Finite Group Databasebeta

← D11×#3233 #15625845

Subgroups — D11×#3233 #15625845

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic, complemented
2D11×#529C211yesmaximal, characteristic
3#13079800C211yesmaximal, characteristic, complemented
4#13079799C211yesmaximal, characteristic, complemented
5#13079798C212yesmaximal, complemented
6#13079797C211yesmaximal, characteristic, complemented
7#13079796C212yesmaximal, complemented
8#13079795C211yesmaximal, characteristic, complemented
9#13079794C211yesmaximal, characteristic, complemented
10#13079793C211yesmaximal, characteristic, complemented
11#13079792C212yesmaximal, complemented
12#13079791C211yesmaximal, characteristic, complemented
13#13079790C212yesmaximal, complemented
14D11×#499C212yesmaximal, complemented
15D11×#488C212yesmaximal, complemented
16D11×#485C212yesmaximal, complemented
17D11×#482C212yesmaximal
18D11×#477C211yesmaximal, characteristic, complemented
19D11×#475C211yesmaximal, characteristic, complemented
20D11×#476C211yesmaximal, characteristic, complemented
21D11×#474C211yesmaximal, characteristic, complemented
22D11×#431C211yesmaximal, characteristic, complemented
23C11×#3233C211yesmaximal, characteristic, complemented
24C11×#533C2211yescharacteristic, complemented
25C11×#529C2211yescharacteristic
26#10623259C2211yescharacteristic, complemented
27#10623259C2211yescharacteristic, complemented
28D11×C4⋊Q8C2211yescharacteristic
29D11×C4⋊Q8C2211yescharacteristic
30#10623237—21no—
31D11×#126—21no—
32#10623222C2211yescharacteristic
33#10623219C2212yescomplemented
34D11×#125C2211yescharacteristic
35D11×#125C2212yes—
36#10623211C2211yescharacteristic
37D11×#124C2211yescharacteristic
38D11×#123—21no—
39#10623180—21no—
40D11×C22⋊Q8—21no—
41D11×C22⋊Q8—21no—
42D11×C22⋊Q8C2211yescharacteristic
43#10623155C2211yescharacteristic
44#10623153—21no—
45#10623153—21no—
46D11×#121C2211yescharacteristic
47#10623131C2211yescharacteristic
48#10623111C2211yescharacteristic
49#10623109—21no—
50#10623109—21no—
51C4×Q8×D11—21no—
52C4×Q8×D11—21no—
53C4×Q8×D11C2211yescharacteristic
54#10623088C2211yescharacteristic
55C4×D4×D11—21no—
56C4×D4×D11C2211yescharacteristic
57#10623069—21no—
58#10623059—21no—
59D11×#117—21no—
60D11×#117C2212yes—
61#10623048C2212yescomplemented
62#10623010C2211yescharacteristic
63C2×C42×D11C2211yescharacteristic
64#10623001C2211yescharacteristic, complemented
65C11×#499C2212yescomplemented
66C11×#488C2212yescomplemented
67C11×#485C2212yescomplemented
68C11×#482C2212yes—
69C11×#477C2211yescharacteristic, complemented
70C11×#476C2211yescharacteristic, complemented
71C11×#475C2211yescharacteristic, complemented
72C11×#474C2211yescharacteristic, complemented
73C11×#431C2211yescharacteristic, complemented
74#10622707C2211yescharacteristic, complemented
75#10622704C2211yescharacteristic, complemented
76#10622700C2211yescharacteristic, complemented
77#10622697C2211yescharacteristic, complemented
78#10622681C2212yescomplemented
79#10622677C2212yescomplemented
80#10622677C2212yescomplemented
81#10622669C2212yescomplemented
82#10622658C2212yescomplemented
83#10622648C2212yes—
84#10622634C2211yescharacteristic, complemented
85#10622633C2211yescharacteristic, complemented
86#10622621C2211yescharacteristic, complemented
87#10622620C2211yescharacteristic, complemented
88#10622616C2212yes—
89#10622609C2212yescomplemented
90#10622538C2211yescharacteristic, complemented
91#10622503C2212yescomplemented
92#10622501C2212yescomplemented
93#10622498C2212yes—
94D11×#107C2212yes—
95D11×#107C2212yes—
96#10622491C2212yescomplemented
97#10622491C2212yescomplemented
98#10622488C2212yescomplemented
99#10622483C2212yescomplemented
