Finite Group Databasebeta

← D11×#3509 #15662207

Subgroups — D11×#3509 #15662207

Order 2816.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082503C211yesmaximal, characteristic, complemented
2#13082502C211yesmaximal, characteristic, complemented
3#13082501C212yesmaximal, complemented
4#13082500C211yesmaximal, characteristic, complemented
5#13082499C214yesmaximal, complemented
6#13082498C214yesmaximal, complemented
7#13082497C212yesmaximal, complemented
8#13082496C214yesmaximal, complemented
9#13082495C214yesmaximal, complemented
10#13082494C218yesmaximal, complemented
11D11×#557C214yesmaximal, complemented
12D11×#556C214yesmaximal, complemented
13D11×#552C218yesmaximal, complemented
14D11×#541C214yesmaximal, complemented
15D11×#536C212yesmaximal
16D11×#533C214yesmaximal, complemented
17D11×#533C211yesmaximal, characteristic, complemented
18C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
19D11×#519C212yesmaximal, complemented
20C4×#41×D11C211yesmaximal, characteristic
21C11×#3509C211yesmaximal, characteristic, complemented
22C2×#41×D11C2211yescharacteristic
23C22×Q8×D11C2212yes—
24C11×#557C2214yescomplemented
25C11×#556C2214yescomplemented
26C11×#552C2218yescomplemented
27C11×#541C2214yescomplemented
28C11×#536C2212yes—
29C11×#533C2214yescomplemented
30C11×#533C2211yescharacteristic, complemented
31C2×C11×C4⋊Q8C2211yescharacteristic, complemented
32C11×#519C2212yescomplemented
33C4×C11×#41C2211yescharacteristic
34#41×Dic11C2211yescharacteristic
35#10623356C2212yes—
36#10623347C2212yes—
37#10623343C2212yescomplemented
38C2×#66997C2212yescomplemented
39#10623263C2214yescomplemented
40#10623262C2214yescomplemented
41#10623259C2212yescomplemented
42#10623259C2214yescomplemented
43#10623259C2214yescomplemented
44#10623255C2214yes—
45D11×C4⋊Q8C2212yes—
46D11×C4⋊Q8C2214yes—
47D11×C4⋊Q8C2212yes—
48D11×C4⋊Q8C2212yes—
49D11×C4⋊Q8C2214yes—
50D11×C4⋊Q8C2212yescomplemented
51D11×C4⋊Q8C2214yescomplemented
52D11×C4⋊Q8C2212yescomplemented
53#10623252C2214yescomplemented
54#10623252C2218yescomplemented
55#10623239C22116yescomplemented
56D11×#126C22116yes—
57#10623233C22116yescomplemented
58#10623232C22116yescomplemented
59#10623228C2214yescomplemented
60#10623227C22116yescomplemented
61#10623225C2218yescomplemented
62#10623224C22116yescomplemented
63#10623219C2218yescomplemented
64#10623219C2212yescomplemented
65D11×#125C2218yes—
66D11×#125C22116yes—
67D11×#125C2212yes—
68#10623216C2218yescomplemented
69#10623216C22116yescomplemented
70#10623206C2214yes—
71D11×#124C2214yes—
72#10623202C2218yescomplemented
73D11×#123C2218yes—
74#10623181C22116yescomplemented
75#10623179C2218yes—
76#10623173C2218yescomplemented
77#10623172C2218yescomplemented
78#10623170C2218yescomplemented
79#10623159C2218yes—
80D11×C22⋊Q8C2214yes—
81D11×C22⋊Q8C2218yes—
82D11×C22⋊Q8C2218yes—
83#10623156C2218yescomplemented
84#10623153C2214yescomplemented
85#10623153C2218yescomplemented
86#10623153C2218yescomplemented
87#10623115C2214yescomplemented
88#10623114C2218yescomplemented
89#10623112C2218yescomplemented
90#10623109C2218yescomplemented
91#10623109C2214yescomplemented
92#10623109C2218yescomplemented
93C4×#4343C2212yes—
94#10623103C2218yescomplemented
95#10623103C2218yescomplemented
96C4×Q8×D11C2218yes—
97C4×Q8×D11C2214yes—
98C4×Q8×D11C2218yes—
99C4×Q8×D11C2218yes—
100C4×Q8×D11C2212yes—
101#10623101C2214yescomplemented
102#10623100C2218yescomplemented
103#10623099C2218yescomplemented
104#10623098C2218yescomplemented
105#10623098C2214yescomplemented
106C4×D4×D11C2214yes—
