Subgroups — #22579913

Order 8864.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984563	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₅₅₄	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₁₀₈	C₂	1	2	yes	maximal, complemented
4	#17984552	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₅₅₄	—	2	1	no	—
7	Dic₅₅₄	C₂²	1	2	yes	—
8	Dic₅₅₄	C₂²	1	1	yes	characteristic
9	D₁₁₀₈	C₂²	1	1	yes	characteristic
10	C₂²⋊D₂₇₇	—	2	1	no	—
11	C₂×Dic₂₇₇	—	2	1	no	—
12	C₄×D₂₇₇	—	2	1	no	—
13	C₂×C₄×C₂₇₇	C₂²	1	1	yes	characteristic
14	C₈×C₂₇₇	C₂²	1	2	yes	—
15	C₂²×C₂₇₇	D₄	1	1	yes	characteristic
16	C₂×D₂₇₇	—	2	1	no	—
17	C₄×C₂₇₇	D₄	1	1	yes	characteristic
18	C₄×C₂₇₇	C₂³	1	1	yes	characteristic
19	Dic₂₇₇	—	2	1	no	—
20	Dic₂₇₇	—	2	2	no	—
21	C₂×C₂₇₇	—	2	1	no	—
22	C₂×C₂₇₇	C₂×D₄	1	1	yes	characteristic
23	D₂₇₇	—	4	1	no	—
24	C₂₇₇	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	277	1	no	maximal, Sylow
26	#41	—	277	1	no	—
27	C₂×Q₈	—	277	1	no	—
28	Q₁₆	—	277	2	no	—
29	SD₁₆	—	277	2	no	—
30	M₁₆	D₂₇₇	1	1	yes	characteristic, complemented
31	Q₈	—	277	2	no	—
32	Q₈	—	277	1	no	—
33	Q₈	—	554	1	no	—
34	D₄	—	277	1	no	—
35	D₄	—	554	1	no	—
36	C₂×C₄	—	554	1	no	—
37	C₂×C₄	—	554	1	no	—
38	C₂×C₄	C₂×D₂₇₇	1	1	yes	characteristic
39	C₈	C₂×D₂₇₇	1	2	yes	—
40	C₂²	—	554	1	no	—
41	C₂²	D₁₁₀₈	1	1	yes	characteristic
42	C₄	—	554	1	no	—
43	C₄	—	554	2	no	—
44	C₄	D₁₁₀₈	1	1	yes	characteristic
45	C₄	C₂²×D₂₇₇	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	1108	1	no	—
48	C₂	C₂×D₁₁₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₁₀₈
commutator	C₄×C₂₇₇	C₂³
Frattini	C₄	C₂²×D₂₇₇
Fitting	M₁₆×C₂₇₇	C₂
socle	C₂×C₂₇₇	C₂×D₄
hypercenter	M₁₆	D₂₇₇
hypocenter	C₂₇₇	#137
LCS	G ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₅₅₄	C₂	semidirect
3. Dic₁₁₀₈	C₂	semidirect
4. #17984552	C₂	semidirect
5. M₁₆×C₂₇₇	C₂	semidirect
24. C₂₇₇	#137	semidirect
30. M₁₆	D₂₇₇	semidirect