Finite Group Databasebeta

← #14720779

Subgroups — #14720779

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082222C211yesmaximal, characteristic
2#13077737C211yesmaximal, characteristic, complemented
3#13077255C211yesmaximal, characteristic, complemented
4#13067083C211yesmaximal, characteristic, complemented
5#13067081C211yesmaximal, characteristic, complemented
6#13067075C211yesmaximal, characteristic, complemented
7#13067057C211yesmaximal, characteristic, complemented
8#13067049C211yesmaximal, characteristic, complemented
9#13067042C211yesmaximal, characteristic, complemented
10#13067028C211yesmaximal, characteristic, complemented
11#13067013C211yesmaximal, characteristic, complemented
12#13067006C211yesmaximal, characteristic, complemented
13#13067002C211yesmaximal, characteristic, complemented
14D11×D4⋊C8C211yesmaximal, characteristic, complemented
15C11×#1482C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623240—21no—
18#10623236—21no—
19#10623226C411yescharacteristic
20#10623221C411yescharacteristic
21#10623212C411yescharacteristic
22#10623207C411yescharacteristic
23#10623189—21no—
24#10623185—21no—
25#10623166C411yescharacteristic
26#10623161C411yescharacteristic
27#10623149C411yescharacteristic
28#10623140C411yescharacteristic
29#10623111C2211yescharacteristic
30C4×#4343C2211yescharacteristic
31#10623079C2211yescharacteristic
32#10623078—21no—
33C4×D4×D11—21no—
34C4×D4×D11C2211yescharacteristic
35#10623059—21no—
36#10623055—21no—
37C4×#4339C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C11×#431C2211yescharacteristic, complemented
40C11×#431C2211yescharacteristic, complemented
41#10622538C2211yescharacteristic, complemented
42#10622537C2211yescharacteristic, complemented
43#10622453—21no—
44#10622452—21no—
45#10622448C2211yescharacteristic, complemented
46#10622448C2211yescharacteristic, complemented
47D11×C4⋊C8C2211yescharacteristic, complemented
48D11×C4⋊C8C2211yescharacteristic, complemented
49#10622341—21no—
50#10622341—21no—
51#10622340—21no—
52#10622333—21no—
53C4×#4313C2211yescharacteristic, complemented
54C8×D44—21no—
55#10622298C2211yescharacteristic, complemented
56#10622298C2211yescharacteristic, complemented
57C4×C8×D11C2211yescharacteristic, complemented
58#10622292—21no—
59C11×Q8⋊C8C2211yescharacteristic, complemented
60C11×Q8⋊C8C2211yescharacteristic, complemented
61C11×D4⋊C8C2211yescharacteristic, complemented
62C11×D4⋊C8C2211yescharacteristic, complemented
63Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
64Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
65D4⋊(C11⋊C8)C2211yescharacteristic, complemented
66D4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622121C2211yescharacteristic
68#10622121C2211yescharacteristic
69#10622121C2211yescharacteristic, complemented
70#10622121C2211yescharacteristic, complemented
71#10622097C2211yescharacteristic
72#10622097C2211yescharacteristic
73#10622097C2211yescharacteristic, complemented