107C4×D4×D11C2212yes—
108#10623073C2214yescomplemented
109#10623072C2218yescomplemented
110C4×#4341C2214yes—
111C4×#4341C2212yes—
112#10623064C2218yescomplemented
113#10623062C22116yescomplemented
114#10623060C2218yescomplemented
115#10623057C2212yes—
116#10623053C2211yescharacteristic
117#10623053C2212yes—
118D11×#117C2218yes—
119D11×#117C2218yes—
120D11×#117C2212yes—
121D11×#117C2212yes—
122D11×#117C2211yescharacteristic
123#10623049C2214yescomplemented
124#10623048C2218yescomplemented
125#10623048C2212yescomplemented
126#10623047C2218yescomplemented
127#10623047C2212yescomplemented
128#10623047C2212yescomplemented
129#10623044C2218yescomplemented
130C2×C4⋊C4×D11C2214yes—
131C2×#66941C2214yescomplemented
132C4×#4339C2212yes—
133C4×#4339C2211yescharacteristic
134C2×C42×D11C2211yescharacteristic
135C2×C42×D11C2212yes—
136#10623001C2214yescomplemented
137#10623001C2211yescharacteristic, complemented
138C2×#66922C2211yescharacteristic, complemented
139C2×C11×#41C2311yescharacteristic
140C22×Q8×C11C2312yes—
141#41×D11—28no—
142C2×#4343C2311yescharacteristic
143C2×Q8×D11—216no—
144C2×Q8×D11C2311yescharacteristic
145C2×Q8×D11C2314yes—
146C2×Q8×D11C2314yes—
147C2×Q8×D11C2314yes—
148C2×Q8×D11C2314yes—
149C2×Q8×D11C2314yes—
150C2×#4341C2312yes—
151C2×#4341C2311yescharacteristic
152C2×D4×D11C2312yes—
153C2×D4×D11C2311yescharacteristic
154C2×#4339C2311yescharacteristic
155C2×#4339C2312yes—
156C22×C4×D11C2312yes—
157C22×C4×D11C2314yes—
158C22×C4×D11C2312yes—
159C22×C4×D11C2314yes—
160C22×C4×D11C2311yescharacteristic
161C22×Dic22C2312yes—
162C22×Dic22C2314yes—
163C11×C4⋊Q8C2314yes—
164C11×C4⋊Q8C2314yes—
165C11×C4⋊Q8C2312yes—
166C11×C4⋊Q8C2312yes—
167C11×C4⋊Q8C2312yes—
168C11×#126C23116yes—
169C11×#125C2312yes—
170C11×#125C2318yes—
171C11×#125C23116yes—
172C11×#124C2314yes—
173C11×#123C2318yes—
174C11×C22⋊Q8C2318yes—
175C11×C22⋊Q8C2314yes—
176C11×C22⋊Q8C2318yes—
177C4×Q8×C11C2312yes—
178C4×Q8×C11C2318yes—
179C4×Q8×C11C2318yes—
180C4×Q8×C11C2314yes—
181C4×Q8×C11C2318yes—
182C4×D4×C11C2314yes—
183C4×D4×C11C2312yes—
184C11×#117C2311yescharacteristic
185C11×#117C2312yes—
186C11×#117C2318yes—
187C11×#117C2318yes—
188C11×#117C2312yes—
189C2×C11×C4⋊C4C2314yes—
190C2×C42×C11C2311yescharacteristic
191C2×C42×C11C2312yes—
192#67000C2314yes—
193#66999C2318yes—
194#66999C2314yes—
195#66999C2318yes—
196Q8×Dic11C2312yes—
197Q8×Dic11C2318yes—
198Q8×Dic11C2318yes—
199Q8×Dic11C2314yes—
200Q8×Dic11C2318yes—
201#66997C2314yes—
202#66997C2314yes—
203#66997C2318yes—
204#66997C2314yes—
205#66997C2314yes—
206#66997C2314yes—
207#66989C2314yes—
208#66988C2318yes—
209D4×Dic11C2314yes—
210D4×Dic11C2312yes—
211#66982C2318yes—
212C4×C22⋊D11C2314yes—
213C4×C22⋊D11C2314yes—
214C4×C22⋊D11C2314yes—
215#66979C2312yes—
216#66979C2318yes—
217#66979C2311yescharacteristic
218#66979C2312yes—
219#66979C2318yes—
220C2×C4⋊Dic11C2314yes—
221#66977C2314yes—
222#66977C2318yes—
223#66977C2318yes—
224C2×Dic11⋊C4C2318yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2314yes—
228C2×C4×Dic11C2312yes—
229#66951C23116yes—
230#66951C23116yes—
231#66951C23116yes—
232#66950C2318yes—
233#66950C2318yes—
234#66950C2314yes—
235#66949C23116yes—
236#66949C2318yes—
237#66949C23116yes—
238#66947C23116yes—
239#66946C2312yes—
240#66946C2314yes—
241#66945C23116yes—
242#66945C2318yes—
243#66945C2318yes—
244#66945C2314yes—
245#66945C2312yes—
246#66945C2314yes—
247C4⋊C4×D11C2318yes—
248C4⋊C4×D11C2318yes—
249C4⋊C4×D11C23116yes—
250C4⋊C4×D11C2318yes—
251C4⋊C4×D11C2318yes—
252C4⋊C4×D11C2314yes—
253C4⋊C4×D11C2314yes—
