect
105. #10622318C22semidirect
106. D11×#97C22semidirect
139. C2×C11×SD16C23semidirect
140. C2×C11×D8C23semidirect
146. C11×#125C23semidirect
147. C11×#124C23semidirect
151. C4×Q8×C11C23semidirect
153. C4×D4×C11C23semidirect
156. #67000C23semidirect
158. Q8×Dic11C23semidirect
159. C2×#4325C23semidirect
174. #66989C23semidirect
177. D4×Dic11C23semidirect
178. C2×#4324C23semidirect
179. C2×#4323C23semidirect
180. C2×#4323C23semidirect
193. C2×D88C23semidirect
194. C2×#4314C23semidirect
205. #66946C23semidirect
214. #66943C23semidirect
215. #66943C23semidirect
219. #66940C23semidirect
241. #66928C23semidirect
247. C4×D44C23semidirect
259. #66923C23semidirect
261. C4×Dic22C23semidirect
262. C11×C4⋊C8C23semidirect
263. C11×#102C23semidirect
264. C11×#102C23semidirect
266. C11×#97C23semidirect
267. #66896C23semidirect
268. #66896C23semidirect
270. #66885C23semidirect
271. #66885C23semidirect
273. #66879C23semidirect
274. Dic11⋊C8C23semidirect
275. #66873C23semidirect
276. #66873C23semidirect
277. C4⋊(C11⋊C8)C23semidirect
278. #66867C23semidirect
456. #3217D11direct (N × H)
582. C2×#127C2×D11semidirect
594. #529C2×D11semidirect
611. #496C2×D11semidirect
617. #490C2×D11semidirect
623. #460C2×D11semidirect
629. #459C2×D11semidirect
635. #450C2×D11semidirect
641. #447C2×D11semidirect
646. #432C2×D11semidirect
734. C2×SD16C22×D11semidirect
739. C2×D8C22×D11semidirect
774. #125C22×D11semidirect
780. #124C22×D11semidirect
806. C4×Q8C22×D11semidirect
820. C4×D4C22×D11semidirect
855. C4⋊C8C22×D11semidirect
862. #102C22×D11semidirect
863. #102C22×D11semidirect
869. #97C22×D11semidirect
879. D11#3217direct (N × H)
1045. C11C2×#3217semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1272
D11×#5292
#130796382
#130796372
#130796362
#130796352
#130796342
#130796332
#130796322
#130796312
#130796302
D11×#4962
D11×#4902
D11×#4602
D11×#4592
D11×#4502
D11×#4472
D11×#4322
C11×#32172
C2×#321711