Subgroups — C₂×#66879 #10622713

Order 704.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#66879	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×Dic₁₁	C₄	1	2	yes	—
7	C₂×C₈×C₁₁	C₄	1	4	yes	complemented
8	C₂×C₈×C₁₁	C₂²	1	2	yes	—
9	C₄×Dic₁₁	C₄	1	2	yes	—
10	C₄×Dic₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁⋊C₈	C₄	1	4	yes	complemented
12	C₂×C₁₁⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₁₁	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₁	—	2	4	no	—
19	C₂×Dic₁₁	C₂×C₄	1	4	yes	—
20	C₈×C₁₁	C₂×C₄	1	4	yes	complemented
21	C₁₁⋊C₈	C₂×C₄	1	4	yes	complemented
22	C₂×#97	—	11	1	no	maximal, Sylow
23	C₂²×C₁₁	C₄²	1	2	yes	—
24	C₂²×C₁₁	M₁₆	1	4	yes	—
25	C₂²×C₁₁	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₁₁	C₄²	1	2	yes	—
27	C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
29	Dic₁₁	—	2	4	no	—
30	C₂²×C₈	—	11	1	no	—
31	C₂²×C₈	D₁₁	1	1	yes	characteristic
32	C₂×C₄²	—	11	1	no	—
33	#97	—	11	4	no	—
34	C₂×C₁₁	#97	1	4	yes	complemented
35	C₂×C₁₁	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₁₁	C₂×M₁₆	1	2	yes	—
37	C₂²×C₄	—	11	2	no	—
38	C₂²×C₄	C₂×D₁₁	1	1	yes	characteristic
39	C₂×C₈	—	11	2	no	—
40	C₂×C₈	—	11	4	no	—
41	C₂×C₈	Dic₁₁	1	4	yes	complemented
42	C₂×C₈	C₂×D₁₁	1	2	yes	—
43	C₄²	—	11	2	no	—
44	C₄²	—	11	2	no	—
45	C₁₁	C₂×#97	1	1	yes	characteristic, complemented, Sylow
46	C₂³	C₄×D₁₁	1	1	yes	characteristic
47	C₂×C₄	—	11	4	no	—
48	C₂×C₄	—	22	4	no	—
49	C₂×C₄	C₄×D₁₁	1	1	yes	characteristic
50	C₂×C₄	C₄×D₁₁	1	2	yes	—
51	C₂×C₄	C₂×Dic₁₁	1	2	yes	—
52	C₂×C₄	C₂²×D₁₁	1	1	yes	characteristic
53	C₈	—	11	4	no	—
54	C₈	C₂×Dic₁₁	1	4	yes	complemented
55	C₂²	#4313	1	4	yes	—
56	C₂²	C₄×Dic₁₁	1	2	yes	—
57	C₂²	C₂×C₄×D₁₁	1	1	yes	characteristic
58	C₄	—	22	4	no	—
59	C₄	C₄×Dic₁₁	1	2	yes	—
60	C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
61	C₄	C₂²×Dic₁₁	1	1	yes	characteristic
62	C₂	#66879	1	4	yes	direct product factor
63	C₂	C₂×#4313	1	2	yes	—
64	C₂	C₂×C₄×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₁
commutator	C₂×C₁₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₁₁
Fitting	C₂²×C₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄
cosocle	C₂×C₄×C₁₁	C₂³
hypercenter	C₂²×C₈	D₁₁
hypocenter	C₁₁	C₂×#97
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #66879	C₂	direct (N × H)
7. C₂×C₈×C₁₁	C₄	semidirect
11. C₂×C₁₁⋊C₈	C₄	semidirect
20. C₈×C₁₁	C₂×C₄	semidirect
21. C₁₁⋊C₈	C₂×C₄	semidirect
34. C₂×C₁₁	#97	semidirect
41. C₂×C₈	Dic₁₁	semidirect
45. C₁₁	C₂×#97	semidirect
54. C₈	C₂×Dic₁₁	semidirect
62. C₂	#66879	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₁₁	2
C₂×C₄×Dic₁₁	2
C₂²×C₁₁⋊C₈	2
#66879	2
C₂×#97	11

Subgroups — C2×#66879 #10622713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#66879 #10622713