254C4⋊C4×D11C23116yes—
255C4⋊C4×D11C2318yes—
256C4⋊C4×D11C2312yes—
257C4⋊C4×D11C2314yes—
258#66943C23116yes—
259#66943C2318yes—
260#66943C23116yes—
261#66943C2318yes—
262#66943C2314yes—
263#66942C2318yes—
264#66942C23116yes—
265#66942C23116yes—
266#66942C23116yes—
267#66942C23116yes—
268#66942C23116yes—
269#66942C23116yes—
270#66941C2318yes—
271#66941C2318yes—
272#66941C2318yes—
273#66941C2318yes—
274#66941C2314yes—
275#66941C2314yes—
276#66941C23116yes—
277#66940C23116yes—
278#66940C2318yes—
279#66940C23116yes—
280#66940C2318yes—
281#66940C23116yes—
282#66940C2318yes—
283#66940C2314yes—
284#66940C2318yes—
285#66940C2312yes—
286#66940C2314yes—
287#66939C2318yes—
288#66938C23116yes—
289#66936C23116yes—
290(C22⋊D11)⋊C4C2314yes—
291(C22⋊D11)⋊C4C2314yes—
292(C22⋊D11)⋊C4C2314yes—
293C22⋊C4×D11C2314yes—
294C22⋊C4×D11C23116yes—
295C22⋊C4×D11C2312yes—
296C22⋊C4×D11C2314yes—
297#66932C23116yes—
298#66932C23116yes—
299#66932C23116yes—
300#66931C23116yes—
301#66931C23116yes—
302#66931C2318yes—
303#66930C2314yes—
304#66930C23116yes—
305#66930C2312yes—
306#66930C2318yes—
307#66930C2314yes—
308#66930C2318yes—
309#66929C23116yes—
310#66928C2314yes—
311C4×D44C2312yes—
312C4×D44C2314yes—
313#66925C23116yes—
314#66925C23116yes—
315#66925C2314yes—
316#66925C2312yes—
317#66925C2312yes—
318#66925C2312yes—
319C42×D11C23116yes—
320C42×D11C2311yescharacteristic
321C42×D11C2311yescharacteristic
322C42×D11C2312yes—
323C42×D11C2314yes—
324C42×D11C2311yescharacteristic
325C42×D11C2311yescharacteristic
326C42×D11C2312yes—
327C42×D11C2312yes—
328C42×D11C2312yes—
329C42×D11C2312yes—
330C42×D11C2314yes—
331C42×D11C2314yes—
332#66923C23116yes—
333#66923C2312yes—
334#66923C2318yes—
335#66922C2312yes—
336#66922C2312yes—
337#66922C2314yes—
338#66922C2312yes—
339#66922C2314yes—
340C4×Dic22C23116yes—
341C4×Dic22C23116yes—
342C4×Dic22C23116yes—
343C4×Dic22C2312yes—
344C4×Dic22C2314yes—
345C4×Dic22C2318yes—
346C4×Dic22C2318yes—
347C4×Dic22C2318yes—
348C4×Dic22C2318yes—
349C4×Dic22C2314yes—
350C2×#3509—111nomaximal, Sylow
351C23×D11C2412yes—
352C23×D11C2411yescharacteristic
353C11×#41—24no—
354C2×Q8×C11—28no—
355C2×Q8×C11C2411yescharacteristic
356C2×Q8×C11C2414yes—
357C2×Q8×C11C2414yes—
358C2×Q8×C11C2414yes—
359C2×D4×C11C2412yes—
360C2×D4×C11C2411yescharacteristic
361C22×C4×C11C2412yes—
362C22×C4×C11C2412yes—
363C22×C4×C11C2414yes—
364C22×C4×C11C2414yes—
365C22×C4×C11C2411yescharacteristic
366C2×C22⋊D11C2412yes—
367C2×C22⋊D11C2412yes—
368C2×C22⋊D11C2412yes—
369C22×Dic11C2414yes—
370C22×Dic11C2414yes—
371C22×Dic11C2412yes—
372C22×Dic11C2412yes—
373C22×Dic11C2411yescharacteristic
374#4343—24no—
375Q8×D11—216no—
376Q8×D11—216no—
377Q8×D11—216no—
378Q8×D11—216no—
379Q8×D11—24no—
380Q8×D11—216no—
381#4341—28no—
382#4341—24no—
383D4×D11—24no—
384D4×D11—28no—
385#4339—28no—
386#4339—24no—
387C2×D44C2411yescharacteristic
388C2×D44C2412yes—
389C2×C4×D11—28no—
390C2×C4×D11—28no—
391C2×C4×D11—216no—
392C2×C4×D11—216no—
393C2×C4×D11#4118yes—
394C2×C4×D11C2414yes—
395C2×C4×D11C2418yes—
396C2×C4×D11C2414yes—
397C2×C4×D11C2412yes—
398C2×C4×D11C2412yes—
399C2×C4×D11C2414yes—
400C2×C4×D11C2412yes—
401C2×C4×D11C2418yes—
402C2×C4×D11C2412yes—
403C2×C4×D11C2412yes—
404C2×C4×D11C2412yes—
405C2×C4×D11C2418yes—
406C2×C4×D11C2411yescharacteristic
407C2×C4×D11C2411yescharacteristic
408C2×C4×D11C2411yescharacteristic
409C2×C4×D11C2411yescharacteristic
410C2×C4×D11C2412yes—
411C2×Dic22—216no—
412C2×Dic22—28no—
413C2×Dic22C2414yes—
414C2×Dic22C2418yes—
415C2×Dic22C2411yescharacteristic
416C2×Dic22C2414yes—
