Subgroups — #14641579

Order 2816.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066827	C₂	1	1	yes	maximal, characteristic
2	#13066749	C₂	1	1	yes	maximal, characteristic
3	C₁₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₆×Dic₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
7	C₁₁×C₆₄	C₄	1	2	yes	complemented
8	C₁₁⋊C₆₄	C₄	1	2	yes	complemented
9	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₁₁	C₈	1	1	yes	characteristic
11	C₂×C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
12	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
13	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
14	C₁₁⋊C₃₂	C₈	1	2	yes	—
15	#7511	—	11	1	no	maximal, Sylow
16	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
17	C₄×Dic₁₁	C₁₆	1	1	yes	characteristic
18	C₂×C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
19	C₁₁×C₁₆	C₄²	1	1	yes	characteristic
20	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
21	C₁₁⋊C₁₆	C₁₆	1	2	yes	—
22	M₁₂₈	—	11	1	no	—
23	M₁₂₈	D₁₁	1	1	yes	characteristic
24	#1397	—	11	1	no	—
25	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
26	C₂×Dic₁₁	—	2	1	no	—
27	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
28	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
29	C₁₁⋊C₈	—	2	1	no	—
30	C₂×C₃₂	—	11	1	no	—
31	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
32	C₄×C₁₆	—	11	1	no	—
33	C₆₄	—	11	2	no	—
34	C₆₄	Dic₁₁	1	2	yes	complemented
35	C₂²×C₁₁	M₆₄	1	1	yes	characteristic
36	C₄×C₁₁	C₄×C₁₆	1	1	yes	characteristic
37	C₄×C₁₁	M₆₄	1	1	yes	characteristic
38	Dic₁₁	—	4	1	no	—
39	C₂×C₁₆	—	11	1	no	—
40	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
41	C₄×C₈	—	11	1	no	—
42	C₃₂	—	11	2	no	—
43	C₃₂	C₄×D₁₁	1	1	yes	characteristic
44	C₃₂	C₂×Dic₁₁	1	1	yes	characteristic
45	C₂×C₁₁	—	2	1	no	—
46	C₂×C₁₁	#1397	1	1	yes	characteristic
47	C₂×C₈	—	11	1	no	—
48	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
49	C₄²	—	11	1	no	—
50	C₁₆	—	11	2	no	—
51	C₁₆	C₈×D₁₁	1	1	yes	characteristic
52	C₁₆	C₄×Dic₁₁	1	1	yes	characteristic
53	C₁₁	#7511	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₄	—	22	1	no	—
55	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
56	C₈	—	22	1	no	—
57	C₈	C₁₆×D₁₁	1	1	yes	characteristic
58	C₈	C₈×Dic₁₁	1	1	yes	characteristic
59	C₂²	#10622085	1	1	yes	characteristic
60	C₄	—	44	1	no	—
61	C₄	#10622085	1	1	yes	characteristic
62	C₄	C₁₆×Dic₁₁	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#13066749	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×Dic₁₁
commutator	C₄×C₁₁	C₄×C₁₆
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×M₁₂₈	C₂
socle	C₂×C₁₁	#1397
prime radical	C₂²×C₁₁	M₆₄
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₁
hypocenter	C₁₁	#7511
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
7. C₁₁×C₆₄	C₄	semidirect
8. C₁₁⋊C₆₄	C₄	semidirect
34. C₆₄	Dic₁₁	semidirect
53. C₁₁	#7511	semidirect

Maximal subgroups

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

subgroup	index
#13066827	2
#13066749	2
C₁₁×M₁₂₈	2
#7511	11