Subgroups — #20268168

Order 6592.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₂₄	C₂	1	4	yes	maximal, complemented
2	#15693018	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₁₂	—	2	4	no	—
5	C₂×D₄₁₂	C₂²	1	4	yes	—
6	D₈₂₄	—	2	8	no	—
7	C₂×C₈×C₁₀₃	C₂²	1	2	yes	—
8	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₂²×D₁₀₃	—	2	4	no	—
10	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
11	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
12	D₄₁₂	—	2	8	no	—
13	D₄₁₂	—	4	8	no	—
14	C₈×C₁₀₃	D₄	1	4	yes	complemented
15	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
16	C₂×D₁₀₃	—	4	4	no	—
17	C₂×D₁₀₃	—	4	8	no	—
18	C₄×C₁₀₃	D₈	1	4	yes	complemented
19	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
20	C₂×C₁₀₃	#127	1	1	yes	characteristic
21	C₂×C₁₀₃	C₂×D₈	1	2	yes	—
22	D₁₀₃	—	8	4	no	—
23	C₁₀₃	#493	1	1	yes	characteristic, complemented, Sylow
24	#493	—	103	1	no	maximal, Sylow
25	C₂×D₈	—	103	4	no	—
26	#127	—	103	2	no	—
27	C₄×C₈	D₁₀₃	1	1	yes	characteristic, complemented
28	C₂×D₄	—	103	4	no	—
29	C₂×D₄	—	206	4	no	—
30	D₈	—	206	8	no	—
31	C₂×C₈	C₂×D₁₀₃	1	2	yes	—
32	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
33	C₂³	—	206	4	no	—
34	D₄	—	412	8	no	—
35	D₄	—	206	8	no	—
36	C₂×C₄	D₄₁₂	1	2	yes	—
37	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
38	C₈	D₄₁₂	1	4	yes	complemented
39	C₂²	—	412	4	no	—
40	C₂²	—	412	8	no	—
41	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
42	C₄	D₈₂₄	1	4	yes	complemented
43	C₄	C₂×D₄₁₂	1	2	yes	—
44	C₂	—	824	4	no	—
45	C₂	#15693018	1	1	yes	characteristic
46	C₂	C₂×D₈₂₄	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄×C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₄×C₈	D₁₀₃
hypocenter	C₁₀₃	#493
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₂₄	C₂	semidirect
2. #15693018	C₂	semidirect
3. C₄×C₈×C₁₀₃	C₂	semidirect
14. C₈×C₁₀₃	D₄	semidirect
18. C₄×C₁₀₃	D₈	semidirect
23. C₁₀₃	#493	semidirect
27. C₄×C₈	D₁₀₃	semidirect
38. C₈	D₄₁₂	semidirect
42. C₄	D₈₂₄	semidirect