Subgroups — #49148864

Order 36928.

56 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	#32914735	C₂	1	1	yes	maximal, characteristic, complemented
3	#32914687	C₂	1	1	yes	maximal, characteristic
4	#22604428	—	2	1	no	—
5	#22604421	—	2	1	no	—
6	#22604419	—	2	1	no	—
7	#22604405	—	2	1	no	—
8	D₄₆₁₆	C₄	1	1	yes	characteristic
9	C₈×D₅₇₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₅₇₇	C₄	1	1	yes	characteristic
11	#17987237	—	4	1	no	—
12	D₂₃₀₈	—	2	1	no	—
13	D₂₃₀₈	—	4	1	no	—
14	C₄×D₅₇₇	—	4	1	no	—
15	C₄×D₅₇₇	D₄	1	1	yes	characteristic
16	#17987230	D₄	1	1	yes	characteristic
17	Q₈×C₅₇₇	—	2	1	no	—
18	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
19	C₂×D₅₇₇	—	4	1	no	—
20	C₂×D₅₇₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₅₇₇	—	4	1	no	—
22	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₅₇₇	D₈	1	1	yes	characteristic
24	C₂×C₅₇₇	#102	1	1	yes	characteristic
25	D₅₇₇	—	2	1	no	—
26	D₅₇₇	—	8	1	no	—
27	C₅₇₇	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	577	1	no	maximal, Sylow
29	#135	—	577	1	no	—
30	C₂×C₁₆	—	577	1	no	—
31	#108	—	577	1	no	—
32	#41	—	1154	1	no	—
33	Q₁₆	#14556313	1	1	yes	characteristic
34	SD₁₆	—	1154	1	no	—
35	D₈	—	577	1	no	—
36	M₁₆	—	1154	1	no	—
37	C₂×C₈	—	577	1	no	—
38	C₁₆	—	1154	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	2308	1	no	—
41	D₄	—	1154	1	no	—
42	C₂×C₄	—	2308	1	no	—
43	C₂×C₄	—	577	1	no	—
44	C₈	—	2308	1	no	—
45	C₈	—	577	1	no	—
46	C₈	C₂×#14556313	1	1	yes	characteristic
47	C₂²	—	2308	1	no	—
48	C₂²	—	577	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	577	1	no	—
51	C₄	C₂²⋊#14556313	1	1	yes	characteristic
52	C₂	—	4616	1	no	—
53	C₂	—	1154	1	no	—
54	C₂	#32914726	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#32914726
commutator	C₈×C₅₇₇	C₂×C₄
Frattini	C₈	C₂×#14556313
Fitting	Q₁₆×C₅₇₇	C₄
socle	C₂×C₅₇₇	#102
prime radical	#32914687	C₂
cosocle	C₈×D₅₇₇	C₂²
hypercenter	Q₁₆	#14556313
hypocenter	C₅₇₇	#359
LCS	G ▷ C₈×C₅₇₇ ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #32914737	C₂	semidirect
2. #32914735	C₂	semidirect
27. C₅₇₇	#359	semidirect

Maximal subgroups

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

subgroup	index
#32914737	2
#32914735	2
#32914687	2
#359	577