Finite Group Databasebeta

← D11×#3240 #15625928

Subgroups — D11×#3240 #15625928

Order 2816.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic, complemented
2D11×#529C211yesmaximal, characteristic
3#13079861C212yesmaximal, complemented
4#13079860C212yesmaximal, complemented
5#13079859C211yesmaximal, characteristic, complemented
6#13079858C211yesmaximal, characteristic, complemented
7#13079857C211yesmaximal, characteristic, complemented
8#13079856C211yesmaximal, characteristic, complemented
9#13079855C212yesmaximal, complemented
10#13079854C212yesmaximal, complemented
11#13079853C211yesmaximal, characteristic, complemented
12#13079852C211yesmaximal, characteristic, complemented
13#13079851C211yesmaximal, characteristic, complemented
14D11×#501C211yesmaximal, characteristic, complemented
15D11×#501C211yesmaximal, characteristic, complemented
16D11×#489C211yesmaximal, characteristic, complemented
17D11×#489C211yesmaximal, characteristic, complemented
18D11×#485C212yesmaximal, complemented
19D11×#482C212yesmaximal
20D11×#479C212yesmaximal, complemented
21D11×#478C212yesmaximal, complemented
22D11×#432C211yesmaximal, characteristic, complemented
23C11×#3240C211yesmaximal, 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×#501C2211yescharacteristic, complemented
66C11×#501C2211yescharacteristic, complemented
67C11×#489C2211yescharacteristic, complemented
68C11×#489C2211yescharacteristic, complemented
69C11×#485C2212yescomplemented
70C11×#482C2212yes—
71C11×#479C2212yescomplemented
72C11×#478C2212yescomplemented
73C11×#432C2211yescharacteristic, complemented
74#10622702C2211yescharacteristic, complemented
75#10622702C2211yescharacteristic, complemented
76#10622693C2211yescharacteristic, complemented
77#10622693C2211yescharacteristic, complemented
78#10622679C2212yescomplemented
79#10622678C2211yescharacteristic, complemented
80#10622678C2211yescharacteristic, complemented
81#10622676C2212yescomplemented
82#10622668C2211yescharacteristic, complemented
83#10622668C2211yescharacteristic, complemented
84#10622658C2212yescomplemented
85#10622648C2212yes—
86#10622635C2212yescomplemented
87#10622622C2212yescomplemented
88#10622616C2212yes—
89#10622609C2212yescomplemented
90#10622539C2211yescharacteristic, complemented
91#10622504C2212yescomplemented
92#10622501C2212yescomplemented
93#10622498C2212yes—
94D11×#107C2212yes—
95D11×#107C2212yes—
96#10622490C2212yescomplemented
97#10622489C2212yescomplemented
98#10622489C2212yescomplemented
99#10622484C2212yescomplemented
100#10622480C2212yescomplemented
101#10622479C2212yes—
102D11×#106C2212yes—
103D11×#106C2212yes—
104#10622470C2212yescomplemented
105#10622469C2212yescomplemented
106#10622469C2212yescomplemented
107#10622460C2212yescomplemented
108#10622448C2212yescomplemented
109D11×C4⋊C8C2212yes—
110#10622442C2212yescomplemented
111#10622428C2212yescomplemented