100#10622480C2212yescomplemented
101#10622479C2212yes—
102D11×#106C2212yes—
103D11×#106C2212yes—
104#10622471C2212yescomplemented
105#10622471C2212yescomplemented
106#10622467C2212yescomplemented
107#10622464C2211yescharacteristic, complemented
108#10622463C2211yescharacteristic, complemented
109#10622459C2211yescharacteristic, complemented
110#10622455C2211yescharacteristic, complemented
111#10622446C2211yescharacteristic, complemented
112#10622446C2211yescharacteristic, complemented
113D11×C4⋊C8C2211yescharacteristic
114D11×C4⋊C8C2211yescharacteristic
115#10622428C2212yescomplemented
116#10622427C2212yescomplemented
117D11×#103C2212yes—
118D11×#103C2212yes—
119#10622413C2212yescomplemented
120#10622413C2212yescomplemented
121#10622407C2212yescomplemented
122#10622404C2212yescomplemented
123#10622397C2212yes—
124#10622392C2212yes—
125D11×#102C2212yes—
126D11×#102C2212yes—
127#10622381C2212yescomplemented
128#10622381C2212yescomplemented
129#10622374C2212yescomplemented
130#10622372C2212yescomplemented
131#10622350C2212yes—
132D11×C22⋊C8C2212yes—
133#10622336C2212yescomplemented
134#10622331C2212yescomplemented
135#10622310C2212yescomplemented
136#10622298C2212yescomplemented
137C4×C8×D11C2212yes—
138#10622296C2212yescomplemented
139C2×Q8×D11—21no—
140C2×Q8×D11—21no—
141C2×Q8×D11C2311yescharacteristic
142C2×D4×D11—21no—
143C2×D4×D11C2311yescharacteristic
144C22×C4×D11—21no—
145C22×C4×D11D411yescharacteristic
146C22×C4×D11D411yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C11×C4⋊Q8C2311yescharacteristic
149C11×C4⋊Q8C2311yescharacteristic
150C11×#126—21no—
151C11×#125C2311yescharacteristic
152C11×#125C2312yes—
153C11×#124C2311yescharacteristic
154C11×#123—21no—
155C11×C22⋊Q8—21no—
156C11×C22⋊Q8—21no—
157C11×C22⋊Q8C2311yescharacteristic
158C11×#121C2311yescharacteristic
159C4×Q8×C11—21no—
160C4×Q8×C11—21no—
161C4×Q8×C11C2311yescharacteristic
162C4×D4×C11—21no—
163C4×D4×C11C2311yescharacteristic
164C11×#117—21no—
165C11×#117C2312yes—
166C2×C42×C11C2311yescharacteristic
167#67000C2311yescharacteristic
168#66999—21no—
169#66999—21no—
170#66999C2311yescharacteristic
171Q8×Dic11—21no—
172Q8×Dic11—21no—
173Q8×Dic11C2311yescharacteristic
174#66997—21no—
175#66997—21no—
176#66992—21no—
177#66991C2311yescharacteristic
178#66989C2311yescharacteristic
179#66988—21no—
180D4×Dic11—21no—
181D4×Dic11C2311yescharacteristic
182#66983C2311yescharacteristic
183#66982—21no—
184C4×C22⋊D11—21no—
185C4×C22⋊D11—21no—
186C4×C22⋊D11—21no—
187#66979—21no—
188#66979C2312yes—
189#66977—21no—
190#66977—21no—
191#66977C2311yescharacteristic
192C2×C4×Dic11D411yescharacteristic
193C2×C4×Dic11D411yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C8×D11C2312yes—
196C2×C8×D11C2312yes—
197#66951—21no—
198#66951—21no—
199#66951—21no—
200#66950—21no—
201#66950—21no—
202#66950C2311yescharacteristic
203#66949—21no—
204#66949—22no—
205#66949—22no—
206#66948C2311yescharacteristic
207#66947—21no—
208#66947—21no—
209#66946—21no—
210#66946C2311yescharacteristic
211#66945—21no—
212#66945—21no—
213#66945C2312yes—
214#66945C2312yes—
215C4⋊C4×D11—21no—
216C4⋊C4×D11—21no—
217C4⋊C4×D11—21no—
218C4⋊C4×D11—21no—
219C4⋊C4×D11—21no—
220C4⋊C4×D11—21no—
221C4⋊C4×D11—22no—
222C4⋊C4×D11—22no—
223C4⋊C4×D11C2311yescharacteristic
224C4⋊C4×D11C2311yescharacteristic
225C4⋊C4×D11C2312yes—
226C4⋊C4×D11C2312yes—
227#66943C2311yescharacteristic
228#66943C2311yescharacteristic
229#66943C2312yes—
230#66943C2312yes—
231#66942—21no—
232#66942—21no—
233#66942—22no—
234#66942—22no—
235#66941—21no—
236#66941—21no—
237#66941C2312yes—
238#66941C2312yes—
239#66940—21no—
240#66940—21no—
241#66940—21no—
242#66940—22no—
243#66940—22no—
