Subgroups — #49148861

Order 36928.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914737	C₂	1	1	yes	maximal, characteristic, complemented
2	#32914733	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₅₇₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#14556313	—	2	1	no	—
5	#22604421	—	2	1	no	—
6	D₄×D₅₇₇	—	2	1	no	—
7	D₄₆₁₆	C₄	1	1	yes	characteristic, complemented
8	#22604403	—	2	1	no	—
9	C₈×D₅₇₇	C₂²	1	1	yes	characteristic
10	D₈×C₅₇₇	C₄	1	1	yes	characteristic, complemented
11	C₂×#14556313	—	4	1	no	—
12	C₂²×D₅₇₇	—	4	1	no	—
13	D₂₃₀₈	—	2	1	no	—
14	C₂²⋊D₅₇₇	—	4	1	no	—
15	C₄×D₅₇₇	D₄	1	1	yes	characteristic
16	#17987230	D₄	1	1	yes	characteristic
17	D₄×C₅₇₇	—	2	1	no	—
18	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₅₇₇	—	4	1	no	—
20	C₂×D₅₇₇	—	4	1	no	—
21	C₂×D₅₇₇	—	8	1	no	—
22	C₂×D₅₇₇	—	8	1	no	—
23	C₂×D₅₇₇	D₈	1	1	yes	characteristic
24	#14556313	—	8	1	no	—
25	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₅₇₇	SD₁₆	1	1	yes	characteristic
27	C₂×C₅₇₇	—	8	1	no	—
28	C₂×C₅₇₇	#102	1	1	yes	characteristic
29	D₅₇₇	—	8	1	no	—
30	D₅₇₇	D₁₆	1	1	yes	characteristic
31	D₅₇₇	SD₃₂	1	1	yes	characteristic
32	C₅₇₇	#357	1	1	yes	characteristic, complemented, Sylow
33	#357	—	577	1	no	maximal, Sylow
34	C₂×D₈	—	577	1	no	—
35	C₂×C₁₆	—	577	1	no	—
36	#107	—	577	1	no	—
37	C₂×D₄	—	1154	1	no	—
38	D₈	—	577	1	no	—
39	D₈	—	1154	1	no	—
40	D₈	#14556313	1	1	yes	characteristic, complemented
41	C₂×C₈	—	577	1	no	—
42	C₄⋊C₄	—	1154	1	no	—
43	C₁₆	—	1154	1	no	—
44	C₂³	—	2308	1	no	—
45	D₄	—	2	1	no	—
46	D₄	—	2308	1	no	—
47	D₄	—	1154	1	no	—
48	C₂×C₄	—	2308	1	no	—
49	C₂×C₄	—	577	1	no	—
50	C₈	—	577	1	no	—
51	C₈	C₂×#14556313	1	1	yes	characteristic
52	C₂²	—	4	1	no	—
53	C₂²	—	2308	1	no	—
54	C₂²	—	4616	1	no	—
55	C₂²	—	4616	1	no	—
56	C₂²	—	577	1	no	—
57	C₄	—	4616	1	no	—
58	C₄	—	577	1	no	—
59	C₄	C₂²⋊#14556313	1	1	yes	characteristic
60	C₂	—	8	1	no	—
61	C₂	—	4616	1	no	—
62	C₂	—	577	1	no	—
63	C₂	—	577	1	no	—
64	C₂	#32914726	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#32914726
commutator	C₈×C₅₇₇	C₂×C₄
Frattini	C₈	C₂×#14556313
Fitting	D₈×C₅₇₇	C₄
socle	C₂×C₅₇₇	#102
prime radical	D₈×D₅₇₇	C₂
cosocle	C₈×D₅₇₇	C₂²
hypercenter	D₈	#14556313
hypocenter	C₅₇₇	#357
LCS	G ▷ C₈×C₅₇₇ ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #32914737	C₂	semidirect
2. #32914733	C₂	semidirect
7. D₄₆₁₆	C₄	semidirect
10. D₈×C₅₇₇	C₄	semidirect
32. C₅₇₇	#357	semidirect
40. D₈	#14556313	semidirect

Maximal subgroups

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

subgroup	index
#32914737	2
#32914733	2
D₈×D₅₇₇	2
#357	577