Subgroups — C₂×#4339 #67034

Order 352.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊D₁₁	C₂	1	2	yes	maximal, complemented
3	#4339	C₂	1	8	yes	maximal, direct product factor
4	C₂×D₄₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₁₁	C₂	1	2	yes	maximal, complemented
6	C₂×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×D₁₁	C₂²	1	2	yes	—
9	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₁	C₂²	1	4	yes	complemented
12	C₂²⋊D₁₁	C₂²	1	8	yes	complemented
13	C₂×Dic₁₁	C₂²	1	2	yes	—
14	D₄₄	C₂²	1	4	yes	complemented
15	C₄×D₁₁	C₂²	1	8	yes	complemented
16	Dic₂₂	C₂²	1	4	yes	complemented
17	C₂²×C₁₁	—	2	2	no	—
18	C₂²×C₁₁	C₂³	1	2	yes	—
19	C₂²×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×D₁₁	—	2	4	no	—
21	C₂×D₁₁	C₂³	1	4	yes	—
22	C₄×C₁₁	C₂³	1	2	yes	—
23	C₄×C₁₁	C₂³	1	2	yes	—
24	Dic₁₁	C₂³	1	4	yes	—
25	C₂×#41	—	11	1	no	maximal, Sylow
26	C₂×C₁₁	—	2	2	no	—
27	C₂×C₁₁	#41	1	2	yes	complemented
28	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
29	D₁₁	—	2	4	no	—
30	#41	—	11	8	no	—
31	C₂×Q₈	—	11	1	no	—
32	C₂×D₄	—	11	2	no	—
33	C₂×D₄	—	11	1	no	—
34	C₂²×C₄	—	11	2	no	—
35	C₂²×C₄	D₁₁	1	1	yes	characteristic, complemented
36	C₁₁	C₂×#41	1	1	yes	characteristic, complemented, Sylow
37	C₂³	—	11	2	no	—
38	C₂³	C₂×D₁₁	1	1	yes	characteristic
39	Q₈	—	11	4	no	—
40	D₄	—	11	8	no	—
41	D₄	—	11	4	no	—
42	C₂×C₄	—	11	2	no	—
43	C₂×C₄	—	11	8	no	—
44	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
45	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₁	1	4	yes	complemented
47	C₂²	—	2	2	no	—
48	C₂²	—	11	4	no	—
49	C₂²	—	22	4	no	—
50	C₂²	C₂²×D₁₁	1	2	yes	—
51	C₂²	C₂²×D₁₁	1	1	yes	characteristic
52	C₄	—	11	4	no	—
53	C₄	C₂²×D₁₁	1	2	yes	—
54	C₄	C₂²×D₁₁	1	2	yes	—
55	C₂	—	2	2	no	—
56	C₂	—	22	4	no	—
57	C₂	#4339	1	2	yes	direct product factor
58	C₂	C₂³×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₁₁
Fitting	C₂²×C₄×C₁₁	C₂
socle	C₂²×C₁₁	C₂³
hypercenter	C₂²×C₄	D₁₁
hypocenter	C₁₁	C₂×#41
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×C₁₁	C₂	semidirect
2. C₂×C₂²⋊D₁₁	C₂	semidirect
3. #4339	C₂	direct (N × H)
4. C₂×D₄₄	C₂	semidirect
5. C₂×C₄×D₁₁	C₂	semidirect
6. C₂×Dic₂₂	C₂	semidirect
11. C₂×C₄×C₁₁	C₂²	semidirect
12. C₂²⋊D₁₁	C₂²	semidirect
14. D₄₄	C₂²	semidirect
15. C₄×D₁₁	C₂²	semidirect
16. Dic₂₂	C₂²	semidirect
27. C₂×C₁₁	#41	semidirect
35. C₂²×C₄	D₁₁	semidirect
36. C₁₁	C₂×#41	semidirect
46. C₂×C₄	C₂×D₁₁	semidirect
57. C₂	#4339	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×C₄×C₁₁	2
C₂×C₂²⋊D₁₁	2
#4339	2
C₂×D₄₄	2
C₂×C₄×D₁₁	2
C₂×Dic₂₂	2
C₂×#41	11

Subgroups — C2×#4339 #67034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4339 #67034