Subgroups — D₂₇₇⋊M₁₆ #22579965

Order 8864.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984573	C₂	1	2	yes	maximal, complemented
2	#17984572	C₂	1	2	yes	maximal, complemented
3	D₂₇₇⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₂₇₇	C₂	1	1	yes	maximal, characteristic
5	#14555667	C₂²	1	4	yes	complemented
6	C₂²×D₂₇₇	C₄	1	1	yes	characteristic
7	C₂×Dic₂₇₇	C₂²	1	1	yes	characteristic
8	C₄×D₂₇₇	C₄	1	1	yes	characteristic
9	C₄×D₂₇₇	C₄	1	1	yes	characteristic
10	C₄×D₂₇₇	C₂²	1	1	yes	characteristic
11	C₄×D₂₇₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₂₇₇	C₄	1	1	yes	characteristic
13	C₂²×C₂₇₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₂₇₇	—	2	2	no	—
15	C₂×D₂₇₇	C₂×C₄	1	1	yes	characteristic
16	C₂×D₂₇₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
19	Dic₂₇₇	C₂×C₄	1	1	yes	characteristic
20	Dic₂₇₇	C₂³	1	1	yes	characteristic
21	C₂×C₂₇₇	—	2	1	no	—
22	C₂×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
23	D₂₇₇	—	2	1	no	—
24	D₂₇₇	M₁₆	1	2	yes	complemented
25	C₂₇₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	277	1	no	maximal, Sylow
27	C₂²×C₄	—	277	1	no	—
28	M₁₆	—	277	2	no	—
29	M₁₆	—	277	2	no	—
30	C₂×C₈	—	277	2	no	—
31	C₂³	—	277	1	no	—
32	C₂×C₄	—	277	1	no	—
33	C₂×C₄	—	277	1	no	—
34	C₂×C₄	—	277	1	no	—
35	C₂×C₄	—	277	1	no	—
36	C₂×C₄	—	277	1	no	—
37	C₂×C₄	#11764308	1	1	yes	characteristic
38	C₈	—	277	4	no	—
39	C₂²	—	277	1	no	—
40	C₂²	—	277	1	no	—
41	C₂²	—	554	2	no	—
42	C₂²	C₂×#11764308	1	1	yes	characteristic
43	C₄	—	277	1	no	—
44	C₄	—	277	1	no	—
45	C₄	C₂×#11764308	1	1	yes	characteristic
46	C₄	C₂×#11764308	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	277	2	no	—
49	C₂	—	554	1	no	—
50	C₂	C₂²×#11764308	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#11764308
commutator, socle	C₂×C₂₇₇	C₂²×C₄
Frattini	C₂	C₂²×#11764308
Fitting	C₂×C₄×C₂₇₇	C₄
hypercenter	C₂×C₄	#11764308
hypocenter	C₂₇₇	C₂×M₁₆
LCS	G ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #17984573	C₂	semidirect
2. #17984572	C₂	semidirect
3. D₂₇₇⋊C₈	C₂	semidirect
5. #14555667	C₂²	semidirect
24. D₂₇₇	M₁₆	semidirect
25. C₂₇₇	C₂×M₁₆	semidirect

Subgroups — D277⋊M16 #22579965

Conjugacy classes of subgroups

Complements

Subgroups — D₂₇₇⋊M₁₆ #22579965