74#10622097C2211yescharacteristic, complemented
75C2×#4343C2×C411yescharacteristic
76C2×D4×D11—21no—
77C2×D4×D11C2×C411yescharacteristic
78C2×#4339—21no—
79C2×#4339D411yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11—21no—
83C11×#126—21no—
84C11×#125C2×C411yescharacteristic
85C11×#124C2×C411yescharacteristic
86C11×#123—21no—
87C11×C22⋊Q8C2×C411yescharacteristic
88C11×#121C2×C411yescharacteristic
89C4×Q8×C11C2311yescharacteristic
90C4×D4×C11—21no—
91C4×D4×C11C2311yescharacteristic
92C11×#117—21no—
93C2×C42×C11C2311yescharacteristic
94#67000C2×C411yescharacteristic
95#66999C2×C411yescharacteristic
96Q8×Dic11C2×C411yescharacteristic
97#66993C2×C411yescharacteristic
98#66992—21no—
99#66991C2×C411yescharacteristic
100#66990—21no—
101D4×Dic11—21no—
102D4×Dic11C2×C411yescharacteristic
103C4×C22⋊D11—21no—
104C4×C22⋊D11—21no—
105C4×C22⋊D11C2×C411yescharacteristic
106C4×C22⋊D11C2×C411yescharacteristic
107C4×C22⋊D11D411yescharacteristic
108C4×C22⋊D11D411yescharacteristic
109C2×(C2×D11)⋊C4—21no—
110#66979D411yescharacteristic
111C2×C4⋊Dic11C2×C411yescharacteristic
112C2×#4318—21no—
113C2×#4313—21no—
114C2×C8×D11—21no—
115C2×C8×D11—21no—
116C2×C8×D11—21no—
117#66951—21no—
118#66951—21no—
119#66950—21no—
120#66950—21no—
121#66949—21no—
122#66949—21no—
123#66948—21no—
124#66948—21no—
125#66948C2×C411yescharacteristic
126#66948C2×C411yescharacteristic
127#66947—21no—
128#66947—21no—
129#66947—21no—
130#66946—21no—
131#66946—21no—
132#66946C2×C411yescharacteristic
133#66946C2×C411yescharacteristic
134#66945—21no—
135#66945C2×C411yescharacteristic
136C4⋊C4×D11—21no—
137C4⋊C4×D11C2×C411yescharacteristic
138#66943C2×C411yescharacteristic
139#66942—21no—
140#66941C2×C411yescharacteristic
141#66939—21no—
142#66939—21no—
143#66938—21no—
144#66938—21no—
145#66937—21no—
146#66937—21no—
147#66937—21no—
148#66936—21no—
149#66936—21no—
150#66935—21no—
151#66935—21no—
152#66935—21no—
153(C22⋊D11)⋊C4—21no—
154(C22⋊D11)⋊C4—21no—
155(C22⋊D11)⋊C4—21no—
156C22⋊C4×D11—21no—
157C22⋊C4×D11—21no—
158C22⋊C4×D11—21no—
159#66932—21no—
160#66931—21no—
161C4×D44—21no—
162C4×D44—21no—
163C4×D44—21no—
164C4×D44—21no—
165C4×D44C2×C411yescharacteristic
166C4×D44C2×C411yescharacteristic
167C4×D44C2×C411yescharacteristic
168C4×D44D411yescharacteristic
169C4×D44C2311yescharacteristic
170C4×D44C2311yescharacteristic
171#66925—21no—
172#66925D411yescharacteristic
173#66925D411yescharacteristic
174C42×D11—21no—
175C42×D11C2311yescharacteristic
176C42×D11C2311yescharacteristic
177C4×Dic22C2×C411yescharacteristic
178C4×Dic22D411yescharacteristic
179C11×C4⋊C8—21no—
180C11×C4⋊C8C2311yescharacteristic
181C11×C4⋊C8C2311yescharacteristic
182C11×C22⋊C8—21no—
183C11×C22⋊C8—21no—
184C4×C8×C11—21no—
185C4×C8×C11C2311yescharacteristic
186C4×C8×C11C2311yescharacteristic
187C22⋊(C11⋊C8)—21no—
188(C2×D11)⋊C8—21no—
189(C2×D11)⋊C8—21no—
190(C2×D11)⋊C8—21no—
191(C2×D11)⋊C8—21no—
192#66879—21no—
193#66879—21no—
194#66879—21no—
195Dic11⋊C8—21no—
196Dic11⋊C8—21no—
197Dic11⋊C8—21no—
198Dic11⋊C8—21no—
