Subgroups — #49148867

Order 36928.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914739	C₂	1	1	yes	maximal, characteristic, complemented
2	#32914734	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₅₇₇	C₂	1	1	yes	maximal, characteristic
4	#22604428	—	2	1	no	—
5	#22604421	—	2	1	no	—
6	D₄×D₅₇₇	—	2	1	no	—
7	D₄₆₁₆	C₄	1	1	yes	characteristic
8	#22604403	—	2	1	no	—
9	C₈×D₅₇₇	C₂²	1	1	yes	characteristic
10	D₈×C₅₇₇	C₄	1	1	yes	characteristic
11	#17987237	—	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	2	no	—
22	C₂×D₅₇₇	SD₁₆	1	1	yes	characteristic
23	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₅₇₇	D₈	1	1	yes	characteristic
25	C₂×C₅₇₇	—	8	1	no	—
26	C₂×C₅₇₇	#102	1	1	yes	characteristic
27	D₅₇₇	—	2	1	no	—
28	D₅₇₇	—	8	1	no	—
29	C₅₇₇	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	577	1	no	maximal, Sylow
31	C₂×D₈	—	577	1	no	—
32	M₃₂	—	577	1	no	—
33	#108	—	577	1	no	—
34	C₂×D₄	—	1154	1	no	—
35	D₈	—	577	1	no	—
36	D₈	—	1154	1	no	—
37	D₈	#14556313	1	1	yes	characteristic
38	M₁₆	—	1154	1	no	—
39	C₂×C₈	—	577	1	no	—
40	C₁₆	—	1154	1	no	—
41	C₂³	—	2308	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	2308	1	no	—
44	D₄	—	1154	1	no	—
45	C₂×C₄	—	577	1	no	—
46	C₈	—	2308	1	no	—
47	C₈	—	577	1	no	—
48	C₈	C₂×#14556313	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	2308	1	no	—
51	C₂²	—	4616	2	no	—
52	C₂²	—	577	1	no	—
53	C₄	—	577	1	no	—
54	C₄	C₂²⋊#14556313	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	4616	1	no	—
57	C₂	—	1154	1	no	—
58	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	#361
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. #32914739	C₂	semidirect
2. #32914734	C₂	semidirect
29. C₅₇₇	#361	semidirect

Maximal subgroups

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

subgroup	index
#32914739	2
#32914734	2
D₈×D₅₇₇	2
#361	577