112#10622427C2212yescomplemented
113D11×#103C2212yes—
114D11×#103C2212yes—
115#10622412C2212yescomplemented
116#10622409C2212yescomplemented
117#10622408C2212yescomplemented
118#10622408C2212yescomplemented
119#10622397C2212yes—
120#10622392C2212yes—
121D11×#102C2212yes—
122D11×#102C2212yes—
123#10622379C2212yescomplemented
124#10622378C2212yescomplemented
125#10622378C2212yescomplemented
126#10622376C2212yescomplemented
127#10622350C2212yes—
128D11×C22⋊C8C2212yes—
129#10622336C2212yescomplemented
130#10622332C2212yescomplemented
131#10622327C2211yescharacteristic, complemented
132#10622327C2211yescharacteristic, complemented
133#10622318C2211yescharacteristic, complemented
134#10622318C2211yescharacteristic, complemented
135D11×#97C2211yescharacteristic
136D11×#97C2211yescharacteristic
137#10622315C2211yescharacteristic, complemented
138#10622315C2211yescharacteristic, complemented
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⋊C8C2312yes—
301C11×#103C2312yes—
302C11×#103C2312yes—
303C11×#102C2312yes—
304C11×#102C2312yes—
305C11×C22⋊C8C2312yes—
306C11×#97C2311yescharacteristic
307C11×#97C2311yescharacteristic
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—
323#66879C2312yes—
324#66879C2312yes—
325Dic11⋊C8C2312yes—
326Dic11⋊C8C2312yes—
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)C2312yes—
340#66867C2311yescharacteristic
341#66867C2311yescharacteristic
342C2×#3240—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—24no—
362Q8×D11—44no—
363Q8×D11—44no—
364D4×D11—24no—
365D4×D11—44no—
366C2×D44—21no—
367C2×D44C2411yescharacteristic
368C2×C4×D11—24no—
369C2×C4×D11—21no—
370C2×C4×D11—21no—
371C2×C4×D11—21no—
372C2×C4×D11—22no—
373C2×C4×D11—22no—
374C2×C4×D11—21no—
375C2×C4×D11—21no—
376C2×C4×D11—42no—
377C2×C4×D11—42no—
378C2×C4×D11—44no—
379C2×C4×D11C2×D411yescharacteristic
380C2×C4×D11C2×D411yescharacteristic
381C2×C4×D11C2×D411yescharacteristic
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×D11C2411yescharacteristic
390C2×C4×D11C2411yescharacteristic
391C2×Dic22—21no—
392C2×Dic22—22no—
393C2×Dic22—22no—
394C2×Dic22—21no—
395C2×Dic22—21no—
396C2×Dic22C2411yescharacteristic
397C2×C8×C11C2412yes—
398C2×C8×C11C2412yes—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2412yes—
410C11×C4⋊C4C2412yes—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C42×C11—22no—
418C42×C11—21no—
419C42×C11C2×D411yescharacteristic
420C42×C11C2×D411yescharacteristic
421C42×C11C2411yescharacteristic
422C42×C11C2411yescharacteristic
423C22⋊Dic11—21no—
424C22⋊Dic11—21no—
425C22⋊Dic11—21no—
426C22⋊Dic11—21no—
427C22⋊Dic11—22no—
428C22⋊Dic11—21no—
429(C2×D11)⋊C4—21no—
430(C2×D11)⋊C4—21no—
431(C2×D11)⋊C4—21no—
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—21no—
438(C2×D11)⋊C4—21no—
439(C2×D11)⋊C4—21no—
440(C2×D11)⋊C4—21no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—21no—
