Subgroups — #49093438

Order 35968.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823297	C₂	1	1	yes	maximal, characteristic
2	#31823238	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985113	C₄	1	1	yes	characteristic
5	C₈×Dic₂₈₁	C₄	1	1	yes	characteristic
6	#22582785	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₈₁	C₄	1	2	yes	complemented
9	C₂×#14555886	C₈	1	1	yes	characteristic
10	C₄×Dic₂₈₁	C₈	1	1	yes	characteristic
11	#17985113	C₈	1	2	yes	—
12	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₂₈₁	—	2	1	no	—
16	#14555886	—	2	1	no	—
17	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
18	C₈×C₂₈₁	C₄²	1	1	yes	characteristic
19	C₈×C₂₈₁	C₂×C₈	1	1	yes	characteristic
20	C₂²×C₂₈₁	M₃₂	1	1	yes	characteristic
21	C₄×C₂₈₁	C₄×C₈	1	1	yes	characteristic
22	C₄×C₂₈₁	M₃₂	1	1	yes	characteristic
23	Dic₂₈₁	—	4	1	no	—
24	C₂×C₂₈₁	—	2	1	no	—
25	C₂×C₂₈₁	#346	1	1	yes	characteristic
26	C₂₈₁	#1398	1	1	yes	characteristic, complemented, Sylow
27	#1398	—	281	1	no	maximal, Sylow
28	M₆₄	—	281	1	no	—
29	M₆₄	D₂₈₁	1	1	yes	characteristic
30	#346	—	281	1	no	—
31	C₂×C₁₆	—	281	1	no	—
32	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
33	C₄×C₈	—	281	1	no	—
34	C₃₂	—	281	2	no	—
35	C₃₂	Dic₂₈₁	1	2	yes	complemented
36	C₂×C₈	—	281	1	no	—
37	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
38	C₄²	—	281	1	no	—
39	C₁₆	—	281	2	no	—
40	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
41	C₁₆	C₂×Dic₂₈₁	1	1	yes	characteristic
42	C₂×C₄	—	562	1	no	—
43	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
44	C₈	—	562	1	no	—
45	C₈	C₄×Dic₂₈₁	1	1	yes	characteristic
46	C₈	C₈×D₂₈₁	1	1	yes	characteristic
47	C₂²	#22582818	1	1	yes	characteristic
48	C₄	—	1124	1	no	—
49	C₄	C₈×Dic₂₈₁	1	1	yes	characteristic
50	C₄	#22582818	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#31823238	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₂₈₁
commutator	C₄×C₂₈₁	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	M₆₄×C₂₈₁	C₂
socle	C₂×C₂₈₁	#346
prime radical	C₂²×C₂₈₁	M₃₂
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	M₆₄	D₂₈₁
hypocenter	C₂₈₁	#1398
LCS	G ▷ C₄×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₈ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
6. #22582785	C₄	semidirect
8. C₃₂×C₂₈₁	C₄	semidirect
26. C₂₈₁	#1398	semidirect
35. C₃₂	Dic₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823297	2
#31823238	2
M₆₄×C₂₈₁	2
#1398	281