Subgroups — #22579942

Order 8864.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₇₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#11764308	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764308	—	2	1	no	—
5	#14555667	—	2	1	no	—
6	C₂²×D₂₇₇	—	2	1	no	—
7	D₁₁₀₈	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊D₂₇₇	—	2	1	no	—
9	C₄×D₂₇₇	C₂²	1	1	yes	characteristic
10	D₄×C₂₇₇	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₂₇₇	—	2	1	no	—
12	C₂×D₂₇₇	—	2	1	no	—
13	C₂×D₂₇₇	—	4	1	no	—
14	C₂×D₂₇₇	—	4	1	no	—
15	C₂×D₂₇₇	D₄	1	1	yes	characteristic
16	#11764308	—	4	1	no	—
17	C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
18	Dic₂₇₇	D₄	1	1	yes	characteristic
19	C₂×C₂₇₇	—	4	1	no	—
20	C₂×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
21	D₂₇₇	—	4	1	no	—
22	D₂₇₇	D₈	1	1	yes	characteristic
23	D₂₇₇	SD₁₆	1	1	yes	characteristic
24	C₂₇₇	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	277	1	no	maximal, Sylow
26	C₂×D₄	—	277	1	no	—
27	C₂×C₈	—	277	1	no	—
28	C₄⋊C₄	—	277	1	no	—
29	C₂³	—	554	1	no	—
30	D₄	—	277	1	no	—
31	D₄	—	554	1	no	—
32	D₄	#11764308	1	1	yes	characteristic, complemented
33	C₂×C₄	—	277	1	no	—
34	C₂×C₄	—	554	1	no	—
35	C₈	—	554	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	277	1	no	—
38	C₂²	—	554	1	no	—
39	C₂²	—	1108	1	no	—
40	C₂²	—	1108	1	no	—
41	C₄	—	277	1	no	—
42	C₄	—	1108	1	no	—
43	C₄	C₂×#11764308	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	277	1	no	—
46	C₂	—	277	1	no	—
47	C₂	—	1108	1	no	—
48	C₂	C₂²⋊#11764308	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11764308
commutator	C₄×C₂₇₇	C₂×C₄
Frattini	C₄	C₂×#11764308
Fitting	D₄×C₂₇₇	C₄
socle	C₂×C₂₇₇	C₂²⋊C₄
hypercenter	D₄	#11764308
hypocenter	C₂₇₇	#102
LCS	G ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. D₂₇₇⋊C₈	C₂	semidirect
2. C₄⋊#11764308	C₂	semidirect
7. D₁₁₀₈	C₄	semidirect
10. D₄×C₂₇₇	C₄	semidirect
24. C₂₇₇	#102	semidirect
32. D₄	#11764308	semidirect