244#66940C2311yescharacteristic
245#66939—21no—
246#66938—21no—
247#66938—21no—
248#66937—21no—
249#66936—21no—
250#66936—21no—
251(C22⋊D11)⋊C4—21no—
252(C22⋊D11)⋊C4—21no—
253(C22⋊D11)⋊C4—21no—
254C22⋊C4×D11—22no—
255C22⋊C4×D11—21no—
256C22⋊C4×D11—21no—
257C22⋊C4×D11—21no—
258C22⋊C4×D11—21no—
259C22⋊C4×D11—21no—
260#66932—21no—
261#66932—21no—
262#66932—21no—
263#66931—22no—
264#66931—22no—
265#66931—21no—
266#66930—22no—
267#66930—21no—
268#66930—21no—
269#66929—21no—
270#66928C2311yescharacteristic
271C4×D44—21no—
272C4×D44C2311yescharacteristic
273#66925—22no—
274#66925—21no—
275#66925—21no—
276C42×D11—21no—
277C42×D11—22no—
278C42×D11D411yescharacteristic
279C42×D11D411yescharacteristic
280C42×D11D411yescharacteristic
281C42×D11D411yescharacteristic
282C42×D11C2311yescharacteristic
283C42×D11C2311yescharacteristic
284C42×D11C2311yescharacteristic
285C42×D11C2311yescharacteristic
286#66923C2312yes—
287#66923C2311yescharacteristic
288#66922C2311yescharacteristic
289#66922C2311yescharacteristic
290C4×Dic22—21no—
291C4×Dic22—21no—
292C4×Dic22—22no—
293C4×Dic22—22no—
294C4×Dic22—21no—
295C4×Dic22C2311yescharacteristic
296C11×#107C2312yes—
297C11×#107C2312yes—
298C11×#106C2312yes—
299C11×#106C2312yes—
300C11×C4⋊C8C2311yescharacteristic
301C11×C4⋊C8C2311yescharacteristic
302C11×#103C2312yes—
303C11×#103C2312yes—
304C11×#102C2312yes—
305C11×#102C2312yes—
306C11×C22⋊C8C2312yes—
307C4×C8×C11C2312yes—
308#66899C2312yes—
309#66899C2312yes—
310#66896C2312yes—
311#66896C2312yes—
312C22⋊(C11⋊C8)C2312yes—
313#66885C2312yes—
314#66885C2312yes—
315(C2×D11)⋊C8C2312yes—
316(C2×D11)⋊C8C2312yes—
317#66882C2312yes—
318#66882C2312yes—
319#66881C2312yes—
320#66881C2312yes—
321#66880C2312yes—
322#66880C2312yes—
323Dic11⋊C8C2312yes—
324Dic11⋊C8C2312yes—
325C8×Dic11C2312yes—
326C8×Dic11C2312yes—
327#66874C2312yes—
328#66874C2312yes—
329#66873C2312yes—
330#66873C2312yes—
331#66872C2312yes—
332#66872C2312yes—
333#66872C2312yes—
334#66872C2312yes—
335#66871C2312yes—
336#66871C2312yes—
337#66871C2312yes—
338#66871C2312yes—
339C4⋊(C11⋊C8)C2311yescharacteristic
340C4⋊(C11⋊C8)C2311yescharacteristic
341C4×C11⋊C8C2312yes—
342C2×#3233—111nomaximal, Sylow
343C23×D11—21no—
344C23×D11C2×D411yescharacteristic
345C2×Q8×C11—21no—
346C2×Q8×C11—21no—
347C2×Q8×C11C2411yescharacteristic
348C2×D4×C11—21no—
349C2×D4×C11C2411yescharacteristic
350C22×C4×C11—21no—
351C22×C4×C11C2×D411yescharacteristic
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2411yescharacteristic
354C2×C22⋊D11—21no—
355C2×C22⋊D11—21no—
356C2×C22⋊D11—21no—
357C22×Dic11—21no—
358C22×Dic11C2×D411yescharacteristic
359C22×Dic11C2×D411yescharacteristic
360C22×Dic11C2×D411yescharacteristic
361Q8×D11—22no—
362Q8×D11—22no—
363Q8×D11—44no—
364Q8×D11—44no—
365D4×D11—22no—
366D4×D11—22no—
367D4×D11—44no—
368C2×D44—21no—
369C2×D44C2411yescharacteristic
370C2×C4×D11—24no—
371C2×C4×D11—22no—
372C2×C4×D11—22no—
373C2×C4×D11—21no—
374C2×C4×D11—21no—
375C2×C4×D11—21no—
376C2×C4×D11—22no—
377C2×C4×D11—22no—
378C2×C4×D11—21no—
379C2×C4×D11—21no—
380C2×C4×D11—42no—
381C2×C4×D11—44no—
382C2×C4×D11C2×D411yescharacteristic
383C2×C4×D11C2×D411yescharacteristic
384C2×C4×D11C2×D411yescharacteristic
385C2×C4×D11C2×D411yescharacteristic
386C2×C4×D11C2×D411yescharacteristic
387C2×C4×D11C2×D411yescharacteristic
388C2×C4×D11C2×D411yescharacteristic
389C2×C4×D11C2×D411yescharacteristic
390C2×C4×D11C2×D411yescharacteristic
391C2×C4×D11C2×D411yescharacteristic
392C2×C4×D11C2411yescharacteristic
393C2×C4×D11C2411yescharacteristic
394C2×Dic22—21no—
395C2×Dic22—22no—
396C2×Dic22—22no—
397C2×Dic22—21no—
398C2×Dic22—21no—
399C2×Dic22C2411yescharacteristic
400C2×C8×C11C2412yes—