199C8×Dic11—21no—
200C4⋊(C11⋊C8)—21no—
201C4⋊(C11⋊C8)—21no—
202C4⋊(C11⋊C8)C2311yescharacteristic
203C4⋊(C11⋊C8)C2311yescharacteristic
204C4×C11⋊C8C2311yescharacteristic
205C4×C11⋊C8C2311yescharacteristic
206#17521—111nomaximal, Sylow
207C23×D11—21no—
208C23×D11—21no—
209C2×Q8×C11C22×C411yescharacteristic
210C2×D4×C11—21no—
211C2×D4×C11C22×C411yescharacteristic
212C22×C4×C11—21no—
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C2×C22⋊D11—21no—
217C2×C22⋊D11—21no—
218C2×C22⋊D11—21no—
219C2×C22⋊D11—21no—
220C2×C22⋊D11C22⋊C411yescharacteristic
221C2×C22⋊D11C22⋊C411yescharacteristic
222C22×Dic11—21no—
223C22×Dic11—21no—
224#4343—22no—
225#4343—41no—
226D4×D11—22no—
227D4×D11—41no—
228D4×D11—44no—
229#4339—42no—
230#4339—81no—
231#4339—81no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—22no—
236C2×D44—21no—
237C2×D44—41no—
238C2×D44C22⋊C411yescharacteristic
239C2×D44C22×C411yescharacteristic
240C2×D44C22×C411yescharacteristic
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—21no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—81no—
250C2×C4×D11—81no—
251C2×C4×D11—81no—
252C2×C4×D11—81no—
253C2×C4×D11C22×C411yescharacteristic
254C2×C4×D11C22×C411yescharacteristic
255C2×C4×D11C2×D411yescharacteristic
256C2×C4×D11C2×D411yescharacteristic
257C2×C4×D11C2×D411yescharacteristic
258C2×C4×D11C2×D411yescharacteristic
259C2×Dic22—21no—
260C2×Dic22C22⋊C411yescharacteristic
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4C22×C411yescharacteristic
270C11×C4⋊C4C22×C411yescharacteristic
271C11×C22⋊C4—21no—
272C11×C22⋊C4—21no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C42×C11—21no—
277C42×C11C22×C411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2411yescharacteristic
281C22⋊Dic11—21no—
282C22⋊Dic11—21no—
283C22⋊Dic11C22⋊C411yescharacteristic
284C22⋊Dic11C22⋊C411yescharacteristic
285(C2×D11)⋊C4—21no—
286(C2×D11)⋊C4—21no—
287(C2×D11)⋊C4—21no—
288(C2×D11)⋊C4—21no—
289(C2×D11)⋊C4—21no—
290(C2×D11)⋊C4—21no—
291(C2×D11)⋊C4—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4C22⋊C411yescharacteristic
298(C2×D11)⋊C4C22⋊C411yescharacteristic
299(C2×D11)⋊C4C22⋊C411yescharacteristic
300(C2×D11)⋊C4C22⋊C411yescharacteristic
301C4⋊Dic11—21no—
302C4⋊Dic11—21no—
303C4⋊Dic11—21no—
304C4⋊Dic11C22⋊C411yescharacteristic
305C4⋊Dic11C22⋊C411yescharacteristic
306C4⋊Dic11C22×C411yescharacteristic
307C4⋊Dic11C22×C411yescharacteristic
308Dic11⋊C4—21no—
309Dic11⋊C4—21no—
310Dic11⋊C4—21no—
311Dic11⋊C4—21no—
312Dic11⋊C4C22⋊C411yescharacteristic
313Dic11⋊C4C22⋊C411yescharacteristic
314Dic11⋊C4C22⋊C411yescharacteristic
315Dic11⋊C4C22⋊C411yescharacteristic
316C4×Dic11—21no—
317C4×Dic11—21no—
318C4×Dic11C22×C411yescharacteristic
319C4×Dic11C22×C411yescharacteristic
320C4×Dic11C2×D411yescharacteristic
321C4×Dic11C2×D411yescharacteristic
322C4×Dic11C2×D411yescharacteristic
323C4×Dic11C2×D411yescharacteristic
324#4318—81no—
325C2×C11⋊C8—21no—
326C2×C11⋊C8—21no—
327C2×C11⋊C8—21no—
328C2×C11⋊C8—21no—
329#4313—42no—
