Subgroups — C₂×#23756438 #34094572

Order 20032.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₅₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#23756438	C₂	1	4	yes	maximal, direct product factor
3	C₂×#19097536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₂₅₂	—	2	1	no	—
6	D₂₅₀₄	—	2	1	no	—
7	D₂₅₀₄	C₂²	1	2	yes	complemented
8	#19097536	C₂²	1	2	yes	complemented
9	C₂×D₄×C₃₁₃	—	2	1	no	—
10	D₈×C₃₁₃	—	2	1	no	—
11	D₈×C₃₁₃	C₂²	1	2	yes	complemented
12	C₂×C₈×C₃₁₃	C₂²	1	1	yes	characteristic
13	C₂²×D₃₁₃	—	4	1	no	—
14	D₁₂₅₂	—	2	2	no	—
15	D₁₂₅₂	—	4	1	no	—
16	C₂³×C₃₁₃	—	4	1	no	—
17	D₄×C₃₁₃	—	2	2	no	—
18	D₄×C₃₁₃	—	4	1	no	—
19	C₂×C₄×C₃₁₃	D₄	1	1	yes	characteristic
20	C₈×C₃₁₃	D₄	1	1	yes	characteristic
21	C₈×C₃₁₃	C₂³	1	1	yes	characteristic
22	C₂²×C₃₁₃	—	4	2	no	—
23	C₂²×C₃₁₃	—	8	2	no	—
24	C₂²×C₃₁₃	D₈	1	1	yes	characteristic
25	C₂×D₃₁₃	—	4	2	no	—
26	C₂×D₃₁₃	—	8	2	no	—
27	C₄×C₃₁₃	D₈	1	1	yes	characteristic
28	C₄×C₃₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₃₁₃	—	8	2	no	—
30	C₂×C₃₁₃	D₁₆	1	2	yes	complemented
31	C₂×C₃₁₃	C₂×D₈	1	1	yes	characteristic
32	D₃₁₃	—	8	2	no	—
33	C₃₁₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	—	313	1	no	maximal, Sylow
35	C₂×D₈	—	313	1	no	—
36	C₂×D₈	D₃₁₃	1	1	yes	characteristic, complemented
37	D₁₆	—	313	4	no	—
38	C₂×C₁₆	—	313	1	no	—
39	C₂×D₄	—	2	1	no	—
40	C₂×D₄	—	626	1	no	—
41	D₈	—	2	1	no	—
42	D₈	—	313	2	no	—
43	D₈	—	626	1	no	—
44	D₈	C₂×D₃₁₃	1	2	yes	complemented
45	C₂×C₈	C₂×D₃₁₃	1	1	yes	characteristic
46	C₁₆	—	313	2	no	—
47	C₂³	—	4	1	no	—
48	C₂³	—	1252	1	no	—
49	D₄	—	2	2	no	—
50	D₄	—	4	1	no	—
51	D₄	—	626	2	no	—
52	D₄	—	1252	1	no	—
53	C₂×C₄	C₂²⋊D₃₁₃	1	1	yes	characteristic
54	C₈	C₂²⋊D₃₁₃	1	1	yes	characteristic
55	C₈	C₂²×D₃₁₃	1	1	yes	characteristic
56	C₂²	—	4	2	no	—
57	C₂²	—	8	2	no	—
58	C₂²	—	2504	2	no	—
59	C₂²	—	1252	2	no	—
60	C₂²	#19097546	1	1	yes	characteristic
61	C₄	#19097546	1	1	yes	characteristic
62	C₄	C₂×C₂²⋊D₃₁₃	1	1	yes	characteristic
63	C₂	—	8	2	no	—
64	C₂	—	2504	2	no	—
65	C₂	#23756438	1	2	yes	direct product factor
66	C₂	C₂×#19097546	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19097546
commutator, cosocle	C₈×C₃₁₃	C₂³
Frattini	C₈	C₂²×D₃₁₃
Fitting	C₂×D₈×C₃₁₃	C₂
socle	C₂²×C₃₁₃	D₈
hypercenter	C₂×D₈	D₃₁₃
hypocenter	C₃₁₃	C₂×D₁₆
LCS	G ▷ C₈×C₃₁₃ ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₅₀₄	C₂	semidirect
2. #23756438	C₂	direct (N × H)
3. C₂×#19097536	C₂	semidirect
4. C₂×D₈×C₃₁₃	C₂	semidirect
7. D₂₅₀₄	C₂²	semidirect
8. #19097536	C₂²	semidirect
11. D₈×C₃₁₃	C₂²	semidirect
30. C₂×C₃₁₃	D₁₆	semidirect
33. C₃₁₃	C₂×D₁₆	semidirect
36. C₂×D₈	D₃₁₃	semidirect
44. D₈	C₂×D₃₁₃	semidirect
65. C₂	#23756438	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×D₂₅₀₄	2
#23756438	2
C₂×#19097536	2
C₂×D₈×C₃₁₃	2
C₂×D₁₆	313

Subgroups — C2×#23756438 #34094572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23756438 #34094572