401C2×C8×C11C2412yes—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4C2411yescharacteristic
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2412yes—
413C11×C4⋊C4C2412yes—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—21no—
420C42×C11—22no—
421C42×C11—21no—
422C42×C11C2×D411yescharacteristic
423C42×C11C2×D411yescharacteristic
424C42×C11C2411yescharacteristic
425C42×C11C2411yescharacteristic
426C22⋊Dic11—21no—
427C22⋊Dic11—21no—
428C22⋊Dic11—21no—
429C22⋊Dic11—21no—
430C22⋊Dic11—22no—
431C22⋊Dic11—21no—
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—21no—
434(C2×D11)⋊C4—21no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—21no—
439(C2×D11)⋊C4—21no—
440(C2×D11)⋊C4—21no—
441(C2×D11)⋊C4—21no—
442(C2×D11)⋊C4—21no—
443(C2×D11)⋊C4—21no—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—21no—
447C4⋊Dic11—21no—
448C4⋊Dic11—21no—
449C4⋊Dic11—21no—
450C4⋊Dic11—21no—
451C4⋊Dic11—21no—
452C4⋊Dic11C2411yescharacteristic
453C4⋊Dic11C2411yescharacteristic
454C4⋊Dic11C2412yes—
455C4⋊Dic11C2412yes—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—21no—
461Dic11⋊C4—21no—
462Dic11⋊C4—21no—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465Dic11⋊C4—21no—
466Dic11⋊C4—21no—
467Dic11⋊C4—21no—
468Dic11⋊C4—22no—
469Dic11⋊C4—22no—
470Dic11⋊C4—21no—
471Dic11⋊C4—21no—
472Dic11⋊C4—21no—
473Dic11⋊C4—21no—
474C4×Dic11—21no—
475C4×Dic11—22no—
476C4×Dic11—22no—
477C4×Dic11—21no—
478C4×Dic11—22no—
479C4×Dic11—21no—
480C4×Dic11C2×D411yescharacteristic
481C4×Dic11C2×D411yescharacteristic
482C4×Dic11C2×D411yescharacteristic
483C4×Dic11C2×D411yescharacteristic
484C4×Dic11C2×D411yescharacteristic
485C4×Dic11C2×D411yescharacteristic
486C4×Dic11C2×D411yescharacteristic
487C4×Dic11C2×D411yescharacteristic
488C4×Dic11C2×D411yescharacteristic
489C4×Dic11C2×D411yescharacteristic
490C4×Dic11C2411yescharacteristic
491C4×Dic11C2411yescharacteristic
492C2×C11⋊C8C2412yes—
493C2×C11⋊C8C2412yes—
494C8×D11—24no—
495C8×D11—24no—
496C2×#533—111no—
497C2×#529—111no—
498#3233—112no—
499#3233—112no—
500#3233—112no—
501#3233—112no—
502#3233—111no—
503#3233—111no—
504#3233—111no—
505#3233—111no—
506#3233—111no—
507#3233—111no—
508#3233—111no—
509#3233D1111yescharacteristic, direct product factor
510C2×#499—112no—
511C2×#488—112no—
512C2×#485—112no—
513C2×#482—112no—
514C2×#477—111no—
515C2×#475—111no—
516C2×#476—111no—
517C2×#474—111no—
518C2×#431—111no—
519C23×C11—21no—
520C23×C11C22×D411yescharacteristic
521C22×D11—22no—
522C22×D11—22no—
523C22×D11—22no—
524C22×D11—21no—
525C22×D11—42no—
526C22×D11—42no—
527C22×D11—42no—
528C22×D11C22×D411yescharacteristic
529C22×D11C22×D411yescharacteristic
530Q8×C11—21no—
531Q8×C11—21no—
532Q8×C11—42no—
533Q8×C11—42no—
534D4×C11—21no—
535D4×C11—21no—
536D4×C11—42no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—41no—
546C2×C4×C11—42no—
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2511yescharacteristic
553C22⋊D11—42no—
554C22⋊D11—42no—
555C22⋊D11—42no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—21no—
561C2×Dic11—21no—
562C2×Dic11—21no—
563C2×Dic11—41no—
564C2×Dic11—42no—
565C2×Dic11C22×D411yescharacteristic
566C2×Dic11C22×D411yescharacteristic
567C2×Dic11C22×D411yescharacteristic
568C2×Dic11C22×D411yescharacteristic
569C2×Dic11C22×D411yescharacteristic
570C2×Dic11C22×D411yescharacteristic
571D44—21no—
572D44—21no—
573D44—42no—
574C4×D11—22no—
575C4×D11—22no—
576C4×D11—22no—
577C4×D11—22no—
578C4×D11—22no—
579C4×D11—21no—
580C4×D11—21no—
581C4×D11—22no—
582C4×D11—22no—
583C4×D11—41no—
584C4×D11—41no—
585C4×D11—42no—
586C4×D11—42no—
587C4×D11—44no—
588C4×D11—42no—
589C4×D11—44no—
590C4×D11—42no—
591C4×D11—42no—
592C4×D11#13514yes—