330C8×D11—42no—
331C8×D11—81no—
332C8×D11—81no—
333#3481—111no—
334#2990—111no—
335#2922—111no—
336#1496—111no—
337#1495—111no—
338#1494—111no—
339#1490—111no—
340#1488—111no—
341#1486—111no—
342#1483—111no—
343#1482D1111yescharacteristic, complemented
344#1480—111no—
345#1478—111no—
346#1477—111no—
347C2×D4⋊C8—111no—
348C23×C11—21no—
349C23×C11C2×C22⋊C411yescharacteristic
350C22×D11—21no—
351C22×D11—21no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—81no—
357C22×D11—81no—
358C22×D11C2×C22⋊C411yescharacteristic
359C22×D11C2×C22⋊C411yescharacteristic
360Q8×C11—21no—
361Q8×C11—21no—
362D4×C11—21no—
363D4×C11—21no—
364D4×C11—42no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11C2×C22⋊C411yescharacteristic
376C2×C4×C11C2×C22⋊C411yescharacteristic
377C2×C4×C11C2×C22⋊C411yescharacteristic
378C2×C4×C11C23×C411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C22⋊D11—22no—
382C22⋊D11—41no—
383C22⋊D11—42no—
384C22⋊D11—42no—
385C22⋊D11—81no—
386C22⋊D11—81no—
387C2×Dic11—21no—
388C2×Dic11—21no—
389C2×Dic11—81no—
390C2×Dic11—81no—
391C2×Dic11C2×C22⋊C411yescharacteristic
392C2×Dic11C2×C22⋊C411yescharacteristic
393C2×Dic11C2×C22⋊C411yescharacteristic
394C2×Dic11C2×C22⋊C411yescharacteristic
395C2×Dic11C2×C22⋊C411yescharacteristic
396C2×Dic11C2×C22⋊C411yescharacteristic
397D44—22no—
398D44—21no—
399D44—21no—
400D44—21no—
401D44—42no—
402D44—42no—
403D44—42no—
404D44—81no—
405D44#13112yes—
406C4×D11—22no—
407C4×D11—21no—
408C4×D11—21no—
409C4×D11—21no—
410C4×D11—21no—
411C4×D11—21no—
412C4×D11—21no—
413C4×D11—21no—
414C4×D11—21no—
415C4×D11—41no—
416C4×D11—42no—
417C4×D11—42no—
418C4×D11—41no—
419C4×D11—41no—
420C4×D11—41no—
421C4×D11—41no—
422C4×D11—81no—
423C4×D11—81no—
424C4×D11—81no—
425C4×D11—81no—
426Dic22—41no—
427Dic22—81no—
428C8×C11—41no—
429C8×C11—41no—
430C8×C11—41no—
431C8×C11—41no—
432C11⋊C8—41no—
433C11⋊C8—41no—
434C11⋊C8—41no—
435C11⋊C8—41no—
436#559—111no—
437#554—111no—
438#554—111no—
439#553—111no—
440#553—111no—
441#553—221no—
442#551—221no—
443#551—221no—
444#546—111no—
445#546—111no—
446#546—221no—
447D42—111no—
448#532—111no—
449#529—111no—
450#529—221no—
451#529C2×D1111yescharacteristic
452#525—221no—
453#525—221no—
454C4×#41—111no—
455C4×#41—111no—
456C2×C4×D4—111no—
457C2×C4×D4—111no—
458C2×C4×D4—221no—
459#446—221no—
460#435—221no—
461#435—221no—
462C8×D4—221no—
463#433—221no—
464#433—221no—
465#432—111no—
466#432—111no—
467#431—111no—
468#431—111no—
469#431—111no—
470#431C2×D1111yescharacteristic, complemented
471#431C2×D1111yescharacteristic, complemented
472#424—221no—
473#423—111no—
474C2×C4⋊C8—111no—
475C2×C4⋊C8—111no—
476#408—221no—
477C4×M16—111no—
478C2×C4×C8—111no—
479Q8⋊C8—111no—
480Q8⋊C8—111no—
481Q8⋊C8C2×D1111yescharacteristic, complemented
482Q8⋊C8C2×D1111yescharacteristic, complemented
483D4⋊C8—111no—
484D4⋊C8—111no—
485D4⋊C8—111no—
486D4⋊C8—111no—
487D4⋊C8—111no—
488D4⋊C8—111no—
489D4⋊C8—111no—
490D4⋊C8—111no—
491D4⋊C8—111no—
492D4⋊C8—111no—
493D4⋊C8C2×D1111yescharacteristic, complemented
