Subgroups — #49093365

Order 35968.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823865	C₂	1	1	yes	maximal, characteristic
2	#31823284	C₂	1	1	yes	maximal, characteristic
3	#364×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#22582871	C₄	1	2	yes	—
5	#22582819	—	2	1	no	—
6	#22582813	—	2	1	no	—
7	#22582811	—	2	1	no	—
8	M₃₂×C₂₈₁	—	2	1	no	—
9	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₈₁	—	2	2	no	—
11	#17985117	—	4	2	no	—
12	#17985113	—	4	1	no	—
13	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
15	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₈₁	—	4	1	no	—
17	C₂×Dic₂₈₁	—	4	2	no	—
18	C₂×C₄×C₂₈₁	—	2	1	no	—
19	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
22	C₈×C₂₈₁	Q₁₆	1	1	yes	characteristic
23	C₈×C₂₈₁	Q₁₆	1	1	yes	characteristic
24	C₂²×C₂₈₁	#100	1	1	yes	characteristic
25	C₄×C₂₈₁	—	4	1	no	—
26	C₄×C₂₈₁	#103	1	1	yes	characteristic
27	C₄×C₂₈₁	#103	1	1	yes	characteristic
28	Dic₂₈₁	—	8	2	no	—
29	C₂×C₂₈₁	—	2	1	no	—
30	C₂×C₂₈₁	#333	1	1	yes	characteristic
31	C₂₈₁	#1366	1	1	yes	characteristic, complemented, Sylow
32	#1366	—	281	1	no	maximal, Sylow
33	#499	—	281	1	no	—
34	#364	—	281	1	no	—
35	#364	D₂₈₁	1	1	yes	characteristic
36	#125	—	281	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	562	1	no	—
39	#107	—	562	1	no	—
40	#106	—	562	1	no	—
41	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
42	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
43	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
44	C₄⋊C₄	—	562	2	no	—
45	C₄⋊C₄	—	1124	2	no	—
46	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	1124	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	1124	2	no	—
51	C₂×C₄	#17985115	1	1	yes	characteristic
52	C₈	#17985126	1	1	yes	characteristic
53	C₈	#17985127	1	1	yes	characteristic
54	C₈	#17985128	1	1	yes	characteristic
55	C₈	Dic₁₁₂₄	1	1	yes	characteristic
56	C₂²	#22582795	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	2248	2	no	—
59	C₄	#22582802	1	1	yes	characteristic
60	C₄	#22582804	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#31823211	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31823211
commutator	C₄²×C₂₈₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#364×C₂₈₁	C₂
socle	C₂×C₂₈₁	#333
prime radical	C₂²×C₂₈₁	#100
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#364	D₂₈₁
hypocenter	C₂₈₁	#1366
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
31. C₂₈₁	#1366	semidirect

Maximal subgroups

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

subgroup	index
#31823865	2
#31823284	2
#364×C₂₈₁	2
#1366	281