593C4×D112−1+412yes—
594C4×D112−1+412yes—
595Dic22—21no—
596Dic22—21no—
597Dic22—44no—
598Dic22—42no—
599Dic22—42no—
600Dic22—42no—
601Dic22—44no—
602C8×C11—22no—
603C8×C11—22no—
604C11⋊C8—22no—
605C11⋊C8—22no—
606#533—111no—
607#533—111no—
608#533—112no—
609#533—112no—
610#533—111no—
611#533—221no—
612#533—221no—
613#533—221no—
614#533—221no—
615#533C2×D1111yescharacteristic, complemented
616C2×C4⋊Q8—111no—
617C2×C4⋊Q8—111no—
618#529—111no—
619#529—111no—
620#529—111no—
621#529—111no—
622#529—111no—
623#529—111no—
624#529—111no—
625#529—221no—
626#529—221no—
627#529—221no—
628#529—221no—
629#529C2×D1111yescharacteristic
630C2×#126—221no—
631C2×#125—112no—
632C2×#125—111no—
633C2×#124—111no—
634C2×#123—221no—
635C2×C22⋊Q8—111no—
636C2×C22⋊Q8—221no—
637C2×C22⋊Q8—221no—
638C2×#121—111no—
639C2×C4×Q8—111no—
640C2×C4×Q8—221no—
641C2×C4×Q8—221no—
642C2×C4×D4—111no—
643C2×C4×D4—221no—
644C2×#117—112no—
645C2×#117—221no—
646C22×C42—111no—
647#499—112no—
648#499—112no—
649#499—112no—
650#499—112no—
651#499—112no—
652#499—112no—
653#499—112no—
654#499C2×D1112yescomplemented
655#488—112no—
656#488—112no—
657#488—112no—
658#488—112no—
659#488—112no—
660#488—112no—
661#488—112no—
662#488C2×D1112yescomplemented
663#485—112no—
664#485—112no—
665#485—112no—
666#485—112no—
667#485—112no—
668#485—112no—
669#485—112no—
670#485C2×D1112yescomplemented
671#482—112no—
672#482—112no—
673#482—112no—
674#482—112no—
675#482—112no—
676#482—112no—
677#482—112no—
678#482C2×D1112yes—
679#477—111no—
680#477—111no—
681#477—112no—
682#477—111no—
683#477—112no—
684#477C2×D1111yescharacteristic, complemented
685#476—111no—
686#476—111no—
687#476—112no—
688#476—111no—
689#476—112no—
690#476C2×D1111yescharacteristic, complemented
691#475—111no—
692#475—111no—
693#475—112no—
694#475—111no—
695#475—112no—
696#475C2×D1111yescharacteristic, complemented
697#474—111no—
698#474—111no—
699#474—112no—
700#474—111no—
701#474—112no—
702#474C2×D1111yescharacteristic, complemented
703#431—111no—
704#431—111no—
705#431—111no—
706#431—112no—
707#431—112no—
708#431C2×D1111yescharacteristic, complemented
709C2×#107—112no—
710C2×#107—112no—
711C2×#106—112no—
712C2×#106—112no—
713C2×C4⋊C8—111no—
714C2×C4⋊C8—111no—
715C2×#103—112no—
716C2×#103—112no—
717C2×#102—112no—
718C2×#102—112no—
719C2×C22⋊C8—112no—
720C2×C4×C8—112no—
721C22×C11—21no—
722C22×C11—21no—
723C22×C11—21no—
724C22×C11—41no—
725C22×C11—41no—
726C22×C11—41no—
727C22×C11C23×D411yescharacteristic
728C2×D11—21no—
729C2×D11—21no—
730C2×D11—21no—
731C2×D11—44no—
732C2×D11—41no—
733C2×D11—41no—
734C2×D11—41no—
735C2×D11—84no—
736C2×D11#53612yes—
737C2×D11C2×#13512yes—
738C2×D11#57512yes—
739C4×C11—21no—
740C4×C11—21no—
741C4×C11—21no—
742C4×C11—21no—
743C4×C11—41no—
744C4×C11—41no—
745C4×C11—42no—
746C4×C11—41no—
747C4×C11—42no—
748C4×C11C2×#13512yes—
749C4×C11C2×2−1+411yescharacteristic
750C4×C11C2×2−1+411yescharacteristic
751Dic11—21no—
752Dic11—21no—
753Dic11—21no—
754Dic11—21no—
755Dic11—41no—
756Dic11—42no—
757Dic11—41no—
758Dic11—42no—
759Dic11—41no—
760Dic11#53612yes—
761Dic11C2×#13512yes—
762C22×Q8—111no—
763C22×Q8—221no—
764C22×Q8—221no—
765C22×D4—111no—
766C22×D4—221no—
767C23×C4—111no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—221no—
771C22×C8—112no—
772C22×C8—112no—
773C4⋊Q8—112no—
774C4⋊Q8—112no—
775C4⋊Q8—111no—
776C4⋊Q8—111no—
777C4⋊Q8—221no—
778C4⋊Q8—221no—
779C4⋊Q8—221no—
780C4⋊Q8—221no—
781C4⋊Q8C22×D1111yescharacteristic
782C4⋊Q8C22×D1111yescharacteristic
783#126—21no—
784#126—221no—
785#126—221no—
786#126—221no—
787#126—221no—
788#126—221no—
789#126—221no—
790#126—221no—
791#125—111no—
792#125—111no—
793#125—112no—
794#125—112no—
