Subgroups — #13076893

Order 1408.

3422 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#67006	C₂	1	7	yes	maximal, complemented
3	#10622860	C₂	1	7	yes	maximal, complemented
4	C₂⁵×C₁₁	—	2	28	no	—
5	C₂⁵×C₁₁	C₂²	1	7	yes	—
6	C₂²×C₂²⋊D₁₁	C₂²	1	7	yes	complemented
7	#67006	—	2	28	no	—
8	C₂×C₂²⋊Dic₁₁	C₂²	1	21	yes	complemented
9	C₂⁴×C₁₁	—	2	224	no	—
10	C₂⁴×C₁₁	—	2	84	no	—
11	C₂⁴×C₁₁	D₄	1	28	yes	complemented
12	C₂⁴×C₁₁	C₂³	1	7	yes	—
13	C₂³×D₁₁	C₂³	1	1	yes	characteristic, complemented
14	C₂×C₂²⋊D₁₁	—	2	42	no	—
15	C₂²×Dic₁₁	C₂³	1	7	yes	complemented
16	C₂²⋊Dic₁₁	—	2	42	no	—
17	#2846	—	11	1	no	maximal, Sylow
18	C₂³×C₁₁	—	2	256	no	—
19	C₂³×C₁₁	—	2	224	no	—
20	C₂³×C₁₁	—	2	168	no	—
21	C₂³×C₁₁	—	2	28	no	—
22	C₂³×C₁₁	C₂×D₄	1	42	yes	—
23	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
24	C₂²×D₁₁	—	2	7	no	—
25	C₂²⋊D₁₁	—	4	28	no	—
26	C₂×Dic₁₁	—	2	21	no	—
27	C₂⁶	D₁₁	1	1	yes	characteristic, complemented
28	C₂×#120	—	11	7	no	—
29	#379	—	11	7	no	—
30	C₂²×C₁₁	—	2	224	no	—
31	C₂²×C₁₁	—	2	84	no	—
32	C₂²×C₁₁	#120	1	28	yes	complemented
33	C₂²×C₁₁	C₂²×D₄	1	7	yes	—
34	C₂×D₁₁	—	4	7	no	—
35	Dic₁₁	—	4	7	no	—
36	C₂⁵	—	2	28	no	—
37	C₂⁵	C₂×D₁₁	1	7	yes	—
38	C₂²×D₄	—	11	7	no	—
39	#120	—	22	28	no	—
40	C₂×C₂²⋊C₄	—	11	21	no	—
41	C₂×C₁₁	—	2	28	no	—
42	C₂×C₁₁	C₂×#120	1	7	yes	—
43	D₁₁	—	8	1	no	—
44	C₂⁴	—	2	224	no	—
45	C₂⁴	—	2	84	no	—
46	C₂⁴	—	11	1	no	—
47	C₂⁴	C₂²⋊D₁₁	1	28	yes	complemented
48	C₂⁴	C₂²×D₁₁	1	7	yes	—
49	C₂×D₄	—	22	42	no	—
50	C₂²×C₄	—	11	7	no	—
51	C₂²⋊C₄	—	22	42	no	—
52	C₁₁	#2846	1	1	yes	characteristic, complemented, Sylow
53	C₂³	—	2	256	no	—
54	C₂³	—	2	224	no	—
55	C₂³	—	2	168	no	—
56	C₂³	—	2	28	no	—
57	C₂³	—	22	7	no	—
58	C₂³	C₂×C₂²⋊D₁₁	1	42	yes	—
59	C₂³	C₂³×D₁₁	1	1	yes	characteristic
60	D₄	—	44	28	no	—
61	C₂×C₄	—	22	21	no	—
62	C₂²	—	2	224	no	—
63	C₂²	—	2	84	no	—
64	C₂²	—	44	7	no	—
65	C₂²	#67006	1	28	yes	complemented
66	C₂²	C₂²×C₂²⋊D₁₁	1	7	yes	—
67	C₄	—	44	7	no	—
68	C₂	—	2	28	no	—
69	C₂	—	88	1	no	—
70	C₂	C₂×#67006	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₂⁶×C₁₁	C₂
hypercenter	C₂⁶	D₁₁
hypocenter	C₁₁	#2846
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁶×C₁₁	C₂	semidirect
2. C₂×#67006	C₂	semidirect
3. #10622860	C₂	semidirect
6. C₂²×C₂²⋊D₁₁	C₂²	semidirect
8. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
11. C₂⁴×C₁₁	D₄	semidirect
13. C₂³×D₁₁	C₂³	semidirect
15. C₂²×Dic₁₁	C₂³	semidirect
27. C₂⁶	D₁₁	semidirect
32. C₂²×C₁₁	#120	semidirect
47. C₂⁴	C₂²⋊D₁₁	semidirect
52. C₁₁	#2846	semidirect
65. C₂²	#67006	semidirect

Maximal subgroups

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

subgroup	index
C₂⁶×C₁₁	2
C₂×#67006	2
#10622860	2
#2846	11