Subgroups — #49093219

Order 35968.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#17985113	C₂	1	1	yes	maximal, characteristic
2	C₈×#14555886	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985113	C₄	1	2	yes	—
5	C₄×#14555886	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₈₁	C₄	1	2	yes	—
7	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
8	C₂×#14555886	C₈	1	4	yes	—
9	#17985113	C₈	1	4	yes	complemented
10	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₈₁	C₈	1	4	yes	complemented
14	#14555886	—	2	4	no	—
15	C₂×C₄×C₂₈₁	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₂₈₁	C₂×C₈	1	2	yes	—
17	C₈×C₂₈₁	C₂×C₈	1	2	yes	—
18	C₈×C₂₈₁	C₂×C₈	1	2	yes	—
19	C₂²×C₂₈₁	C₄×C₈	1	1	yes	characteristic
20	C₄×C₂₈₁	C₄×C₈	1	1	yes	characteristic
21	C₄×C₂₈₁	C₄×C₈	1	1	yes	characteristic
22	C₄×C₂₈₁	M₃₂	1	4	yes	—
23	C₂×C₂₈₁	C₈²	1	1	yes	characteristic
24	C₂×C₂₈₁	#346	1	2	yes	—
25	C₂₈₁	#1311	1	1	yes	characteristic, complemented, Sylow
26	#1311	—	281	1	no	maximal, Sylow
27	C₄×C₁₆	—	281	1	no	—
28	C₄×C₁₆	D₂₈₁	1	1	yes	characteristic
29	C₈²	—	281	1	no	—
30	C₂×C₁₆	—	281	2	no	—
31	C₂×C₁₆	Dic₂₈₁	1	2	yes	—
32	C₄×C₈	—	281	2	no	—
33	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
34	C₂×C₈	—	281	4	no	—
35	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₂₈₁	1	1	yes	characteristic
37	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
38	C₁₆	—	281	4	no	—
39	C₁₆	#14555886	1	4	yes	complemented
40	C₂×C₄	C₄×Dic₂₈₁	1	1	yes	characteristic
41	C₂×C₄	C₈×D₂₈₁	1	2	yes	—
42	C₈	—	562	4	no	—
43	C₈	C₈×D₂₈₁	1	2	yes	—
44	C₈	C₂×#14555886	1	2	yes	—
45	C₂²	C₈×Dic₂₈₁	1	1	yes	characteristic
46	C₄	C₈×Dic₂₈₁	1	1	yes	characteristic
47	C₄	C₄×#14555886	1	1	yes	characteristic
48	C₄	#22582818	1	4	yes	—
49	C₂	C₈×#14555886	1	1	yes	characteristic
50	C₂	#31823238	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₈₁
commutator	C₂×C₂₈₁	C₈²
Fitting	C₄×C₁₆×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₄×C₈
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	C₄×C₁₆	D₂₈₁
hypocenter	C₂₈₁	#1311
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
9. #17985113	C₈	semidirect
13. C₁₆×C₂₈₁	C₈	semidirect
25. C₂₈₁	#1311	semidirect
39. C₁₆	#14555886	semidirect

Maximal subgroups

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

subgroup	index
C₄×#17985113	2
C₈×#14555886	2
C₄×C₁₆×C₂₈₁	2
#1311	281