795#125—111no—
796#125—112no—
797#125—221no—
798#125—221no—
799#125—222no—
800#125—222no—
801#125C22×D1111yescharacteristic
802#125C22×D1112yes—
803#124—111no—
804#124—111no—
805#124—111no—
806#124—221no—
807#124—221no—
808#124C22×D1111yescharacteristic
809#123—21no—
810#123—221no—
811#123—221no—
812#123—221no—
813#123—221no—
814#123—221no—
815#123—221no—
816#123—221no—
817C22⋊Q8—21no—
818C22⋊Q8—21no—
819C22⋊Q8—111no—
820C22⋊Q8—111no—
821C22⋊Q8—111no—
822C22⋊Q8—221no—
823C22⋊Q8—222no—
824C22⋊Q8—222no—
825C22⋊Q8—221no—
826C22⋊Q8—222no—
827C22⋊Q8—222no—
828C22⋊Q8—221no—
829C22⋊Q8—221no—
830C22⋊Q8—221no—
831C22⋊Q8—221no—
832C22⋊Q8—221no—
833C22⋊Q8—221no—
834C22⋊Q8C22×D1111yescharacteristic
835#121—111no—
836#121—111no—
837#121—111no—
838#121—221no—
839#121—221no—
840#121C22×D1111yescharacteristic
841C4×Q8—21no—
842C4×Q8—21no—
843C4×Q8—111no—
844C4×Q8—111no—
845C4×Q8—111no—
846C4×Q8—221no—
847C4×Q8—222no—
848C4×Q8—222no—
849C4×Q8—221no—
850C4×Q8—222no—
851C4×Q8—221no—
852C4×Q8—222no—
853C4×Q8—221no—
854C4×Q8—221no—
855C4×Q8—221no—
856C4×Q8—221no—
857C4×Q8—221no—
858C4×Q8C22×D1111yescharacteristic
859C4×D4—21no—
860C4×D4—111no—
861C4×D4—111no—
862C4×D4—111no—
863C4×D4—221no—
864C4×D4—221no—
865C4×D4—221no—
866C4×D4—221no—
867C4×D4—221no—
868C4×D4—221no—
869C4×D4—221no—
870C4×D4—221no—
871C4×D4—221no—
872C4×D4C22×D1111yescharacteristic
873#117—21no—
874#117—112no—
875#117—112no—
876#117—112no—
877#117—221no—
878#117—222no—
879#117—221no—
880#117—221no—
881#117—221no—
882#117—221no—
883#117—221no—
884#117—222no—
885#117—221no—
886#117C22×D1112yes—
887C2×C4⋊C4—112no—
888C2×C4⋊C4—112no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—221no—
892C2×C4⋊C4—221no—
893C2×C4⋊C4—221no—
894C2×C4⋊C4—221no—
895C2×C4⋊C4—222no—
896C2×C4⋊C4—222no—
897C2×C4⋊C4—221no—
898C2×C4⋊C4—221no—
899C2×C22⋊C4—221no—
900C2×C22⋊C4—221no—
901C2×C22⋊C4—221no—
902C2×C22⋊C4—221no—
903C2×C22⋊C4—222no—
904C2×C22⋊C4—221no—
905C2×C42—111no—
906C2×C42—111no—
907C2×C42—111no—
908C2×C42—111no—
909C2×C42—111no—
910C2×C42—111no—
911C2×C42—111no—
912C2×C42—111no—
913C2×C42—111no—
914C2×C42—111no—
915C2×C42—111no—
916C2×C42—222no—
917C2×C42—221no—
918C2×C42C22×D1111yescharacteristic
919#107—112no—
920#107—112no—
921#107—112no—
922#107—112no—
923#107—112no—
924#107—112no—
925#107C22×D1112yes—
926#107C22×D1112yes—
927#106—112no—
928#106—112no—
929#106—112no—
930#106—112no—
931#106—112no—
932#106—112no—
933#106C22×D1112yes—
934#106C22×D1112yes—
935C4⋊C8—112no—
936C4⋊C8—112no—
937C4⋊C8—111no—
938C4⋊C8—111no—
939C4⋊C8C22×D1111yescharacteristic
940C4⋊C8C22×D1111yescharacteristic
941#103—112no—
942#103—112no—
943#103—112no—
944#103—112no—
945#103—112no—
946#103—112no—
947#103C22×D1112yes—
948#103C22×D1112yes—
949#102—112no—
950#102—112no—
951#102—112no—
952#102—112no—
953#102—112no—
954#102—112no—
955#102C22×D1112yes—
956#102C22×D1112yes—
957C22⋊C8—112no—
958C22⋊C8—112no—
959C22⋊C8—112no—
960C22⋊C8C22×D1112yes—
961C4×C8—112no—
962C4×C8—112no—
963C4×C8—112no—
964C4×C8C22×D1112yes—
965C2×C11—41no—
966C2×C11—81no—
967C2×C11C2×#53611yescharacteristic
968C2×C11C22×#13511yescharacteristic
969C2×C11C2×#57511yescharacteristic
970D11—41no—
971D11—81no—
972D11#323314yesdirect product factor
973C24—111no—
974C24—221no—
975C2×Q8—21no—
976C2×Q8—21no—
977C2×Q8—111no—
978C2×Q8—221no—
979C2×Q8—222no—
980C2×Q8—222no—
981C2×Q8—222no—
982C2×Q8—222no—
983C2×Q8—221no—
984C2×Q8—221no—
985C2×Q8—444no—
986C2×Q8—444no—
987C2×Q8C23×D1111yescharacteristic
988C2×D4—21no—
989C2×D4—111no—
990C2×D4—221no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—221no—
994C2×D4—221no—
995C2×D4—221no—
996C2×D4—444no—
997C2×D4C23×D1111yescharacteristic