444C4⋊Dic11—21no—
445C4⋊Dic11—21no—
446C4⋊Dic11—21no—
447C4⋊Dic11—21no—
448C4⋊Dic11—21no—
449C4⋊Dic11C2411yescharacteristic
450C4⋊Dic11C2411yescharacteristic
451C4⋊Dic11C2412yes—
452C4⋊Dic11C2412yes—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—21no—
458Dic11⋊C4—21no—
459Dic11⋊C4—21no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—21no—
463Dic11⋊C4—21no—
464Dic11⋊C4—21no—
465Dic11⋊C4—22no—
466Dic11⋊C4—22no—
467Dic11⋊C4—21no—
468Dic11⋊C4—21no—
469Dic11⋊C4—21no—
470Dic11⋊C4—21no—
471C4×Dic11—21no—
472C4×Dic11—22no—
473C4×Dic11—22no—
474C4×Dic11—21no—
475C4×Dic11—22no—
476C4×Dic11—21no—
477C4×Dic11C2×D411yescharacteristic
478C4×Dic11C2×D411yescharacteristic
479C4×Dic11C2×D411yescharacteristic
480C4×Dic11C2×D411yescharacteristic
481C4×Dic11C2×D411yescharacteristic
482C4×Dic11C2×D411yescharacteristic
483C4×Dic11C2×D411yescharacteristic
484C4×Dic11C2×D411yescharacteristic
485C4×Dic11C2×D411yescharacteristic
486C4×Dic11C2×D411yescharacteristic
487C4×Dic11C2411yescharacteristic
488C4×Dic11C2411yescharacteristic
489C2×C11⋊C8C2412yes—
490C2×C11⋊C8C2412yes—
491C8×D11—24no—
492C8×D11—24no—
493C2×#533—111no—
494C2×#529—111no—
495#3240—111no—
496#3240—111no—
497#3240—111no—
498#3240—111no—
499#3240—112no—
500#3240—112no—
501#3240—112no—
502#3240—112no—
503#3240—111no—
504#3240—111no—
505#3240—111no—
506#3240D1111yescharacteristic, direct product factor
507C2×#501—111no—
508C2×#501—111no—
509C2×#489—111no—
510C2×#489—111no—
511C2×#485—112no—
512C2×#482—112no—
513C2×#479—112no—
514C2×#478—112no—
515C2×#432—111no—
516C23×C11—21no—
517C23×C11C22×D411yescharacteristic
518C22×D11—22no—
519C22×D11—22no—
520C22×D11—22no—
521C22×D11—21no—
522C22×D11—42no—
523C22×D11—42no—
524C22×D11—42no—
525C22×D11C22×D411yescharacteristic
526C22×D11C22×D411yescharacteristic
527Q8×C11—22no—
528Q8×C11—42no—
529Q8×C11—42no—
530D4×C11—22no—
531D4×C11—42no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—42no—
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D411yescharacteristic
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C2511yescharacteristic
547C22⋊D11—42no—
548C22⋊D11—42no—
549C22⋊D11—42no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—21no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—42no—
559C2×Dic11C22×D411yescharacteristic
560C2×Dic11C22×D411yescharacteristic
561C2×Dic11C22×D411yescharacteristic
562C2×Dic11C22×D411yescharacteristic
563C2×Dic11C22×D411yescharacteristic
564C2×Dic11C22×D411yescharacteristic
565D44—22no—
566D44—42no—
567C4×D11—22no—
568C4×D11—22no—
569C4×D11—22no—
570C4×D11—22no—
571C4×D11—22no—
572C4×D11—22no—
573C4×D11—22no—
574C4×D11—41no—
575C4×D11—41no—
576C4×D11—41no—
577C4×D11—41no—
578C4×D11—42no—
579C4×D11—42no—
580C4×D11—42no—
581C4×D11—42no—
582C4×D11—42no—
583C4×D11—44no—
584C4×D11—44no—
585C4×D112−1+414yes—
586Dic22—22no—
587Dic22—44no—
588Dic22—44no—