417C2×Dic22C2414yes—
418C2×Dic22C2418yes—
419C2×Dic22C2418yes—
420C2×Dic22C2412yes—
421C11×C4⋊C4C2412yes—
422C11×C4⋊C4C2414yes—
423C11×C4⋊C4C24116yes—
424C11×C4⋊C4C2418yes—
425C11×C4⋊C4C24116yes—
426C11×C4⋊C4C2414yes—
427C11×C4⋊C4C2414yes—
428C11×C4⋊C4C2418yes—
429C11×C4⋊C4C2418yes—
430C11×C22⋊C4C2412yes—
431C11×C22⋊C4C2414yes—
432C11×C22⋊C4C24116yes—
433C11×C22⋊C4C2414yes—
434C42×C11C2414yes—
435C42×C11C2412yes—
436C42×C11C2412yes—
437C42×C11C2414yes—
438C42×C11C24116yes—
439C42×C11C2411yescharacteristic
440C42×C11C2411yescharacteristic
441C22⋊Dic11C2412yes—
442C22⋊Dic11C2414yes—
443C22⋊Dic11C24116yes—
444C22⋊Dic11C2414yes—
445(C2×D11)⋊C4C2414yes—
446(C2×D11)⋊C4C2418yes—
447(C2×D11)⋊C4C2414yes—
448(C2×D11)⋊C4C2414yes—
449(C2×D11)⋊C4C24116yes—
450(C2×D11)⋊C4C24116yes—
451C4⋊Dic11C2412yes—
452C4⋊Dic11C2414yes—
453C4⋊Dic11C24116yes—
454C4⋊Dic11C2418yes—
455C4⋊Dic11C2414yes—
456C4⋊Dic11C24116yes—
457C4⋊Dic11C2418yes—
458C4⋊Dic11C2414yes—
459C4⋊Dic11C2418yes—
460Dic11⋊C4C2414yes—
461Dic11⋊C4C24116yes—
462Dic11⋊C4C2418yes—
463Dic11⋊C4C24116yes—
464Dic11⋊C4C2414yes—
465Dic11⋊C4C24116yes—
466Dic11⋊C4C2418yes—
467Dic11⋊C4C24116yes—
468Dic11⋊C4C2418yes—
469Dic11⋊C4C24116yes—
470Dic11⋊C4C2414yes—
471Dic11⋊C4C2418yes—
472Dic11⋊C4C24116yes—
473C4×Dic11C2414yes—
474C4×Dic11C2414yes—
475C4×Dic11C2412yes—
476C4×Dic11C24116yes—
477C4×Dic11C2414yes—
478C4×Dic11C2412yes—
479C4×Dic11C2414yes—
480C4×Dic11C24116yes—
481C4×Dic11C2418yes—
482C4×Dic11C2412yes—
483C4×Dic11C2411yescharacteristic
484C4×Dic11C2412yes—
485C4×Dic11C2411yescharacteristic
486C4×Dic11C2412yes—
487C4×Dic11C2412yes—
488C4×Dic11C2414yes—
489C4×Dic11C24116yes—
490#3509—114no—
491#3509—114no—
492#3509—118no—
493#3509—114no—
494#3509—112no—
495#3509—114no—
496#3509—111no—
497#3509—111no—
498#3509—112no—
499#3509—111no—
500#3509D1111yescharacteristic, direct product factor
501C2×#557—114no—
502C2×#556—114no—
503C2×#552—118no—
504C2×#541—114no—
505C2×#536—112no—
506C2×#533—111no—
507C2×#533—114no—
508C22×C4⋊Q8—111no—
509C2×#519—112no—
510C2×C4×#41—111no—
511C23×C11C2512yes—
512C23×C11C2511yescharacteristic
513C22×D11—24no—
514C22×D11—24no—
515C22×D11—28no—
516C22×D11C2×#4114yes—
517C22×D11C2512yes—
518C22×D11C2511yescharacteristic
519C22×D11C2511yescharacteristic
520Q8×C11—28no—
521Q8×C11—28no—
522Q8×C11—22no—
523Q8×C11—28no—
524D4×C11—24no—
525D4×C11—22no—
526C2×C4×C11—28no—
527C2×C4×C11—24no—
528C2×C4×C11—24no—
529C2×C4×C11—28no—
530C2×C4×C11C2×#4114yes—
531C2×C4×C11C2514yes—
532C2×C4×C11C2518yes—
533C2×C4×C11C2512yes—
534C2×C4×C11C2512yes—
535C2×C4×C11C2518yes—
536C2×C4×C11C2511yescharacteristic
537C2×C4×C11C2511yescharacteristic
538C2×C4×C11C2512yes—
539C22⋊D11—24no—
540C22⋊D11—24no—
541C22⋊D11—24no—
542C2×Dic11—28no—
543C2×Dic11—24no—
544C2×Dic11—24no—
545C2×Dic11—28no—
546C2×Dic11C2×#4114yes—
547C2×Dic11C2514yes—
548C2×Dic11C2518yes—
549C2×Dic11C2512yes—
550C2×Dic11C2512yes—
551C2×Dic11C2518yes—
552C2×Dic11C2511yescharacteristic
553C2×Dic11C2511yescharacteristic
554C2×Dic11C2512yes—
555D44—24no—
556D44—22no—
557C4×D11—24no—
558C4×D11—216no—
559C4×D11—216no—
560C4×D11—28no—
561C4×D11—24no—
562C4×D11—216no—
563C4×D11—24no—
564C4×D11—24no—
565C4×D11—28no—
566C4×D11—24no—
567C4×D11—24no—
568C4×D11—28no—
569C4×D11C2×#4114yes—
570C4×D11C2×#4114yes—
571C4×D11C2×#4114yes—
572C4×D11C2×#4114yes—
573C4×D112−1+418yes—
574Dic22—28no—
575Dic22—28no—
576Dic22—22no—
577Dic22—28no—
578Dic22—216no—
579Dic22—216no—
580Dic22—24no—
581Dic22—216no—
582C22×#41—111no—
583C23×Q8—112no—
584#557—118no—
585#557—114no—