494D4⋊C8C2×D1111yescharacteristic, complemented
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—41no—
501C22×C11C22×C22⋊C411yescharacteristic
502C2×D11—21no—
503C2×D11—21no—
504C2×D11—22no—
505C2×D11—21no—
506C2×D11—21no—
507C2×D11—21no—
508C2×D11—41no—
509C2×D11—41no—
510C2×D11—41no—
511C2×D11—41no—
512C2×D11—41no—
513C2×D11—84no—
514C2×D11—84no—
515C2×D11#42112yes—
516C4×C11—21no—
517C4×C11—21no—
518C4×C11—21no—
519C4×C11—21no—
520C4×C11—41no—
521C4×C11—41no—
522C4×C11—41no—
523C4×C11C2×#13111yescharacteristic
524C4×C11#56811yescharacteristic
525C4×C11#57611yescharacteristic
526C4×C11#57711yescharacteristic
527Dic11—21no—
528Dic11—21no—
529Dic11—21no—
530Dic11—21no—
531Dic11—21no—
532Dic11—21no—
533Dic11—41no—
534Dic11—41no—
535C2×#41—111no—
536C2×#41—111no—
537C2×#41—221no—
538C22×D4—111no—
539C22×D4—111no—
540C22×D4—221no—
541C23×C4—221no—
542C23×C4—221no—
543C2×M16—221no—
544C2×M16—221no—
545C22×C8—221no—
546C22×C8—221no—
547C22×C8—221no—
548C4⋊Q8—111no—
549#127—111no—
550#126—21no—
551#126—221no—
552#126—221no—
553#126—221no—
554#125—111no—
555#125—221no—
556#125C4×D1111yescharacteristic
557#124—111no—
558#124—221no—
559#124—221no—
560#124C4×D1111yescharacteristic
561#123—21no—
562#123—221no—
563#123—221no—
564#123—221no—
565#123—221no—
566#123—221no—
567#123—221no—
568#123—221no—
569C22⋊Q8—111no—
570C22⋊Q8—221no—
571C22⋊Q8—221no—
572C22⋊Q8—221no—
573C22⋊Q8—221no—
574C22⋊Q8—221no—
575C22⋊Q8C4×D1111yescharacteristic
576#121—111no—
577#121—111no—
578#121—111no—
579#121—221no—
580#121—221no—
581#121—221no—
582#121—221no—
583#121—221no—
584#121—221no—
585#121C4×D1111yescharacteristic
586#120—221no—
587#120—221no—
588#120—221no—
589#120—221no—
590C4×Q8—111no—
591C4×Q8—111no—
592C4×Q8—111no—
593C4×Q8C22×D1111yescharacteristic
594C4×D4—21no—
595C4×D4—111no—
596C4×D4—111no—
597C4×D4—111no—
598C4×D4—111no—
599C4×D4—111no—
600C4×D4—111no—
601C4×D4—111no—
602C4×D4—111no—
603C4×D4—111no—
604C4×D4—111no—
605C4×D4—111no—
606C4×D4—111no—
607C4×D4—111no—
608C4×D4—221no—
609C4×D4—221no—
610C4×D4—221no—
611C4×D4—221no—
612C4×D4—221no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4—221no—
616C4×D4—221no—
617C4×D4—221no—
618C4×D4—221no—
619C4×D4—221no—
620C4×D4C22×D1111yescharacteristic
621#117—21no—
622#117—111no—
623#117—111no—
624#117—111no—
625#117—111no—
626#117—221no—
627#117—221no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C22⋊C4—221no—
635C2×C42—111no—
636C2×C42—111no—
637C2×C42—221no—
638C2×C42C22×D1111yescharacteristic
639C4⋊C8—21no—
640C4⋊C8—111no—
641C4⋊C8—111no—
642C4⋊C8—221no—
643C4⋊C8—221no—
644C4⋊C8—221no—
645C4⋊C8—221no—
646C4⋊C8—221no—
647C4⋊C8—221no—
648C4⋊C8C22×D1111yescharacteristic
649C4⋊C8C22×D1111yescharacteristic
650C22⋊C8—21no—
651C22⋊C8—21no—
652C22⋊C8—221no—
653C22⋊C8—221no—
654C22⋊C8—221no—
655C22⋊C8—221no—
656C22⋊C8—221no—
657#97—221no—
658#97—221no—
659#97—221no—
660C4×C8—21no—
661C4×C8—111no—
662C4×C8—111no—
663C4×C8—221no—
664C4×C8C22×D1111yescharacteristic