589Dic22—42no—
590Dic22—42no—
591Dic22—42no—
592C8×C11—22no—
593C8×C11—22no—
594C11⋊C8—22no—
595C11⋊C8—22no—
596#533—111no—
597#533—111no—
598#533—112no—
599#533—112no—
600#533—111no—
601#533—221no—
602#533—221no—
603#533—221no—
604#533—221no—
605#533C2×D1111yescharacteristic, complemented
606C2×C4⋊Q8—111no—
607C2×C4⋊Q8—111no—
608#529—111no—
609#529—111no—
610#529—111no—
611#529—111no—
612#529—111no—
613#529—111no—
614#529—111no—
615#529—221no—
616#529—221no—
617#529—221no—
618#529—221no—
619#529C2×D1111yescharacteristic
620C2×#126—221no—
621C2×#125—112no—
622C2×#125—111no—
623C2×#124—111no—
624C2×#123—221no—
625C2×C22⋊Q8—111no—
626C2×C22⋊Q8—221no—
627C2×C22⋊Q8—221no—
628C2×#121—111no—
629C2×C4×Q8—111no—
630C2×C4×Q8—221no—
631C2×C4×Q8—221no—
632C2×C4×D4—111no—
633C2×C4×D4—221no—
634C2×#117—112no—
635C2×#117—221no—
636C22×C42—111no—
637#501—111no—
638#501—111no—
639#501—111no—
640#501—111no—
641#501—112no—
642#501—112no—
643#501—112no—
644#501—112no—
645#501—111no—
646#501—111no—
647#501C2×D1111yescharacteristic, complemented
648#501C2×D1111yescharacteristic, complemented
649#489—111no—
650#489—111no—
651#489—111no—
652#489—111no—
653#489—112no—
654#489—112no—
655#489—112no—
656#489—112no—
657#489—111no—
658#489—111no—
659#489C2×D1111yescharacteristic, complemented
660#489C2×D1111yescharacteristic, complemented
661#485—112no—
662#485—112no—
663#485—112no—
664#485—112no—
665#485—112no—
666#485—112no—
667#485—112no—
668#485C2×D1112yescomplemented
669#482—112no—
670#482—112no—
671#482—112no—
672#482—112no—
673#482—112no—
674#482—112no—
675#482—112no—
676#482C2×D1112yes—
677#479—112no—
678#479—112no—
679#479—112no—
680#479—112no—
681#479—112no—
682#479—112no—
683#479—112no—
684#479C2×D1112yescomplemented
685#478—112no—
686#478—112no—
687#478—112no—
688#478—112no—
689#478—112no—
690#478—112no—
691#478—112no—
692#478C2×D1112yescomplemented
693#432—111no—
694#432—112no—
695#432—112no—
696#432—111no—
697#432—111no—
698#432C2×D1111yescharacteristic, complemented
699C2×#107—112no—
700C2×#107—112no—
701C2×#106—112no—
702C2×#106—112no—
703C2×C4⋊C8—112no—
704C2×#103—112no—
705C2×#103—112no—
706C2×#102—112no—
707C2×#102—112no—
708C2×C22⋊C8—112no—
709C2×#97—111no—
710C2×#97—111no—
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—21no—
714C22×C11—41no—
715C22×C11—41no—
716C22×C11—41no—
717C22×C11C23×D411yescharacteristic
718C2×D11—21no—
719C2×D11—21no—
720C2×D11—21no—
721C2×D11—44no—
722C2×D11—41no—
723C2×D11—41no—
724C2×D11—41no—
725C2×D11—84no—
726C2×D11#53612yes—
727C2×D11#57512yes—
728C2×D11#57512yes—
729C4×C11—21no—
730C4×C11—21no—
731C4×C11—21no—
732C4×C11—21no—
733C4×C11—21no—
734C4×C11—41no—
735C4×C11—41no—
736C4×C11—41no—
737C4×C11—42no—
738C4×C11—42no—
739C4×C11C2×2−1+412yes—
740Dic11—21no—
741Dic11—21no—
742Dic11—21no—
743Dic11—21no—
744Dic11—21no—
745Dic11—41no—
746Dic11—42no—
747Dic11—42no—