586#557—1116no—
587#557—118no—
588#557—118no—
589#557—114no—
590#557—118no—
591#557—114no—
592#557C2×D1114yescomplemented
593#556—114no—
594#556—1116no—
595#556—118no—
596#556—118no—
597#556—118no—
598#556—114no—
599#556—114no—
600#556—118no—
601#556C2×D1114yescomplemented
602#552—1116no—
603#552—1116no—
604#552—118no—
605#552—1116no—
606#552—118no—
607#552—118no—
608#552—118no—
609#552—118no—
610#552—118no—
611#552—1116no—
612#552—118no—
613#552C2×D1118yescomplemented
614#541—114no—
615#541—1116no—
616#541—1116no—
617#541—114no—
618#541—118no—
619#541—118no—
620#541—114no—
621#541C2×D1114yescomplemented
622#536—112no—
623#536—112no—
624#536—114no—
625#536—114no—
626#536—118no—
627#536—118no—
628#536—112no—
629#536C2×D1112yes—
630#533—112no—
631#533—114no—
632#533—114no—
633#533—112no—
634#533—118no—
635#533—114no—
636#533—118no—
637#533—118no—
638#533—114no—
639#533—118no—
640#533—118no—
641#533—112no—
642#533—118no—
643#533—111no—
644#533—114no—
645#533C2×D1111yescharacteristic, complemented
646#533C2×D1114yescomplemented
647C2×C4⋊Q8—112no—
648C2×C4⋊Q8—112no—
649C2×C4⋊Q8—112no—
650C2×C4⋊Q8—114no—
651C2×C4⋊Q8—112no—
652C2×C4⋊Q8—114no—
653C2×C4⋊Q8—112no—
654C2×C4⋊Q8—112no—
655C2×C4⋊Q8—114no—
656C2×C4⋊Q8—114no—
657C2×C4⋊Q8—111no—
658C2×C4⋊Q8C2×D1111yescharacteristic, complemented
659C2×#126—1116no—
660C2×#125—112no—
661C2×#125—118no—
662C2×#125—1116no—
663C2×#124—114no—
664C2×#123—118no—
665C2×C22⋊Q8—118no—
666C2×C22⋊Q8—114no—
667C2×C22⋊Q8—118no—
668#519—112no—
669#519—118no—
670#519—118no—
671#519—112no—
672#519—112no—
673#519—118no—
674#519C2×D1112yescomplemented
675C4×#41—111no—
676C4×#41—112no—
677C4×#41—114no—
678C4×#41—112no—
679C4×#41—111no—
680C4×#41—112no—
681C4×#41—112no—
682C4×#41—111no—
683C4×#41C2×D1111yescharacteristic
684C2×C4×Q8—112no—
685C2×C4×Q8—118no—
686C2×C4×Q8—118no—
687C2×C4×Q8—118no—
688C2×C4×Q8—114no—
689C2×C4×D4—114no—
690C2×C4×D4—112no—
691C2×#117—111no—
692C2×#117—112no—
693C2×#117—112no—
694C2×#117—118no—
695C2×#117—118no—
696C22×C4⋊C4—114no—
697C22×C42—111no—
698C22×C42—112no—
699C22×C11—22no—
700C22×C11—22no—
701C22×C11—24no—
702C22×C11C22×#4112yes—
703C22×C11C2611yescharacteristic
704C2×D11—22no—
705C2×D11—28no—
706C2×D11—22no—
707C2×D11—24no—
708C2×D11—48no—
709C2×D11C22×#4112yes—
710C2×D11C22×#4112yes—
711C2×D11C2×2−1+414yes—
712C4×C11—22no—
713C4×C11—28no—
714C4×C11—24no—
715C4×C11—22no—
716C4×C11—28no—
717C4×C11C22×#4112yes—
718C4×C11C22×#4112yes—
719C4×C11C2×2−1+414yes—
720Dic11—28no—
721Dic11—22no—
722Dic11—28no—
723Dic11—24no—
724Dic11—22no—
725Dic11C22×#4112yes—
726Dic11C22×#4112yes—
727Dic11C2×2−1+414yes—
728C2×#41—111no—
729C2×#41—112no—
730C2×#41—111no—
731C2×#41—112no—
732C2×#41—111no—
733C2×#41—228no—
734C2×#41C22×D1111yescharacteristic
735C22×Q8—114no—
736C22×Q8—114no—
737C22×Q8—114no—
738C22×Q8—111no—
739C22×Q8—114no—
740C22×Q8—114no—
741C22×Q8—114no—
742C22×Q8—112no—
743C22×Q8—2216no—
744C22×Q8C22×D1112yes—
745C22×D4—112no—
746C22×D4—111no—
747C23×C4—111no—
748C23×C4—114no—
749C23×C4—112no—
750C23×C4—114no—
751C23×C4—112no—
752C4⋊Q8—114no—
753C4⋊Q8—114no—
754C4⋊Q8—118no—
755C4⋊Q8—114no—
756C4⋊Q8—114no—
757C4⋊Q8—114no—
758C4⋊Q8—118no—
759C4⋊Q8—118no—
760C4⋊Q8—118no—
761C4⋊Q8—118no—
762C4⋊Q8—114no—
763C4⋊Q8—114no—
764C4⋊Q8—1116no—
765C4⋊Q8—112no—
766C4⋊Q8—112no—
767C4⋊Q8—114no—
768C4⋊Q8—112no—
769C4⋊Q8—114no—
770C4⋊Q8C22×D1112yes—
771C4⋊Q8C22×D1112yes—
772C4⋊Q8C22×D1114yes—
773C4⋊Q8C22×D1112yes—
774C4⋊Q8C22×D1114yes—
775#126—1116no—
776#126—1116no—
777#126—1116no—
778#126—1116no—
779#126—1116no—
