Subgroups — C₂×#4325 #66994

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄₄	C₂	1	1	yes	maximal, characteristic
3	#4325	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₁	—	2	1	no	—
6	Q₈×C₁₁	—	2	1	no	—
7	Q₈×C₁₁	C₂²	1	2	yes	complemented
8	C₂×C₄×C₁₁	—	2	1	no	—
9	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	D₄₄	—	2	1	no	—
11	D₄₄	C₂²	1	2	yes	—
12	C₁₁⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₁₁	D₄	1	1	yes	characteristic
14	C₂×D₁₁	—	2	2	no	—
15	C₂×D₁₁	—	4	2	no	—
16	C₄×C₁₁	—	2	2	no	—
17	C₄×C₁₁	D₄	1	1	yes	characteristic
18	C₄×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×SD₁₆	—	11	1	no	maximal, Sylow
20	C₂×C₁₁	SD₁₆	1	2	yes	complemented
21	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
22	D₁₁	—	4	2	no	—
23	C₂×Q₈	D₁₁	1	1	yes	characteristic, complemented
24	C₂×D₄	—	11	1	no	—
25	SD₁₆	—	11	4	no	—
26	C₂×C₈	—	11	1	no	—
27	C₁₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂³	—	22	1	no	—
29	Q₈	—	2	1	no	—
30	Q₈	C₂×D₁₁	1	2	yes	complemented
31	D₄	—	11	2	no	—
32	D₄	—	22	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
35	C₈	—	11	2	no	—
36	C₂²	—	22	2	no	—
37	C₂²	—	44	2	no	—
38	C₂²	C₂²⋊D₁₁	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	C₂²⋊D₁₁	1	1	yes	characteristic
41	C₄	C₂²×D₁₁	1	1	yes	characteristic
42	C₂	—	44	2	no	—
43	C₂	#4325	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₁₁
commutator, cosocle	C₄×C₁₁	C₂³
Frattini	C₄	C₂²×D₁₁
Fitting	C₂×Q₈×C₁₁	C₂
socle	C₂²×C₁₁	D₄
prime radical	C₂×D₄₄	C₂
hypercenter	C₂×Q₈	D₁₁
hypocenter	C₁₁	C₂×SD₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₁₁	C₂	semidirect
3. #4325	C₂	direct (N × H)
4. C₂×C₁₁⋊C₈	C₂	semidirect
7. Q₈×C₁₁	C₂²	semidirect
12. C₁₁⋊C₈	C₂²	semidirect
20. C₂×C₁₁	SD₁₆	semidirect
23. C₂×Q₈	D₁₁	semidirect
27. C₁₁	C₂×SD₁₆	semidirect
30. Q₈	C₂×D₁₁	semidirect
43. C₂	#4325	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₁	2
C₂×D₄₄	2
#4325	2
C₂×C₁₁⋊C₈	2
C₂×SD₁₆	11

Subgroups — C2×#4325 #66994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4325 #66994