748Dic11—41no—
749Dic11—41no—
750Dic11#53612yes—
751C22×Q8—111no—
752C22×Q8—221no—
753C22×Q8—221no—
754C22×D4—111no—
755C22×D4—221no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—111no—
759C23×C4—221no—
760C22×C8—112no—
761C22×C8—112no—
762C4⋊Q8—112no—
763C4⋊Q8—112no—
764C4⋊Q8—111no—
765C4⋊Q8—111no—
766C4⋊Q8—221no—
767C4⋊Q8—221no—
768C4⋊Q8—221no—
769C4⋊Q8—221no—
770C4⋊Q8C22×D1111yescharacteristic
771C4⋊Q8C22×D1111yescharacteristic
772#126—21no—
773#126—221no—
774#126—221no—
775#126—221no—
776#126—221no—
777#126—221no—
778#126—221no—
779#126—221no—
780#125—111no—
781#125—111no—
782#125—112no—
783#125—112no—
784#125—111no—
785#125—112no—
786#125—221no—
787#125—221no—
788#125—222no—
789#125—222no—
790#125C22×D1111yescharacteristic
791#125C22×D1112yes—
792#124—111no—
793#124—111no—
794#124—111no—
795#124—221no—
796#124—221no—
797#124C22×D1111yescharacteristic
798#123—21no—
799#123—221no—
800#123—221no—
801#123—221no—
802#123—221no—
803#123—221no—
804#123—221no—
805#123—221no—
806C22⋊Q8—21no—
807C22⋊Q8—21no—
808C22⋊Q8—111no—
809C22⋊Q8—111no—
810C22⋊Q8—111no—
811C22⋊Q8—221no—
812C22⋊Q8—222no—
813C22⋊Q8—222no—
814C22⋊Q8—221no—
815C22⋊Q8—222no—
816C22⋊Q8—222no—
817C22⋊Q8—221no—
818C22⋊Q8—221no—
819C22⋊Q8—221no—
820C22⋊Q8—221no—
821C22⋊Q8—221no—
822C22⋊Q8—221no—
823C22⋊Q8C22×D1111yescharacteristic
824#121—111no—
825#121—111no—
826#121—111no—
827#121—221no—
828#121—221no—
829#121C22×D1111yescharacteristic
830C4×Q8—21no—
831C4×Q8—21no—
832C4×Q8—111no—
833C4×Q8—111no—
834C4×Q8—111no—
835C4×Q8—221no—
836C4×Q8—222no—
837C4×Q8—222no—
838C4×Q8—221no—
839C4×Q8—222no—
840C4×Q8—221no—
841C4×Q8—222no—
842C4×Q8—221no—
843C4×Q8—221no—
844C4×Q8—221no—
845C4×Q8—221no—
846C4×Q8—221no—
847C4×Q8C22×D1111yescharacteristic
848C4×D4—21no—
849C4×D4—111no—
850C4×D4—111no—
851C4×D4—111no—
852C4×D4—221no—
853C4×D4—221no—
854C4×D4—221no—
855C4×D4—221no—
856C4×D4—221no—
857C4×D4—221no—
858C4×D4—221no—
859C4×D4—221no—
860C4×D4—221no—
861C4×D4C22×D1111yescharacteristic
862#117—21no—
863#117—112no—
864#117—112no—
865#117—112no—
866#117—221no—
867#117—222no—
868#117—221no—
869#117—221no—
870#117—221no—
871#117—221no—
872#117—221no—
873#117—222no—
874#117—221no—
875#117C22×D1112yes—
876C2×C4⋊C4—112no—
877C2×C4⋊C4—112no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—221no—
881C2×C4⋊C4—221no—
882C2×C4⋊C4—221no—
883C2×C4⋊C4—221no—
884C2×C4⋊C4—222no—
885C2×C4⋊C4—222no—
886C2×C4⋊C4—221no—
887C2×C4⋊C4—221no—
888C2×C22⋊C4—221no—
889C2×C22⋊C4—221no—
890C2×C22⋊C4—221no—
891C2×C22⋊C4—221no—
892C2×C22⋊C4—222no—
893C2×C22⋊C4—221no—
894C2×C42—111no—
895C2×C42—111no—
896C2×C42—111no—
897C2×C42—111no—
898C2×C42—111no—
899C2×C42—111no—
900C2×C42—111no—
901C2×C42—111no—
902C2×C42—111no—
903C2×C42—111no—
904C2×C42—111no—
905C2×C42—222no—
906C2×C42—221no—
907C2×C42C22×D1111yescharacteristic
908#107—112no—
909#107—112no—
910#107—112no—
911#107—112no—