780#126—1116no—
781#126—1116no—
782#126C22×D11116yes—
783#125—118no—
784#125—114no—
785#125—1116no—
786#125—1116no—
787#125—118no—
788#125—118no—
789#125—1116no—
790#125—1116no—
791#125—1116no—
792#125—1116no—
793#125—1116no—
794#125—1116no—
795#125—112no—
796#125—118no—
797#125—1116no—
798#125C22×D1112yes—
799#125C22×D1118yes—
800#125C22×D11116yes—
801#124—114no—
802#124—114no—
803#124—1116no—
804#124—114no—
805#124C22×D1114yes—
806#123—118no—
807#123—118no—
808#123—1116no—
809#123—1116no—
810#123—118no—
811#123C22×D1118yes—
812C22⋊Q8—118no—
813C22⋊Q8—114no—
814C22⋊Q8—118no—
815C22⋊Q8—118no—
816C22⋊Q8—114no—
817C22⋊Q8—118no—
818C22⋊Q8—1116no—
819C22⋊Q8—118no—
820C22⋊Q8—118no—
821C22⋊Q8—114no—
822C22⋊Q8—1116no—
823C22⋊Q8—118no—
824C22⋊Q8—1116no—
825C22⋊Q8—118no—
826C22⋊Q8—1116no—
827C22⋊Q8C22×D1118yes—
828C22⋊Q8C22×D1114yes—
829C22⋊Q8C22×D1118yes—
830C4×Q8—112no—
831C4×Q8—118no—
832C4×Q8—118no—
833C4×Q8—118no—
834C4×Q8—114no—
835C4×Q8—114no—
836C4×Q8—112no—
837C4×Q8—1116no—
838C4×Q8—118no—
839C4×Q8—1116no—
840C4×Q8—118no—
841C4×Q8—1116no—
842C4×Q8—118no—
843C4×Q8—118no—
844C4×Q8—114no—
845C4×Q8—112no—
846C4×Q8—114no—
847C4×Q8—1116no—
848C4×Q8—118no—
849C4×Q8—118no—
850C4×Q8—1116no—
851C4×Q8—1116no—
852C4×Q8—118no—
853C4×Q8—118no—
854C4×Q8—114no—
855C4×Q8C22×D1112yes—
856C4×Q8C22×D1118yes—
857C4×Q8C22×D1118yes—
858C4×Q8C22×D1118yes—
859C4×Q8C22×D1114yes—
860C4×D4—114no—
861C4×D4—112no—
862C4×D4—114no—
863C4×D4—114no—
864C4×D4—114no—
865C4×D4—114no—
866C4×D4—112no—
867C4×D4—114no—
868C4×D4—114no—
869C4×D4—114no—
870C4×D4—114no—
871C4×D4—112no—
872C4×D4C22×D1114yes—
873C4×D4C22×D1112yes—
874#117—111no—
875#117—112no—
876#117—112no—
877#117—118no—
878#117—118no—
879#117—112no—
880#117—114no—
881#117—114no—
882#117—1116no—
883#117—118no—
884#117—118no—
885#117—112no—
886#117—114no—
887#117—114no—
888#117—118no—
889#117—118no—
890#117—1116no—
891#117—112no—
892#117—112no—
893#117—112no—
894#117—114no—
895#117—1116no—
896#117—1116no—
897#117C22×D1111yescharacteristic
898#117C22×D1112yes—
899#117C22×D1112yes—
900#117C22×D1118yes—
901#117C22×D1118yes—
902C2×C4⋊C4—118no—
903C2×C4⋊C4—114no—
904C2×C4⋊C4—118no—
905C2×C4⋊C4—118no—
906C2×C4⋊C4—118no—
907C2×C4⋊C4—118no—
908C2×C4⋊C4—114no—
909C2×C4⋊C4—112no—
910C2×C4⋊C4—114no—
911C2×C4⋊C4—114no—
912C2×C4⋊C4—1116no—
913C2×C4⋊C4—1116no—
914C2×C4⋊C4—118no—
915C2×C4⋊C4C22×D1114yes—
916C2×C22⋊C4—112no—
917C2×C22⋊C4—114no—
918C2×C22⋊C4—114no—
919C2×C22⋊C4—1116no—
920C2×C42—112no—
921C2×C42—111no—
922C2×C42—112no—
923C2×C42—114no—
924C2×C42—112no—
925C2×C42—1116no—
926C2×C42—111no—
927C2×C42—114no—
928C2×C42—114no—
929C2×C42—112no—
930C2×C42—112no—
931C2×C42—111no—
932C2×C42—111no—
933C2×C42—114no—
934C2×C42—112no—
935C2×C42—112no—
936C2×C42—111no—
937C2×C42C22×D1111yescharacteristic
938C2×C42C22×D1112yes—
939C2×C11—22no—
940C2×C11—42no—
941C2×C11C23×#4111yescharacteristic
942C2×C11C22×2−1+412yes—
943D11—22no—
944D11—42no—
945D11#350914yesdirect product factor
946C24—111no—
947C24—112no—
948#41—24no—
949#41—228no—
950#41—228no—
951#41—224no—
952#41—224no—
953#41—224no—
954C2×Q8—28no—
955C2×Q8—118no—
956C2×Q8—114no—
957C2×Q8—118no—
958C2×Q8—114no—
959C2×Q8—118no—
960C2×Q8—114no—
961C2×Q8—112no—
962C2×Q8—111no—
963C2×Q8—2216no—
964C2×Q8—2216no—
965C2×Q8—2216no—
966C2×Q8—2216no—
967C2×Q8—2216no—
968C2×Q8—224no—
969C2×Q8—2216no—
970C2×Q8—228no—
971C2×Q8C23×D1114yes—
972C2×Q8C23×D1114yes—
973C2×Q8C23×D1114yes—
974C2×Q8C23×D1111yescharacteristic
975C2×D4—112no—
976C2×D4—112no—
977C2×D4—112no—
978C2×D4—112no—
979C2×D4—111no—