998C22×C4—21no—
999C22×C4—111no—
1000C22×C4—111no—
1001C22×C4—111no—
1002C22×C4—111no—
1003C22×C4—111no—
1004C22×C4—111no—
1005C22×C4—111no—
1006C22×C4—111no—
1007C22×C4—111no—
1008C22×C4—111no—
1009C22×C4—111no—
1010C22×C4—111no—
1011C22×C4—111no—
1012C22×C4—111no—
1013C22×C4—111no—
1014C22×C4—224no—
1015C22×C4—222no—
1016C22×C4—222no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—222no—
1021C22×C4—222no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—444no—
1026C22×C4—442no—
1027C22×C4D4×D1111yescharacteristic
1028C22×C4D4×D1111yescharacteristic
1029C22×C4C23×D1111yescharacteristic
1030C2×C8—112no—
1031C2×C8—112no—
1032C2×C8—224no—
1033C2×C8—224no—
1034C2×C8C23×D1112yes—
1035C2×C8C23×D1112yes—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—112no—
1045C4⋊C4—112no—
1046C4⋊C4—111no—
1047C4⋊C4—111no—
1048C4⋊C4—222no—
1049C4⋊C4—222no—
1050C4⋊C4—221no—
1051C4⋊C4—221no—
1052C4⋊C4—221no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—221no—
1056C4⋊C4—221no—
1057C4⋊C4—221no—
1058C4⋊C4—221no—
1059C4⋊C4—221no—
1060C4⋊C4—222no—
1061C4⋊C4—222no—
1062C4⋊C4—222no—
1063C4⋊C4—222no—
1064C4⋊C4—222no—
1065C4⋊C4—222no—
1066C4⋊C4—221no—
1067C4⋊C4—221no—
1068C4⋊C4—221no—
1069C4⋊C4—221no—
1070C4⋊C4—222no—
1071C4⋊C4—222no—
1072C4⋊C4—221no—
1073C4⋊C4—221no—
1074C4⋊C4C23×D1112yes—
1075C4⋊C4C23×D1112yes—
1076C4⋊C4C23×D1111yescharacteristic
1077C4⋊C4C23×D1111yescharacteristic
1078C22⋊C4—22no—
1079C22⋊C4—21no—
1080C22⋊C4—21no—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—221no—
1085C22⋊C4—221no—
1086C22⋊C4—221no—
1087C22⋊C4—221no—
1088C22⋊C4—222no—
1089C22⋊C4—222no—
1090C22⋊C4—221no—
1091C22⋊C4—221no—
1092C22⋊C4—221no—
1093C22⋊C4—221no—
1094C22⋊C4—221no—
1095C22⋊C4—221no—
1096C22⋊C4—222no—
1097C22⋊C4—221no—
1098C22⋊C4—221no—
1099C22⋊C4—221no—
1100C22⋊C4—221no—
1101C22⋊C4—221no—
1102C42—21no—
1103C42—22no—
1104C42—111no—
1105C42—111no—
1106C42—111no—
1107C42—111no—
1108C42—111no—
1109C42—111no—
1110C42—111no—
1111C42—111no—
1112C42—111no—
1113C42—111no—
1114C42—111no—
1115C42—111no—
1116C42—222no—
1117C42—222no—
1118C42—221no—
1119C42—221no—
1120C42—222no—
1121C42—221no—
1122C42D4×D1111yescharacteristic
1123C42D4×D1111yescharacteristic
1124C42C23×D1111yescharacteristic
1125C42C23×D1111yescharacteristic
1126C11C2×#323311yescharacteristic, complemented, Sylow
1127C23—21no—
1128C23—111no—
1129C23—111no—
1130C23—222no—
1131C23—222no—
1132C23—222no—
1133C23—221no—
1134C23—442no—
1135C23—442no—
1136C23—442no—
1137C23C2×D4×D1111yescharacteristic
1138Q8—21no—
1139Q8—21no—
1140Q8—42no—
1141Q8—42no—
1142Q8—221no—
1143Q8—221no—
1144Q8—442no—
1145Q8—442no—
1146Q8—444no—
1147Q8—444no—
1148Q8—442no—
1149D4—21no—
1150D4—21no—
1151D4—42no—
1152D4—221no—
1153D4—221no—
1154D4—442no—
1155D4—442no—
1156D4—442no—
1157D4—442no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—111no—
1169C2×C4—111no—
1170C2×C4—114no—
1171C2×C4—112no—
1172C2×C4—112no—
1173C2×C4—111no—
1174C2×C4—111no—
1175C2×C4—111no—
1176C2×C4—111no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—221no—
1187C2×C4—221no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—221no—
1193C2×C4—441no—
1194C2×C4—441no—
1195C2×C4—442no—
1196C2×C4—442no—
1197C2×C4—442no—
1198C2×C4—442no—
1199C2×C4—444no—
1200C2×C4—444no—
1201C2×C4—442no—
1202C2×C4—441no—
1203C2×C4—442no—
1204C2×C4C2×D4×D1111yescharacteristic
1205C2×C4C2×D4×D1111yescharacteristic
1206C2×C4C2×D4×D1111yescharacteristic
1207C2×C4C2×D4×D1111yescharacteristic
1208C2×C4C2×D4×D1111yescharacteristic
1209C2×C4C24×D1111yescharacteristic
1210C8—22no—
1211C8—22no—
1212C8—222no—
1213C8—222no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—112no—
1221C22—112no—