912#107—112no—
913#107—112no—
914#107C22×D1112yes—
915#107C22×D1112yes—
916#106—112no—
917#106—112no—
918#106—112no—
919#106—112no—
920#106—112no—
921#106—112no—
922#106C22×D1112yes—
923#106C22×D1112yes—
924C4⋊C8—112no—
925C4⋊C8—112no—
926C4⋊C8—112no—
927C4⋊C8C22×D1112yes—
928#103—112no—
929#103—112no—
930#103—112no—
931#103—112no—
932#103—112no—
933#103—112no—
934#103C22×D1112yes—
935#103C22×D1112yes—
936#102—112no—
937#102—112no—
938#102—112no—
939#102—112no—
940#102—112no—
941#102—112no—
942#102C22×D1112yes—
943#102C22×D1112yes—
944C22⋊C8—112no—
945C22⋊C8—112no—
946C22⋊C8—112no—
947C22⋊C8C22×D1112yes—
948#97—112no—
949#97—112no—
950#97—111no—
951#97—111no—
952#97C22×D1111yescharacteristic
953#97C22×D1111yescharacteristic
954C2×C11—41no—
955C2×C11—81no—
956C2×C11C2×#53611yescharacteristic
957C2×C11C2×#57511yescharacteristic
958C2×C11C2×#57511yescharacteristic
959D11—41no—
960D11—81no—
961D11#324014yesdirect product factor
962C24—111no—
963C24—221no—
964C2×Q8—21no—
965C2×Q8—21no—
966C2×Q8—111no—
967C2×Q8—221no—
968C2×Q8—222no—
969C2×Q8—222no—
970C2×Q8—224no—
971C2×Q8—221no—
972C2×Q8—221no—
973C2×Q8—444no—
974C2×Q8—444no—
975C2×Q8C23×D1111yescharacteristic
976C2×D4—21no—
977C2×D4—111no—
978C2×D4—221no—
979C2×D4—224no—
980C2×D4—221no—
981C2×D4—221no—
982C2×D4—221no—
983C2×D4—444no—
984C2×D4C23×D1111yescharacteristic
985C22×C4—21no—
986C22×C4—111no—
987C22×C4—111no—
988C22×C4—111no—
989C22×C4—111no—
990C22×C4—111no—
991C22×C4—111no—
992C22×C4—111no—
993C22×C4—111no—
994C22×C4—111no—
995C22×C4—111no—
996C22×C4—111no—
997C22×C4—111no—
998C22×C4—111no—
999C22×C4—111no—
1000C22×C4—111no—
1001C22×C4—224no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—222no—
1006C22×C4—222no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—442no—
1011C22×C4—442no—
1012C22×C4—444no—
1013C22×C4D4×D1111yescharacteristic
1014C22×C4D4×D1111yescharacteristic
1015C22×C4C23×D1111yescharacteristic
1016C2×C8—112no—
1017C2×C8—112no—
1018C2×C8—224no—
1019C2×C8—224no—
1020C2×C8C23×D1112yes—
1021C2×C8C23×D1112yes—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—112no—
1031C4⋊C4—112no—
1032C4⋊C4—111no—
1033C4⋊C4—111no—
1034C4⋊C4—222no—
1035C4⋊C4—222no—
1036C4⋊C4—221no—
1037C4⋊C4—221no—
1038C4⋊C4—221no—
1039C4⋊C4—221no—
1040C4⋊C4—221no—
1041C4⋊C4—221no—
1042C4⋊C4—221no—
1043C4⋊C4—221no—
1044C4⋊C4—221no—
1045C4⋊C4—221no—
1046C4⋊C4—222no—
1047C4⋊C4—222no—
1048C4⋊C4—222no—
1049C4⋊C4—222no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—221no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—221no—
1056C4⋊C4—222no—
1057C4⋊C4—222no—
1058C4⋊C4—221no—
1059C4⋊C4—221no—
1060C4⋊C4C23×D1112yes—
1061C4⋊C4C23×D1112yes—
1062C4⋊C4C23×D1111yescharacteristic
1063C4⋊C4C23×D1111yescharacteristic
1064C22⋊C4—22no—
1065C22⋊C4—21no—
1066C22⋊C4—21no—
1067C22⋊C4—21no—
1068C22⋊C4—21no—
1069C22⋊C4—21no—
1070C22⋊C4—221no—
1071C22⋊C4—221no—