980C2×D4—224no—
981C2×D4—228no—
982C2×D4C23×D1112yes—
983C2×D4C23×D1111yescharacteristic
984C22×C4—111no—
985C22×C4—118no—
986C22×C4—111no—
987C22×C4—112no—
988C22×C4—111no—
989C22×C4—111no—
990C22×C4—111no—
991C22×C4—112no—
992C22×C4—114no—
993C22×C4—112no—
994C22×C4—114no—
995C22×C4—114no—
996C22×C4—118no—
997C22×C4—112no—
998C22×C4—118no—
999C22×C4—112no—
1000C22×C4—112no—
1001C22×C4—112no—
1002C22×C4—114no—
1003C22×C4—114no—
1004C22×C4—112no—
1005C22×C4—112no—
1006C22×C4—118no—
1007C22×C4—228no—
1008C22×C4—228no—
1009C22×C4—2216no—
1010C22×C4—2216no—
1011C22×C4C23×D1112yes—
1012C22×C4C23×D1114yes—
1013C22×C4C23×D1112yes—
1014C22×C4C23×D1114yes—
1015C22×C4C23×D1111yescharacteristic
1016C4⋊C4—1116no—
1017C4⋊C4—118no—
1018C4⋊C4—1116no—
1019C4⋊C4—118no—
1020C4⋊C4—118no—
1021C4⋊C4—114no—
1022C4⋊C4—114no—
1023C4⋊C4—112no—
1024C4⋊C4—114no—
1025C4⋊C4—114no—
1026C4⋊C4—114no—
1027C4⋊C4—118no—
1028C4⋊C4—114no—
1029C4⋊C4—1116no—
1030C4⋊C4—1116no—
1031C4⋊C4—1116no—
1032C4⋊C4—1116no—
1033C4⋊C4—1116no—
1034C4⋊C4—1116no—
1035C4⋊C4—118no—
1036C4⋊C4—118no—
1037C4⋊C4—118no—
1038C4⋊C4C23×D1118yes—
1039C4⋊C4C23×D1118yes—
1040C4⋊C4C23×D1114yes—
1041C4⋊C4C23×D1112yes—
1042C4⋊C4C23×D1114yes—
1043C4⋊C4C23×D1114yes—
1044C4⋊C4C23×D11116yes—
1045C4⋊C4C23×D11116yes—
1046C4⋊C4C23×D1118yes—
1047C22⋊C4—112no—
1048C22⋊C4—114no—
1049C22⋊C4—114no—
1050C22⋊C4—1116no—
1051C22⋊C4—114no—
1052C22⋊C4—118no—
1053C22⋊C4—114no—
1054C22⋊C4—114no—
1055C22⋊C4—1116no—
1056C22⋊C4—1116no—
1057C22⋊C4C23×D1112yes—
1058C22⋊C4C23×D1114yes—
1059C22⋊C4C23×D1114yes—
1060C22⋊C4C23×D11116yes—
1061C42—111no—
1062C42—112no—
1063C42—114no—
1064C42—112no—
1065C42—112no—
1066C42—111no—
1067C42—114no—
1068C42—114no—
1069C42—114no—
1070C42—112no—
1071C42—112no—
1072C42—112no—
1073C42—1116no—
1074C42—1116no—
1075C42—1116no—
1076C42—118no—
1077C42—114no—
1078C42C23×D1111yescharacteristic
1079C42C23×D1112yes—
1080C42C23×D1111yescharacteristic
1081C42C23×D1114yes—
1082C42C23×D1112yes—
1083C42C23×D11116yes—
1084C42C23×D1114yes—
1085C11C2×#350911yescharacteristic, complemented, Sylow
1086C23—111no—
1087C23—114no—
1088C23—111no—
1089C23—112no—
1090C23—224no—
1091C23—224no—
1092C23—228no—
1093C23C24×D1112yes—
1094C23C24×D1111yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—22no—
1098Q8—28no—
1099Q8—2216no—
1100Q8—2216no—
1101Q8—224no—
1102Q8—2216no—
1103Q8—228no—
1104Q8—228no—
1105Q8—222no—
1106Q8—228no—
1107D4—24no—
1108D4—22no—
1109D4—224no—
1110D4—224no—
1111D4—224no—
1112D4—224no—
1113D4—222no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—28no—
1118C2×C4—114no—
1119C2×C4—111no—
1120C2×C4—112no—
1121C2×C4—111no—
1122C2×C4—114no—
1123C2×C4—114no—
1124C2×C4—114no—
1125C2×C4—114no—
1126C2×C4—118no—
1127C2×C4—114no—
1128C2×C4—118no—
1129C2×C4—112no—
1130C2×C4—118no—
1131C2×C4—112no—
1132C2×C4—224no—
1133C2×C4—224no—
1134C2×C4—228no—
1135C2×C4—224no—
1136C2×C4—2216no—
1137C2×C4—2216no—
1138C2×C4—228no—
1139C2×C4—224no—
1140C2×C4—2216no—
1141C2×C4—224no—
1142C2×C4—224no—
1143C2×C4—228no—
1144C2×C4—228no—
1145C2×C4—224no—
1146C2×C4—224no—
1147C2×C4—228no—
1148C2×C4#41×D1114yes—
1149C2×C4C24×D1114yes—
1150C2×C4C24×D1118yes—
1151C2×C4C24×D1112yes—
1152C2×C4C24×D1118yes—
1153C2×C4C24×D1112yes—
1154C2×C4C24×D1111yescharacteristic
1155C2×C4C24×D1111yescharacteristic
1156C2×C4C24×D1112yes—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—112no—
1161C22—114no—
1162C22—112no—
1163C22—228no—
1164C22—222no—
1165C22—222no—
1166C22—224no—
1167C22—448no—
1168C22C2×#41×D1112yes—
1169C22C25×D1111yescharacteristic
