Finite Group Databasebeta

← #14739039

Subgroups — #14739039

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079770C211yesmaximal, characteristic, complemented
2#13078717C211yesmaximal, characteristic
3#13078623C211yesmaximal, characteristic
4#13077637C211yesmaximal, characteristic
5#13068066C211yesmaximal, characteristic, complemented
6#13068065C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13068004C211yesmaximal, characteristic, complemented
9#13068003C211yesmaximal, characteristic, complemented
10#13067992C211yesmaximal, characteristic, complemented
11#13067991C211yesmaximal, characteristic, complemented
12#13067393C211yesmaximal, characteristic, complemented
13#13067323C211yesmaximal, characteristic, complemented
14#13067279C211yesmaximal, characteristic, complemented
15C11×#1679C211yesmaximal, characteristic, complemented
16#10623259C2211yescharacteristic
17#10623259C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C11×#487C2211yescharacteristic, complemented
20C11×#474C2211yescharacteristic
21C11×#461C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622782—21no—
24SD16×Dic11—21no—
25C8×C22⋊D11—21no—
26C2×(C2×D11)⋊C8—21no—
27#10622700C2211yescharacteristic
28#10622696C2211yescharacteristic
29#10622694C2211yescharacteristic, complemented
30#10622691C2211yescharacteristic, complemented
31#10622632C2211yescharacteristic
32D4×C11⋊C8C2211yescharacteristic
33#10622621C2211yescharacteristic
34#10622502—21no—
35#10622497—21no—
36#10622455C2211yescharacteristic
37#10622454C2211yescharacteristic
38#10622448C2211yescharacteristic
39#10622447C2211yescharacteristic
40#10622446C2211yescharacteristic
41#10622446C2211yescharacteristic
42#10622428—21no—
43#10622428—21no—
44#10622418—21no—
45#10622412—21no—
46#10622412—21no—
47#10622401—21no—
48#10622389—21no—
49#10622370—21no—
50(C22⋊D11)⋊C8—21no—
51D11×C22⋊C8—21no—
52C8×D44C2211yescharacteristic
53#10622298C2211yescharacteristic
54#10622293C2211yescharacteristic, complemented
55C11×#334C2211yescharacteristic, complemented
56C11×#332C2211yescharacteristic, complemented
57C11×#332C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622185C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622120C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C2×D4×D11D411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16—21no—
70C22×C8×C11—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66999—21no—
75#66999—21no—
76Q8×Dic11—21no—
77Q8×Dic11—21no—
78C2×#4325—21no—
79D4×Dic11D411yescharacteristic
80C2×#4324—21no—
81C4×C22⋊D11—21no—
82C22×C11⋊C8—21no—
83C2×#4314—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86#66950—21no—
87#66950—21no—
88#66946D411yescharacteristic
89#66945—21no—
90#66945—21no—
91C4⋊C4×D11D411yescharacteristic
92#66943—21no—
93#66943—21no—
94#66940—21no—
95#66940—21no—
96(C22⋊D11)⋊C4—21no—
97C22⋊C4×D11—21no—
98C4×D44C2311yescharacteristic
99C42×D11C2311yescharacteristic
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C11×#107—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#102—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11C2311yescharacteristic
112#66899—21no—
113#66899—21no—
114#66899—21no—
115#66896—21no—
116C22⋊(C11⋊C8)—21no—
117#66885—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8D411yescharacteristic
124(C2×D11)⋊C8D411yescharacteristic
125#66881—21no—
126#66881—21no—
127#66881—21no—
128#66880—21no—
129#66879—21no—
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11—21no—
133C8×Dic11—21no—
134#66874—21no—
135#66873—21no—
136#66872—21no—
137#66871—21no—
138#66871—21no—
139#66871—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19395—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11C2×D411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152D4×D11—22no—
153D4×D11—22no—
154C2×D44C2×D411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11#4111yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C11×SD16—42no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4325—42no—
181#4324—42no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—41no—
191C4⋊Dic11—41no—
192C4⋊Dic11C2×D411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196C4×Dic11—41no—
197C4×Dic11—41no—
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11#4111yescharacteristic
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#4314—42no—
208C8×D11—81no—
209C8×D11—81no—
210#3231—111no—
211#3110—111no—
212#3101—111no—
213#2972—111no—
214#1683—111no—
215#1683—111no—
216#1679—111no—
217#1679D1111yescharacteristic, complemented
218#1673—111no—
219#1673—111no—
220#1671—111no—
221#1671—111no—
222#1572—111no—
223#1554—111no—
224#1544—111no—
225C23×C11—21no—
226C22×D11—21no—
227C22×D11—24no—
228C22×D11—81no—
229C22×D11—81no—
230C22×D11#12111yescharacteristic
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—21no—
236D4×C11#13512yes—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—24no—
246C2×Dic11—21no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—81no—
250C2×Dic11#12111yescharacteristic
251C2×Dic11#12111yescharacteristic
252C2×Dic11#12111yescharacteristic
253D44—21no—
254D44#13512yes—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—21no—
258C4×D11—21no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—81no—
263C4×D11—81no—
264Dic22—41no—
265Dic22—41no—
266Dic22—81no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277#533—111no—
278#533—111no—
279C2×C4×D4—111no—
280#500—111no—
281#498—111no—
282#487—111no—
283#487C2×D1111yescharacteristic, complemented
284#485—221no—
285#485—221no—
286#484—221no—
287#483—221no—
288#479—221no—
289#479—221no—
290#476—111no—