1072C22⋊C4—221no—
1073C22⋊C4—221no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—221no—
1077C22⋊C4—221no—
1078C22⋊C4—221no—
1079C22⋊C4—221no—
1080C22⋊C4—221no—
1081C22⋊C4—221no—
1082C22⋊C4—222no—
1083C22⋊C4—221no—
1084C22⋊C4—221no—
1085C22⋊C4—221no—
1086C22⋊C4—221no—
1087C22⋊C4—221no—
1088C42—21no—
1089C42—22no—
1090C42—111no—
1091C42—111no—
1092C42—111no—
1093C42—111no—
1094C42—111no—
1095C42—111no—
1096C42—111no—
1097C42—111no—
1098C42—111no—
1099C42—111no—
1100C42—111no—
1101C42—111no—
1102C42—222no—
1103C42—222no—
1104C42—221no—
1105C42—221no—
1106C42—222no—
1107C42—221no—
1108C42D4×D1111yescharacteristic
1109C42D4×D1111yescharacteristic
1110C42C23×D1111yescharacteristic
1111C42C23×D1111yescharacteristic
1112C11C2×#324011yescharacteristic, complemented, Sylow
1113C23—21no—
1114C23—111no—
1115C23—111no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—221no—
1120C23—442no—
1121C23—442no—
1122C23—442no—
1123C23C2×D4×D1111yescharacteristic
1124Q8—22no—
1125Q8—42no—
1126Q8—42no—
1127Q8—222no—
1128Q8—442no—
1129Q8—442no—
1130Q8—442no—
1131Q8—444no—
1132Q8—444no—
1133D4—22no—
1134D4—42no—
1135D4—222no—
1136D4—442no—
1137D4—442no—
1138D4—442no—
1139D4—442no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—111no—
1150C2×C4—114no—
1151C2×C4—111no—
1152C2×C4—111no—
1153C2×C4—111no—
1154C2×C4—111no—
1155C2×C4—111no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—222no—
1164C2×C4—221no—
1165C2×C4—221no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—221no—
1169C2×C4—441no—
1170C2×C4—441no—
1171C2×C4—441no—
1172C2×C4—441no—
1173C2×C4—442no—
1174C2×C4—442no—
1175C2×C4—442no—
1176C2×C4—442no—
1177C2×C4—442no—
1178C2×C4—444no—
1179C2×C4—444no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—442no—
1183C2×C4C2×D4×D1111yescharacteristic
1184C2×C4C2×D4×D1111yescharacteristic
1185C2×C4C2×D4×D1111yescharacteristic
1186C2×C4C2×D4×D1111yescharacteristic
1187C2×C4C2×D4×D1111yescharacteristic
1188C2×C4C24×D1111yescharacteristic
1189C8—22no—
1190C8—22no—
1191C8—222no—
1192C8—222no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—112no—
1200C22—112no—
1201C22—112no—
1202C22—221no—
1203C22—221no—
1204C22—221no—
1205C22—444no—
1206C22—441no—
1207C22—441no—
1208C22—441no—
1209C22—884no—
1210C22C22×D4×D1111yescharacteristic
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—42no—
1220C4—42no—
1221C4—112no—
1222C4—221no—
1223C4—221no—
1224C4—221no—
1225C4—221no—
1226C4—221no—
1227C4—441no—
1228C4—441no—
1229C4—441no—
1230C4—442no—
1231C4—442no—
1232C4D11×2−1+412yes—
1233C2—41no—
1234C2—81no—
1235C2—114no—
1236C2—441no—
1237C2—881no—
1238C2D11×#53611yescharacteristic
1239C2D11×#57511yescharacteristic
1240C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3240C2
socleC22×C11C23×D4
prime radicalD11×#121C22
hypercenter#3240D11
hypocenterC11C2×#3240
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3240