1222C22—112no—
1223C22—221no—
1224C22—221no—
1225C22—221no—
1226C22—444no—
1227C22—441no—
1228C22—441no—
1229C22—441no—
1230C22—884no—
1231C22C22×D4×D1111yescharacteristic
1232C4—21no—
1233C4—21no—
1234C4—21no—
1235C4—21no—
1236C4—41no—
1237C4—41no—
1238C4—42no—
1239C4—41no—
1240C4—42no—
1241C4—112no—
1242C4—112no—
1243C4—221no—
1244C4—221no—
1245C4—221no—
1246C4—221no—
1247C4—441no—
1248C4—441no—
1249C4—442no—
1250C4—441no—
1251C4—442no—
1252C4D11×#13512yes—
1253C4D11×2−1+411yescharacteristic
1254C4D11×2−1+411yescharacteristic
1255C2—41no—
1256C2—81no—
1257C2—114no—
1258C2—441no—
1259C2—881no—
1260C2D11×#53611yescharacteristic
1261C2C2×D11×#13511yescharacteristic
1262C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3233C2
socleC22×C11C23×D4
prime radicalD11×#121C22
hypercenter#3233D11
hypocenterC11C2×#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
1. D11×#533C2semidirect
3. #13079800C2semidirect
4. #13079799C2semidirect
5. #13079798C2semidirect
6. #13079797C2semidirect
7. #13079796C2semidirect
8. #13079795C2semidirect
9. #13079794C2semidirect
10. #13079793C2semidirect
11. #13079792C2semidirect
12. #13079791C2semidirect
13. #13079790C2semidirect
14. D11×#499C2semidirect
15. D11×#488C2semidirect
16. D11×#485C2semidirect
18. D11×#477C2semidirect
19. D11×#475C2semidirect
20. D11×#476C2semidirect
21. D11×#474C2semidirect
22. D11×#431C2semidirect
23. C11×#3233C2semidirect
24. C11×#533C22semidirect
26. #10623259C22semidirect
27. #10623259C22semidirect
33. #10623219C22semidirect
61. #10623048C22semidirect
64. #10623001C22semidirect
65. C11×#499C22semidirect
66. C11×#488C22semidirect
67. C11×#485C22semidirect
69. C11×#477C22semidirect
70. C11×#476C22semidirect
71. C11×#475C22semidirect
72. C11×#474C22semidirect
73. C11×#431C22semidirect
74. #10622707C22semidirect
75. #10622704C22semidirect
76. #10622700C22semidirect
77. #10622697C22semidirect
78. #10622681C22semidirect
79. #10622677C22semidirect
80. #10622677C22semidirect
81. #10622669C22semidirect
82. #10622658C22semidirect
84. #10622634C22semidirect
85. #10622633C22semidirect
86. #10622621C22semidirect
87. #10622620C22semidirect
89. #10622609C22semidirect
90. #10622538C22semidirect
91. #10622503C22semidirect
92. #10622501C22semidirect
96. #10622491C22semidirect
97. #10622491C22semidirect
98. #10622488C22semidirect
99. #10622483C22semidirect
100. #10622480C22semidirect
104. #10622471C22semidirect
105. #10622471C22semidirect
106. #10622467C22semidirect
107. #10622464C22semidirect
108. #10622463C22semidirect
109. #10622459C22semidirect
110. #10622455C22semidirect
111. #10622446C22semidirect
112. #10622446C22semidirect
115. #10622428C22semidirect
116. #10622427C22semidirect
119. #10622413C22semidirect
120. #10622413C22semidirect
121. #10622407C22semidirect
122. #10622404C22semidirect
127. #10622381C22semidirect
128. #10622381C22semidirect
129. #10622374C22semidirect
130. #10622372C22semidirect
133. #10622336C22semidirect
134. #10622331C22semidirect
135. #10622310C22semidirect
136. #10622298C22semidirect
138. #10622296C22semidirect
509. #3233D11direct (N × H)
615. #533C2×D11semidirect
654. #499C2×D11semidirect
662. #488C2×D11semidirect
670. #485C2×D11semidirect
684. #477C2×D11semidirect
690. #476C2×D11semidirect
696. #475C2×D11semidirect
702. #474C2×D11semidirect
708. #431C2×D11semidirect
972. D11#3233direct (N × H)
1126. C11C2×#3233semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#5292
#130798002
#130797992
#130797982
#130797972
#130797962
#130797952
#130797942
#130797932
#130797922
#130797912
#130797902
D11×#4992
D11×#4882
D11×#4852
D11×#4822
D11×#4772
D11×#4752
D11×#4762
D11×#4742
D11×#4312
C11×#32332
C2×#323311