Subgroups — #31800901

Order 17728.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579954	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17984566	C₂	1	1	yes	maximal, characteristic, complemented
3	#22579888	C₂	1	1	yes	maximal, characteristic
4	#17984566	—	2	1	no	—
5	#17984566	—	2	1	no	—
6	#17984563	C₄	1	1	yes	characteristic
7	#17984546	—	2	1	no	—
8	C₂×#14555660	C₂²	1	1	yes	characteristic
9	C₈×D₂₇₇	—	2	1	no	—
10	M₁₆×C₂₇₇	C₄	1	1	yes	characteristic
11	Dic₅₅₄	C₈	1	1	yes	characteristic
12	D₁₁₀₈	C₈	1	1	yes	characteristic
13	C₂²⋊D₂₇₇	—	2	1	no	—
14	C₄×D₂₇₇	—	2	1	no	—
15	#14555660	D₄	1	1	yes	characteristic
16	#14555660	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₇₇	—	2	1	no	—
19	C₂²×C₂₇₇	M₁₆	1	1	yes	characteristic
20	C₂×D₂₇₇	—	2	1	no	—
21	C₄×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₇₇	C₂×C₈	1	1	yes	characteristic
23	Dic₂₇₇	—	2	1	no	—
24	C₂×C₂₇₇	—	2	1	no	—
25	C₂×C₂₇₇	C₂²⋊C₈	1	1	yes	characteristic
26	D₂₇₇	—	4	1	no	—
27	C₂₇₇	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	277	1	no	maximal, Sylow
29	#131	—	277	1	no	—
30	M₃₂	—	277	1	no	—
31	C₂×C₁₆	—	277	1	no	—
32	#41	—	277	1	no	—
33	M₁₆	—	554	1	no	—
34	M₁₆	#11764308	1	1	yes	characteristic
35	C₂×C₈	—	277	1	no	—
36	C₂×C₈	—	554	1	no	—
37	C₁₆	—	554	1	no	—
38	C₁₆	—	554	1	no	—
39	Q₈	—	277	1	no	—
40	D₄	—	277	1	no	—
41	D₄	—	554	1	no	—
42	C₂×C₄	—	554	1	no	—
43	C₂×C₄	C₂×#11764308	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	277	1	no	—
46	C₈	—	277	1	no	—
47	C₂²	—	554	1	no	—
48	C₂²	#17984573	1	1	yes	characteristic
49	C₄	—	554	1	no	—
50	C₄	C₂²⋊#11764308	1	1	yes	characteristic
51	C₄	D₂₇₇⋊C₈	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	1108	1	no	—
54	C₂	#22579937	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11764308
commutator	C₄×C₂₇₇	C₂×C₈
Frattini	C₂×C₄	C₂×#11764308
Fitting	M₁₆×C₂₇₇	C₄
socle	C₂×C₂₇₇	C₂²⋊C₈
prime radical	#17984563	C₄
cosocle	C₂×#14555660	C₂²
hypercenter	M₁₆	#11764308
hypocenter	C₂₇₇	#350
LCS	G ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #22579954	C₂	semidirect
2. C₂×#17984566	C₂	semidirect
27. C₂₇₇	#350	semidirect

Maximal subgroups

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

subgroup	index
#22579954	2
C₂×#17984566	2
#22579888	2
#350	277