Finite Group Databasebeta

← #14738740

Subgroups — #14738740

Order 2816.

622 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#13080003C211yesmaximal, characteristic
2#13079810C211yesmaximal, characteristic
3#13079361C211yesmaximal, characteristic, complemented
4#13068191C211yesmaximal, characteristic, complemented
5#13068163C211yesmaximal, characteristic, complemented
6#13068115C211yesmaximal, characteristic, complemented
7#13068105C211yesmaximal, characteristic, complemented
8#13068067C211yesmaximal, characteristic, complemented
9#13068039C211yesmaximal, characteristic, complemented
10#13067991C211yesmaximal, characteristic, complemented
11#13067981C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067314C211yesmaximal, characteristic, complemented
14#13067304C211yesmaximal, characteristic, complemented
15C11×#2935C211yesmaximal, characteristic
16C2×C11×#131—21no—
17C11×#532C2211yescharacteristic
18#10623001C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#408—21no—
28C4×C11×M16C2211yescharacteristic
29#10622750—21no—
30#10622750—21no—
31#10622704—21no—
32#10622693—21no—
33#10622688—21no—
34#10622684—21no—
35#10622655—21no—
36#10622655—21no—
37#10622648—21no—
38#10622648—21no—
39#10622632C2211yescharacteristic
40#10622632C2211yescharacteristic
41#10622621C2211yescharacteristic
42#10622621C2211yescharacteristic
43#10622620C2211yescharacteristic
44#10622620C2211yescharacteristic
45#10622620C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622329—21no—
50#10622329—21no—
51#10622312C2211yescharacteristic
52#10622294C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622120C2211yescharacteristic
58#10622120C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C11×#131—44no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8D411yescharacteristic
77C11×#127D411yescharacteristic
78C11×#124—21no—
79C11×#121—21no—
80C11×#121D411yescharacteristic
81C11×#121D411yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4324—21no—
87C2×#4324—21no—
88#66979—21no—
89#66979—21no—
90#66977—21no—
91#66977—21no—
92#66977—21no—
93#66977—21no—
94C2×#4318—21no—
95C2×Dic44—21no—
96C2×Dic44—21no—
97#66923—21no—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×#97D411yescharacteristic
115C11×#97D411yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C4×C8×C11C2311yescharacteristic
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125#66881—21no—
126#66881—21no—
127#66880—21no—
128#66880—21no—
129#66880—21no—
130#66880—21no—
131#66874—21no—
132#66874—21no—
133#66872—21no—
134#66872—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144#66867—21no—
145#19371—111nomaximal, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—42no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11—42no—
172C2×C8×C11—42no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189C22⋊Dic11—41no—
190#4324—81no—
191#4324—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—41no—
201Dic11⋊C4—41no—
202Dic11⋊C4—41no—
203Dic11⋊C4—41no—
204C4×Dic11—41no—
205C4×Dic11—41no—
206#4318—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211Dic44—42no—
212Dic44—42no—
213#3254—111no—
214#3235—111no—
215#3185—111no—
216#2935D1111yescharacteristic
217#1703—111no—
218#1699—111no—
219#1691—111no—
220#1689—111no—
221#1683—111no—
222#1679—111no—
223#1671—111no—
224#1669—111no—
225#1569—111no—
226#1552—111no—
227#1550—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11#12111yescharacteristic
231Q8×C11—42no—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—81no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—81no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11AGL(1,ℤ/8)12yes—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C2×#131—21no—
279#533—111no—
280#533—111no—
281#532C2×D1111yescharacteristic
282#501—221no—
283#498—111no—
284#494—111no—
285#490—221no—
286#487—111no—
287#487—111no—
288#482—221no—
289#482—221no—
290#477—221no—
291#476—111no—
292#476—111no—
293#474—111no—
294#474—111no—
295#474—111no—
296#474—111no—
297#470—221no—
298#470—221no—
299#468—221no—
300#468—221no—
301#461—111no—
302#461—111no—
303#460—221no—
304#441—221no—
305#441—221no—
306#436C2×D1111yescharacteristic
307#436C2×D1111yescharacteristic
308#435—21no—
309#435—21no—
310C8×D4C2×D1111yescharacteristic
311C8×D4C2×D1111yescharacteristic
312#432—111no—
