Subgroups — #31800917

Order 17728.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₇₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#22579951	C₂	1	1	yes	maximal, characteristic, complemented
3	#22579903	C₂	1	1	yes	maximal, characteristic
4	#17984573	—	2	1	no	—
5	#17984566	—	2	1	no	—
6	#17984564	—	2	1	no	—
7	#17984550	—	2	1	no	—
8	D₂₂₁₆	C₄	1	1	yes	characteristic
9	C₈×D₂₇₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₂₇₇	C₄	1	1	yes	characteristic
11	#14555667	—	4	1	no	—
12	D₁₁₀₈	—	2	1	no	—
13	D₁₁₀₈	—	4	1	no	—
14	C₄×D₂₇₇	—	4	1	no	—
15	C₄×D₂₇₇	D₄	1	1	yes	characteristic
16	#14555660	D₄	1	1	yes	characteristic
17	Q₈×C₂₇₇	—	2	1	no	—
18	C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
19	C₂×D₂₇₇	—	4	1	no	—
20	C₂×D₂₇₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₇₇	—	4	1	no	—
22	C₄×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₂₇₇	D₈	1	1	yes	characteristic
24	C₂×C₂₇₇	#102	1	1	yes	characteristic
25	D₂₇₇	—	2	1	no	—
26	D₂₇₇	—	8	1	no	—
27	C₂₇₇	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	277	1	no	maximal, Sylow
29	#135	—	277	1	no	—
30	C₂×C₁₆	—	277	1	no	—
31	#108	—	277	1	no	—
32	#41	—	554	1	no	—
33	Q₁₆	#11764308	1	1	yes	characteristic
34	SD₁₆	—	554	1	no	—
35	D₈	—	277	1	no	—
36	M₁₆	—	554	1	no	—
37	C₂×C₈	—	277	1	no	—
38	C₁₆	—	554	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	554	1	no	—
41	D₄	—	1108	1	no	—
42	C₂×C₄	—	277	1	no	—
43	C₂×C₄	—	1108	1	no	—
44	C₈	—	277	1	no	—
45	C₈	—	1108	1	no	—
46	C₈	C₂×#11764308	1	1	yes	characteristic
47	C₂²	—	277	1	no	—
48	C₂²	—	1108	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	277	1	no	—
51	C₄	C₂²⋊#11764308	1	1	yes	characteristic
52	C₂	—	554	1	no	—
53	C₂	—	2216	1	no	—
54	C₂	#22579942	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22579942
commutator	C₈×C₂₇₇	C₂×C₄
Frattini	C₈	C₂×#11764308
Fitting	Q₁₆×C₂₇₇	C₄
socle	C₂×C₂₇₇	#102
prime radical	#22579903	C₂
cosocle	C₈×D₂₇₇	C₂²
hypercenter	Q₁₆	#11764308
hypocenter	C₂₇₇	#359
LCS	G ▷ C₈×C₂₇₇ ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. D₂₇₇⋊C₁₆	C₂	semidirect
2. #22579951	C₂	semidirect
27. C₂₇₇	#359	semidirect

Maximal subgroups

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

subgroup	index
D₂₇₇⋊C₁₆	2
#22579951	2
#22579903	2
#359	277