Subgroups — #49148326

Order 36928.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₆₁₆	C₂	1	4	yes	maximal, complemented
2	#32914661	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₅₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₃₀₈	—	2	4	no	—
5	C₂×D₂₃₀₈	C₂²	1	4	yes	—
6	D₄₆₁₆	—	2	8	no	—
7	C₂×C₈×C₅₇₇	C₂²	1	2	yes	—
8	C₄²×C₅₇₇	C₂²	1	1	yes	characteristic
9	C₂²×D₅₇₇	—	2	4	no	—
10	D₂₃₀₈	—	2	8	no	—
11	D₂₃₀₈	—	4	8	no	—
12	C₂×C₄×C₅₇₇	D₄	1	2	yes	—
13	C₂×C₄×C₅₇₇	C₂³	1	1	yes	characteristic
14	C₈×C₅₇₇	D₄	1	4	yes	complemented
15	C₂²×C₅₇₇	C₂×D₄	1	1	yes	characteristic
16	C₂×D₅₇₇	—	4	4	no	—
17	C₂×D₅₇₇	—	4	8	no	—
18	C₄×C₅₇₇	D₈	1	4	yes	complemented
19	C₄×C₅₇₇	C₂×D₄	1	2	yes	—
20	C₂×C₅₇₇	#127	1	1	yes	characteristic
21	C₂×C₅₇₇	C₂×D₈	1	2	yes	—
22	D₅₇₇	—	8	4	no	—
23	C₅₇₇	#493	1	1	yes	characteristic, complemented, Sylow
24	#493	—	577	1	no	maximal, Sylow
25	C₂×D₈	—	577	4	no	—
26	#127	—	577	2	no	—
27	C₄×C₈	D₅₇₇	1	1	yes	characteristic, complemented
28	C₂×D₄	—	577	4	no	—
29	C₂×D₄	—	1154	4	no	—
30	D₈	—	1154	8	no	—
31	C₂×C₈	C₂×D₅₇₇	1	2	yes	—
32	C₄²	C₂×D₅₇₇	1	1	yes	characteristic
33	C₂³	—	1154	4	no	—
34	D₄	—	2308	8	no	—
35	D₄	—	1154	8	no	—
36	C₂×C₄	D₂₃₀₈	1	2	yes	—
37	C₂×C₄	C₂²×D₅₇₇	1	1	yes	characteristic
38	C₈	D₂₃₀₈	1	4	yes	complemented
39	C₂²	—	2308	4	no	—
40	C₂²	—	2308	8	no	—
41	C₂²	C₂×D₂₃₀₈	1	1	yes	characteristic
42	C₄	D₄₆₁₆	1	4	yes	complemented
43	C₄	C₂×D₂₃₀₈	1	2	yes	—
44	C₂	—	4616	4	no	—
45	C₂	#32914661	1	1	yes	characteristic
46	C₂	C₂×D₄₆₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₃₀₈
commutator, cosocle	C₂×C₄×C₅₇₇	C₂³
Frattini	C₂×C₄	C₂²×D₅₇₇
Fitting	C₄×C₈×C₅₇₇	C₂
socle	C₂²×C₅₇₇	C₂×D₄
hypercenter	C₄×C₈	D₅₇₇
hypocenter	C₅₇₇	#493
LCS	G ▷ C₂×C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₄₆₁₆	C₂	semidirect
2. #32914661	C₂	semidirect
3. C₄×C₈×C₅₇₇	C₂	semidirect
14. C₈×C₅₇₇	D₄	semidirect
18. C₄×C₅₇₇	D₈	semidirect
23. C₅₇₇	#493	semidirect
27. C₄×C₈	D₅₇₇	semidirect
38. C₈	D₂₃₀₈	semidirect
42. C₄	D₄₆₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₆₁₆	2
#32914661	2
C₄×C₈×C₅₇₇	2
#493	577