313#423—111no—
314C2×C4⋊C8C2×D1111yescharacteristic
315#408—21no—
316C4×M16C2×D1111yescharacteristic
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321#333—111no—
322#333—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×#12111yescharacteristic
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57811yescharacteristic
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353C2×#41—21no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×SD16—221no—
357C2×SD16—221no—
358#131—44no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—221no—
362C2×M16C22⋊D1111yescharacteristic
363C2×M16C22⋊D1111yescharacteristic
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8—111no—
371C4⋊Q8D4411yescharacteristic
372#127D4411yescharacteristic
373#125—221no—
374#125—221no—
375#124—21no—
376C22⋊Q8—221no—
377C22⋊Q8—221no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380#121—21no—
381#121D4411yescharacteristic
382#121D4411yescharacteristic
383C4×Q8—221no—
384C4×Q8—221no—
385C4×Q8—221no—
386C4×Q8—221no—
387C4×D4—21no—
388C4×D4C22×D1111yescharacteristic
389C4×D4C22×D1111yescharacteristic
390#117—221no—
391#117—221no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#107—221no—
395#107—221no—
396#107—221no—
397#106—221no—
398#106—221no—
399#106—221no—
400#106—221no—
401C4⋊C8—21no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8C22×D1111yescharacteristic
408C4⋊C8C22×D1111yescharacteristic
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#103—221no—
414#103—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—221no—
426#97—221no—
427#97C22⋊D1111yescharacteristic
428#97C22⋊D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11—81no—
433C2×C11—81no—
434C2×C11#303611yescharacteristic
435C2×C11#306311yescharacteristic
436C2×C11#306911yescharacteristic
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C2×D4411yescharacteristic
449C2×D4C2×D4411yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4C2×D4411yescharacteristic
453C22×C4#433911yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456Q16—442no—
457SD16—881no—
458SD16—881no—
459M16—22no—
460M16—41no—
461M16—42no—
462M16—42no—
463M16—881no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—42no—
468C2×C8—42no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C2×C8C2×C22⋊D1111yescharacteristic
476C2×C8C2×C22⋊D1111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4C2×D4411yescharacteristic
491C4⋊C4C2×D4411yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C42—441no—
499C42—441no—
500C42C2×D4411yescharacteristic
501C42#433911yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C23×D1111yescharacteristic
504C11#1937111yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23#6698311yescharacteristic
508Q8—42no—
509Q8—441no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—881no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—81no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4#6698311yescharacteristic
540C2×C4#6698311yescharacteristic
541C2×C4#6698311yescharacteristic
542C2×C4C22×D4411yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—441no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8#6698512yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22C2×#6698311yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—881no—
572C4—881no—
573C4—881no—
574C4—881no—
575C4#1062328211yescharacteristic
576C4#1062328411yescharacteristic
577C4C2×#6698511yescharacteristic
578C4#1062335311yescharacteristic
579C2—41no—
580C2—81no—
581C2—81no—
582C2#1307808011yescharacteristic
583C2#1307830711yescharacteristic
584C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#2935D11
hypocenterC11#19371
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
3. #13079361C2semidirect
4. #13068191C2semidirect
5. #13068163C2semidirect
6. #13068115C2semidirect
7. #13068105C2semidirect
8. #13068067C2semidirect
9. #13068039C2semidirect
10. #13067991C2semidirect
11. #13067981C2semidirect
12. #13067383C2semidirect
13. #13067314C2semidirect
14. #13067304C2semidirect
504. C11#19371semidirect

Maximal subgroups

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

subgroupindex
#130800032
#130798102
#130793612
#130681912
#130681632
#130681152
#130681052
#130680672
#130680392
#130679912
#130679812
#130673832
#130673142
#130673042
C11×#29352
#1937111