Complements

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

NH ≅ G/Ntype
1. D11×#533C2semidirect
3. #13079861C2semidirect
4. #13079860C2semidirect
5. #13079859C2semidirect
6. #13079858C2semidirect
7. #13079857C2semidirect
8. #13079856C2semidirect
9. #13079855C2semidirect
10. #13079854C2semidirect
11. #13079853C2semidirect
12. #13079852C2semidirect
13. #13079851C2semidirect
14. D11×#501C2semidirect
15. D11×#501C2semidirect
16. D11×#489C2semidirect
17. D11×#489C2semidirect
18. D11×#485C2semidirect
20. D11×#479C2semidirect
21. D11×#478C2semidirect
22. D11×#432C2semidirect
23. C11×#3240C2semidirect
24. C11×#533C22semidirect
26. #10623259C22semidirect
27. #10623259C22semidirect
33. #10623219C22semidirect
61. #10623048C22semidirect
64. #10623001C22semidirect
65. C11×#501C22semidirect
66. C11×#501C22semidirect
67. C11×#489C22semidirect
68. C11×#489C22semidirect
69. C11×#485C22semidirect
71. C11×#479C22semidirect
72. C11×#478C22semidirect
73. C11×#432C22semidirect
74. #10622702C22semidirect
75. #10622702C22semidirect
76. #10622693C22semidirect
77. #10622693C22semidirect
78. #10622679C22semidirect
79. #10622678C22semidirect
80. #10622678C22semidirect
81. #10622676C22semidirect
82. #10622668C22semidirect
83. #10622668C22semidirect
84. #10622658C22semidirect
86. #10622635C22semidirect
87. #10622622C22semidirect
89. #10622609C22semidirect
90. #10622539C22semidirect
91. #10622504C22semidirect
92. #10622501C22semidirect
96. #10622490C22semidirect
97. #10622489C22semidirect
98. #10622489C22semidirect
99. #10622484C22semidirect
100. #10622480C22semidirect
104. #10622470C22semidirect
105. #10622469C22semidirect
106. #10622469C22semidirect
107. #10622460C22semidirect
108. #10622448C22semidirect
110. #10622442C22semidirect
111. #10622428C22semidirect
112. #10622427C22semidirect
115. #10622412C22semidirect
116. #10622409C22semidirect
117. #10622408C22semidirect
118. #10622408C22semidirect
123. #10622379C22semidirect
124. #10622378C22semidirect
125. #10622378C22semidirect
126. #10622376C22semidirect
129. #10622336C22semidirect
130. #10622332C22semidirect
131. #10622327C22semidirect
132. #10622327C22semidirect
133. #10622318C22semidirect
134. #10622318C22semidirect
137. #10622315C22semidirect
138. #10622315C22semidirect
506. #3240D11direct (N × H)
605. #533C2×D11semidirect
647. #501C2×D11semidirect
648. #501C2×D11semidirect
659. #489C2×D11semidirect
660. #489C2×D11semidirect
668. #485C2×D11semidirect
684. #479C2×D11semidirect
692. #478C2×D11semidirect
698. #432C2×D11semidirect
961. D11#3240direct (N × H)
1112. C11C2×#3240semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#5292
#130798612
#130798602
#130798592
#130798582
#130798572
#130798562
#130798552
#130798542
#130798532
#130798522
#130798512
D11×#5012
D11×#4892
D11×#4852
D11×#4822
D11×#4792
D11×#4782
D11×#4322
C11×#32402
C2×#324011