291#476—111no—
292#474—111no—
293#474C2×D1111yescharacteristic
294#461—111no—
295#461—111no—
296#461—111no—
297#461C2×D1111yescharacteristic
298#450—221no—
299#450—221no—
300#440—221no—
301#440—221no—
302C4×SD16—221no—
303C4×SD16—221no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—111no—
307C8×D4—221no—
308C8×D4—221no—
309C8×D4C2×D1111yescharacteristic
310#432—111no—
311#431—111no—
312#431—111no—
313#431—111no—
314C2×C22⋊C8—221no—
315C2×C22⋊C8—221no—
316#335—111no—
317#335—111no—
318#334—111no—
319#334C2×D1111yescharacteristic, complemented
320#333—111no—
321#333—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332C2×D1111yescharacteristic, complemented
327#332C2×D1111yescharacteristic, complemented
328C22×C11—22no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11C2×#12111yescharacteristic
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—22no—
335C2×D11—21no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—84no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×#13511yescharacteristic
344C4×C11C2×#13511yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57711yescharacteristic
347Dic11—21no—
348Dic11—21no—
349Dic11—21no—
350Dic11—41no—
351Dic11—81no—
352Dic11—81no—
353C22×D4—111no—
354C23×C4—221no—
355C2×SD16—21no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×SD16—221no—
359C22×C8—21no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363C4⋊Q8—111no—
364C4⋊Q8—111no—
365C4⋊Q8C22×D1111yescharacteristic
366C4⋊Q8C22×D1111yescharacteristic
367#125—221no—
368#125—221no—
369C22⋊Q8—221no—
370C22⋊Q8—221no—
371C22⋊Q8—221no—
372C22⋊Q8—221no—
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×Q8—221no—
377C4×D4—111no—
378C4×D4—111no—
379C4×D4—111no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4C22×D1111yescharacteristic
383#117—221no—
384#117—221no—
385C2×C4⋊C4—111no—
386C2×C22⋊C4—221no—
387C2×C42—111no—
388#107—21no—
389#107—221no—
390#107—221no—
391#107—221no—
392#106—221no—
393#106—221no—
394#106—221no—
395#106—221no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403C4⋊C8C22×D1111yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—221no—
412#102—21no—
413#102—221no—
414#102—221no—
415#102—221no—
416C22⋊C8—21no—
417C22⋊C8—111no—
418C22⋊C8—111no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—221no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C2×C11—42no—
431C2×C11#304211yescharacteristic
432C2×C11#305011yescharacteristic
433C2×C11#306911yescharacteristic
434D11—41no—
435D11—42no—
436C24—221no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×D4—111no—
442C2×D4—221no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4D4×D1111yescharacteristic
446C22×C4—21no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—881no—
455C22×C4—881no—
456SD16—42no—
457SD16—442no—
458SD16—442no—
459SD16—442no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—81no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—881no—
470C2×C8—881no—
471C2×C8—881no—
472C2×C8D4×D1111yescharacteristic
473C2×C8D4×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—111no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4D4×D1111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—441no—
494C22⋊C4—441no—
495C42—111no—
496C42—111no—
497C42—111no—
498C42—441no—
499C42—441no—
500C42C23×D1111yescharacteristic
501C11#1939511yescharacteristic, complemented, Sylow
502C23—21no—
503C23—111no—
504C23—224no—
505C23—221no—
506C23—881no—
507C23—881no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—441no—
513Q8—441no—
514Q8—881no—
515D4—21no—
516D4—112no—
517D4—224no—
518D4—221no—
519D4#6696912yes—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—111no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—881no—
539C2×C4—881no—
540C2×C4—881no—
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4#41×D1111yescharacteristic
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22—222no—
561C22—441no—
562C22—441no—
563C22—884no—
564C22D11×#12111yescharacteristic
565C4—21no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—221no—
570C4—221no—
571C4—221no—
572C4—441no—
573C4—881no—
574C4—881no—
575C4C2×#6696911yescharacteristic
576C4D11×#13511yescharacteristic
577C4#1062330111yescharacteristic
578C4#1062330611yescharacteristic
579C2—42no—
580C2—441no—
581C2—442no—
582C2#1307812611yescharacteristic
583C2#1307819211yescharacteristic
584C2#1307835111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1679C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1679D11
hypocenterC11#19395
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #13079770C2semidirect
5. #13068066C2semidirect
6. #13068065C2semidirect
7. #13068036C2semidirect
8. #13068004C2semidirect
9. #13068003C2semidirect
10. #13067992C2semidirect
11. #13067991C2semidirect
12. #13067393C2semidirect
13. #13067323C2semidirect
14. #13067279C2semidirect
15. C11×#1679C2semidirect
19. C11×#487C22semidirect
29. #10622694C22semidirect
30. #10622691C22semidirect
54. #10622293C22semidirect
55. C11×#334C22semidirect
56. C11×#332C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622185C22semidirect
60. #10622124C22semidirect
61. #10622120C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622117C22semidirect
66. #10622095C22semidirect
217. #1679D11semidirect
283. #487C2×D11semidirect
319. #334C2×D11semidirect
326. #332C2×D11semidirect
327. #332C2×D11semidirect
501. C11#19395semidirect

Maximal subgroups

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

subgroupindex
#130797702
#130787172
#130786232
#130776372
#130680662
#130680652
#130680362
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