Subgroups — #49147755

Order 36928.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914686	C₂	1	1	yes	maximal, characteristic
2	C₂×#22604393	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₅₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#22604418	—	2	1	no	—
5	Dic₂₃₀₈	C₄	1	1	yes	characteristic
6	#22604407	—	2	1	no	—
7	D₄₆₁₆	C₄	1	1	yes	characteristic
8	#22604393	—	2	1	no	—
9	M₁₆×C₅₇₇	—	2	1	no	—
10	C₂×C₈×C₅₇₇	C₂²	1	1	yes	characteristic
11	Dic₁₁₅₄	—	2	1	no	—
12	D₂₃₀₈	—	2	1	no	—
13	C₂²⋊D₅₇₇	—	4	1	no	—
14	C₄×D₅₇₇	—	4	1	no	—
15	C₂×C₄×C₅₇₇	D₄	1	1	yes	characteristic
16	C₈×C₅₇₇	—	4	1	no	—
17	C₈×C₅₇₇	C₂×C₄	1	1	yes	characteristic
18	C₈×C₅₇₇	D₄	1	1	yes	characteristic
19	C₂²×C₅₇₇	SD₁₆	1	1	yes	characteristic
20	C₂×D₅₇₇	—	4	1	no	—
21	C₄×C₅₇₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₅₇₇	D₈	1	1	yes	characteristic
23	Dic₅₇₇	—	4	1	no	—
24	C₂×C₅₇₇	—	2	1	no	—
25	C₂×C₅₇₇	#102	1	1	yes	characteristic
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	D₅₇₇	1	1	yes	characteristic, complemented
32	#41	—	1154	1	no	—
33	Q₁₆	—	577	1	no	—
34	SD₁₆	—	1154	1	no	—
35	D₈	—	577	1	no	—
36	M₁₆	—	2	1	no	—
37	C₂×C₈	C₂×D₅₇₇	1	1	yes	characteristic
38	C₁₆	—	1154	1	no	—
39	Q₈	—	1154	1	no	—
40	D₄	—	2308	1	no	—
41	D₄	—	1154	1	no	—
42	C₂×C₄	—	2308	1	no	—
43	C₂×C₄	C₂²⋊D₅₇₇	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	C₄×D₅₇₇	1	1	yes	characteristic
46	C₈	D₂₃₀₈	1	1	yes	characteristic
47	C₂²	—	2308	1	no	—
48	C₂²	#22604405	1	1	yes	characteristic
49	C₄	—	2308	1	no	—
50	C₄	#22604395	1	1	yes	characteristic
51	C₄	#22604403	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	4616	1	no	—
54	C₂	#32914584	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22604403
commutator	C₈×C₅₇₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₅₇₇
Fitting	#108×C₅₇₇	C₂
socle	C₂×C₅₇₇	#102
prime radical	#32914686	C₂
cosocle	C₂×C₈×C₅₇₇	C₂²
hypercenter	#108	D₅₇₇
hypocenter	C₅₇₇	#359
LCS	G ▷ C₈×C₅₇₇ ▷ C₄×C₅₇₇ ▷ C₂×C₅₇₇ ▷ C₅₇₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×#22604393	C₂	semidirect
3. #108×C₅₇₇	C₂	semidirect
27. C₅₇₇	#359	semidirect
31. #108	D₅₇₇	semidirect

Maximal subgroups

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

subgroup	index
#32914686	2
C₂×#22604393	2
#108×C₅₇₇	2
#359	577