Subgroups — #20293004

Order 6848.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₅₆	C₂	1	4	yes	maximal, complemented
2	#16812106	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₂₈	—	2	4	no	—
5	C₂×D₄₂₈	C₂²	1	4	yes	—
6	D₈₅₆	—	2	8	no	—
7	C₂×C₈×C₁₀₇	C₂²	1	2	yes	—
8	C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₂²×D₁₀₇	—	2	4	no	—
10	C₂×C₄×C₁₀₇	D₄	1	2	yes	—
11	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
12	D₄₂₈	—	2	8	no	—
13	D₄₂₈	—	4	8	no	—
14	C₈×C₁₀₇	D₄	1	4	yes	complemented
15	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
16	C₂×D₁₀₇	—	4	4	no	—
17	C₂×D₁₀₇	—	4	8	no	—
18	C₄×C₁₀₇	D₈	1	4	yes	complemented
19	C₄×C₁₀₇	C₂×D₄	1	2	yes	—
20	C₂×C₁₀₇	#127	1	1	yes	characteristic
21	C₂×C₁₀₇	C₂×D₈	1	2	yes	—
22	D₁₀₇	—	8	4	no	—
23	C₁₀₇	#493	1	1	yes	characteristic, complemented, Sylow
24	#493	—	107	1	no	maximal, Sylow
25	C₂×D₈	—	107	4	no	—
26	#127	—	107	2	no	—
27	C₄×C₈	D₁₀₇	1	1	yes	characteristic, complemented
28	C₂×D₄	—	107	4	no	—
29	C₂×D₄	—	214	4	no	—
30	D₈	—	214	8	no	—
31	C₂×C₈	C₂×D₁₀₇	1	2	yes	—
32	C₄²	C₂×D₁₀₇	1	1	yes	characteristic
33	C₂³	—	214	4	no	—
34	D₄	—	428	8	no	—
35	D₄	—	214	8	no	—
36	C₂×C₄	D₄₂₈	1	2	yes	—
37	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
38	C₈	D₄₂₈	1	4	yes	complemented
39	C₂²	—	428	4	no	—
40	C₂²	—	428	8	no	—
41	C₂²	C₂×D₄₂₈	1	1	yes	characteristic
42	C₄	D₈₅₆	1	4	yes	complemented
43	C₄	C₂×D₄₂₈	1	2	yes	—
44	C₂	—	856	4	no	—
45	C₂	#16812106	1	1	yes	characteristic
46	C₂	C₂×D₈₅₆	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₂₈
commutator	C₂×C₄×C₁₀₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	C₄×C₈×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	C₄×C₈	D₁₀₇
hypocenter	C₁₀₇	#493
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₅₆	C₂	semidirect
2. #16812106	C₂	semidirect
3. C₄×C₈×C₁₀₇	C₂	semidirect
14. C₈×C₁₀₇	D₄	semidirect
18. C₄×C₁₀₇	D₈	semidirect
23. C₁₀₇	#493	semidirect
27. C₄×C₈	D₁₀₇	semidirect
38. C₈	D₄₂₈	semidirect
42. C₄	D₈₅₆	semidirect