665C4×C8C22×D1111yescharacteristic
666C2×C11—41no—
667C2×C11—81no—
668C2×C11#288011yescharacteristic
669C2×C11#289711yescharacteristic
670C2×C11C2×#42111yescharacteristic
671D11—22no—
672D11—41no—
673D11—42no—
674D11—81no—
675C24—221no—
676C24—221no—
677#41—222no—
678#41—442no—
679#41—441no—
680#41—881no—
681#41—881no—
682C2×Q8—111no—
683C2×Q8—221no—
684C2×Q8C2×C4×D1111yescharacteristic
685C2×D4—21no—
686C2×D4—111no—
687C2×D4—111no—
688C2×D4—111no—
689C2×D4—111no—
690C2×D4—111no—
691C2×D4—222no—
692C2×D4—221no—
693C2×D4—221no—
694C2×D4—221no—
695C2×D4—221no—
696C2×D4—221no—
697C2×D4—221no—
698C2×D4—222no—
699C2×D4—221no—
700C2×D4—221no—
701C2×D4—441no—
702C2×D4—441no—
703C2×D4—444no—
704C2×D4C2×C4×D1111yescharacteristic
705C22×C4—21no—
706C22×C4—111no—
707C22×C4—111no—
708C22×C4—111no—
709C22×C4—111no—
710C22×C4—111no—
711C22×C4—111no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—881no—
723C22×C4—881no—
724C22×C4—881no—
725C22×C4—881no—
726C22×C4C2×C4×D1111yescharacteristic
727C22×C4D4×D1111yescharacteristic
728C22×C4D4×D1111yescharacteristic
729M16—442no—
730M16—881no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—221no—
736C2×C8—221no—
737C2×C8—221no—
738C2×C8—221no—
739C2×C8—442no—
740C2×C8—881no—
741C2×C8—881no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—111no—
747C4⋊C4—111no—
748C4⋊C4—111no—
749C4⋊C4—111no—
750C4⋊C4—111no—
751C4⋊C4—111no—
752C4⋊C4—111no—
753C4⋊C4—111no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—221no—
761C4⋊C4C2×C4×D1111yescharacteristic
762C4⋊C4C2×C4×D1111yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—111no—
769C22⋊C4—111no—
770C22⋊C4—111no—
771C22⋊C4—111no—
772C22⋊C4—111no—
773C22⋊C4—111no—
774C22⋊C4—221no—
775C22⋊C4—221no—
776C22⋊C4—221no—
777C22⋊C4—221no—
778C22⋊C4—221no—
779C22⋊C4—221no—
780C22⋊C4—221no—
781C22⋊C4—221no—
782C22⋊C4—221no—
783C22⋊C4—221no—
784C22⋊C4—221no—
785C22⋊C4—221no—
786C22⋊C4—221no—
787C22⋊C4—221no—
788C42—21no—
789C42—111no—
790C42—111no—
791C42—111no—
792C42—111no—
793C42—111no—
794C42—111no—
795C42—221no—
796C42—221no—
797C42C2×C4×D1111yescharacteristic
798C42D4×D1111yescharacteristic
799C42D4×D1111yescharacteristic
800C42C23×D1111yescharacteristic
801C11#1752111yescharacteristic, complemented, Sylow
802C23—21no—
803C23—111no—
804C23—111no—
805C23—221no—
806C23—221no—
807C23—442no—
808C23—442no—
809C23—442no—
810C23—442no—
811C23—881no—
812C23—881no—
813C23C22⋊C4×D1111yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—441no—
817Q8—881no—
818D4—21no—
819D4—21no—
820D4—42no—
821D4—112no—
822D4—222no—
823D4—222no—
824D4—221no—
825D4—221no—
826D4—221no—
827D4—442no—
828D4—442no—
829D4—442no—
830D4—441no—
831D4—442no—
832D4—442no—
833D4—881no—
834D4—881no—
835D4—881no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—111no—
847C2×C4—111no—
848C2×C4—111no—
849C2×C4—111no—
850C2×C4—111no—
851C2×C4—111no—
852C2×C4—222no—
853C2×C4—221no—
854C2×C4—221no—
855C2×C4—221no—
856C2×C4—221no—
857C2×C4—221no—
858C2×C4—221no—