1170C4—22no—
1171C4—28no—
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—112no—
1176C4—112no—
1177C4—114no—
1178C4—222no—
1179C4—228no—
1180C4—224no—
1181C4—222no—
1182C4—228no—
1183C4C2×#41×D1112yes—
1184C4C2×#41×D1112yes—
1185C4D11×2−1+414yes—
1186C2—22no—
1187C2—42no—
1188C2—114no—
1189C2—222no—
1190C2—442no—
1191C2C22×#41×D1111yescharacteristic
1192C2C2×D11×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3509C2
prime radicalC2×#41×D11C22
hypercenter#3509D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13082503C2semidirect
2. #13082502C2semidirect
3. #13082501C2semidirect
4. #13082500C2semidirect
5. #13082499C2semidirect
6. #13082498C2semidirect
7. #13082497C2semidirect
8. #13082496C2semidirect
9. #13082495C2semidirect
10. #13082494C2semidirect
11. D11×#557C2semidirect
12. D11×#556C2semidirect
13. D11×#552C2semidirect
14. D11×#541C2semidirect
16. D11×#533C2semidirect
17. D11×#533C2semidirect
18. C2×D11×C4⋊Q8C2semidirect
19. D11×#519C2semidirect
21. C11×#3509C2semidirect
24. C11×#557C22semidirect
25. C11×#556C22semidirect
26. C11×#552C22semidirect
27. C11×#541C22semidirect
29. C11×#533C22semidirect
30. C11×#533C22semidirect
31. C2×C11×C4⋊Q8C22semidirect
32. C11×#519C22semidirect
37. #10623343C22semidirect
38. C2×#66997C22semidirect
39. #10623263C22semidirect
40. #10623262C22semidirect
41. #10623259C22semidirect
42. #10623259C22semidirect
43. #10623259C22semidirect
50. D11×C4⋊Q8C22semidirect
51. D11×C4⋊Q8C22semidirect
52. D11×C4⋊Q8C22semidirect
53. #10623252C22semidirect
54. #10623252C22semidirect
55. #10623239C22semidirect
57. #10623233C22semidirect
58. #10623232C22semidirect
59. #10623228C22semidirect
60. #10623227C22semidirect
61. #10623225C22semidirect
62. #10623224C22semidirect
63. #10623219C22semidirect
64. #10623219C22semidirect
68. #10623216C22semidirect
69. #10623216C22semidirect
72. #10623202C22semidirect
74. #10623181C22semidirect
76. #10623173C22semidirect
77. #10623172C22semidirect
78. #10623170C22semidirect
83. #10623156C22semidirect
84. #10623153C22semidirect
85. #10623153C22semidirect
86. #10623153C22semidirect
87. #10623115C22semidirect
88. #10623114C22semidirect
89. #10623112C22semidirect
90. #10623109C22semidirect
91. #10623109C22semidirect
92. #10623109C22semidirect
94. #10623103C22semidirect
95. #10623103C22semidirect
101. #10623101C22semidirect
102. #10623100C22semidirect
103. #10623099C22semidirect
104. #10623098C22semidirect
105. #10623098C22semidirect
108. #10623073C22semidirect
109. #10623072C22semidirect
112. #10623064C22semidirect
113. #10623062C22semidirect
114. #10623060C22semidirect
123. #10623049C22semidirect
124. #10623048C22semidirect
125. #10623048C22semidirect
126. #10623047C22semidirect
127. #10623047C22semidirect
128. #10623047C22semidirect
129. #10623044C22semidirect
131. C2×#66941C22semidirect
136. #10623001C22semidirect
137. #10623001C22semidirect
138. C2×#66922C22semidirect
500. #3509D11direct (N × H)
592. #557C2×D11semidirect
601. #556C2×D11semidirect
613. #552C2×D11semidirect
621. #541C2×D11semidirect
645. #533C2×D11semidirect
646. #533C2×D11semidirect
658. C2×C4⋊Q8C2×D11semidirect
674. #519C2×D11semidirect
945. D11#3509direct (N × H)
1085. C11C2×#3509semidirect

Maximal subgroups

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

subgroupindex
#130825032
#130825022
#130825012
#130825002
#130824992
#130824982
#130824972
#130824962
#130824952
#130824942
D11×#5572
D11×#5562
D11×#5522
D11×#5412
D11×#5362
D11×#5332
C2×D11×C4⋊Q82
D11×#5192
C4×#41×D112
C11×#35092
C2×#350911