859C2×C4—221no—
860C2×C4—221no—
861C2×C4—221no—
862C2×C4—221no—
863C2×C4—441no—
864C2×C4—442no—
865C2×C4—442no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—881no—
871C2×C4—881no—
872C2×C4—881no—
873C2×C4—881no—
874C2×C4—881no—
875C2×C4—881no—
876C2×C4C22⋊C4×D1111yescharacteristic
877C2×C4C22⋊C4×D1111yescharacteristic
878C2×C4C22⋊C4×D1111yescharacteristic
879C2×C4C22×C4×D1111yescharacteristic
880C2×C4C2×D4×D1111yescharacteristic
881C2×C4C2×D4×D1111yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—441no—
887C8—441no—
888C8—441no—
889C8—441no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—112no—
897C22—221no—
898C22—221no—
899C22—221no—
900C22—222no—
901C22—221no—
902C22—221no—
903C22—441no—
904C22—441no—
905C22—441no—
906C22—441no—
907C22—441no—
908C22—884no—
909C22—884no—
910C22C2×C22⋊C4×D1111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—221no—
919C4—221no—
920C4—221no—
921C4—221no—
922C4—221no—
923C4—221no—
924C4—441no—
925C4—441no—
926C4D11×#13111yescharacteristic
927C4#1062328111yescharacteristic
928C4#1062330011yescharacteristic
929C4#1062330111yescharacteristic
930C2—41no—
931C2—81no—
932C2—222no—
933C2—441no—
934C2—442no—
935C2—881no—
936C2#1307706411yescharacteristic
937C2#1307713811yescharacteristic
938C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1482C2
socleC22×C11C22×C22⋊C4
prime radical#13082222C2
cosocleC42×C11C24
hypercenter#1482D11
hypocenterC11#17521
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #13077737C2semidirect
3. #13077255C2semidirect
4. #13067083C2semidirect
5. #13067081C2semidirect
6. #13067075C2semidirect
7. #13067057C2semidirect
8. #13067049C2semidirect
9. #13067042C2semidirect
10. #13067028C2semidirect
11. #13067013C2semidirect
12. #13067006C2semidirect
13. #13067002C2semidirect
14. D11×D4⋊C8C2semidirect
15. C11×#1482C2semidirect
39. C11×#431C22semidirect
40. C11×#431C22semidirect
41. #10622538C22semidirect
42. #10622537C22semidirect
45. #10622448C22semidirect
46. #10622448C22semidirect
47. D11×C4⋊C8C22semidirect
48. D11×C4⋊C8C22semidirect
53. C4×#4313C22semidirect
55. #10622298C22semidirect
56. #10622298C22semidirect
57. C4×C8×D11C22semidirect
59. C11×Q8⋊C8C22semidirect
60. C11×Q8⋊C8C22semidirect
61. C11×D4⋊C8C22semidirect
62. C11×D4⋊C8C22semidirect
63. Q8⋊(C11⋊C8)C22semidirect
64. Q8⋊(C11⋊C8)C22semidirect
65. D4⋊(C11⋊C8)C22semidirect
66. D4⋊(C11⋊C8)C22semidirect
69. #10622121C22semidirect
70. #10622121C22semidirect
73. #10622097C22semidirect
74. #10622097C22semidirect
343. #1482D11semidirect
470. #431C2×D11semidirect
471. #431C2×D11semidirect
481. Q8⋊C8C2×D11semidirect
482. Q8⋊C8C2×D11semidirect
493. D4⋊C8C2×D11semidirect
494. D4⋊C8C2×D11semidirect
801. C11#17521semidirect

Maximal subgroups

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

subgroupindex
#130822222
#130777372
#130772552
#130670832
#130670812
#130670752
#130670572
#130670492
#130670422
#130670282
#130670132
#130670062
#130670022
D11×D4⋊C82
C11×#14822
#1752111