Subgroups — #49093222

Order 35968.

92 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	1	yes	characteristic
6	C₄×#14555886	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₂₈₁	C₄	1	2	yes	—
8	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
9	C₂×#14555886	C₈	1	2	yes	—
10	C₂×#14555886	C₈	1	2	yes	—
11	#17985113	—	2	2	no	—
12	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
14	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₂₈₁	—	2	2	no	—
16	#14555886	—	2	2	no	—
17	#14555886	C₁₆	1	4	yes	complemented
18	C₂×C₄×C₂₈₁	C₄²	1	1	yes	characteristic
19	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
20	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
21	C₈×C₂₈₁	M₁₆	1	2	yes	—
22	C₈×C₂₈₁	M₁₆	1	2	yes	—
23	C₂²×C₂₈₁	C₄×C₈	1	1	yes	characteristic
24	C₄×C₂₈₁	#97	1	1	yes	characteristic
25	C₄×C₂₈₁	#97	1	1	yes	characteristic
26	C₄×C₂₈₁	C₂×C₁₆	1	2	yes	—
27	C₄×C₂₈₁	M₃₂	1	2	yes	—
28	C₂×C₂₈₁	#322	1	1	yes	characteristic
29	C₂×C₂₈₁	C₄×C₁₆	1	1	yes	characteristic
30	C₂×C₂₈₁	#346	1	1	yes	characteristic
31	C₂₈₁	#1312	1	1	yes	characteristic, complemented, Sylow
32	#1312	—	281	1	no	maximal, Sylow
33	C₄×C₁₆	—	281	1	no	—
34	C₄×C₁₆	D₂₈₁	1	1	yes	characteristic
35	C₈²	—	281	1	no	—
36	C₂×C₁₆	—	281	2	no	—
37	C₂×C₁₆	Dic₂₈₁	1	2	yes	—
38	C₄×C₈	—	281	1	no	—
39	C₄×C₈	—	281	1	no	—
40	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
41	C₂×C₈	—	281	2	no	—
42	C₂×C₈	—	281	2	no	—
43	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₂₈₁	1	1	yes	characteristic
45	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	562	2	no	—
48	C₂×C₄	C₄×Dic₂₈₁	1	1	yes	characteristic
49	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
50	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
51	C₈	—	281	4	no	—
52	C₈	—	562	2	no	—
53	C₈	#17985121	1	2	yes	—
54	C₈	#17985122	1	2	yes	—
55	C₂²	C₈×Dic₂₈₁	1	1	yes	characteristic
56	C₄	#22582789	1	1	yes	characteristic
57	C₄	#22582790	1	1	yes	characteristic
58	C₄	C₁₆×D₂₈₁	1	2	yes	—
59	C₄	#22582818	1	2	yes	—
60	C₂	#31823185	1	1	yes	characteristic
61	C₂	C₁₆×Dic₂₈₁	1	1	yes	characteristic
62	C₂	#31823238	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₈₁
commutator	C₂×C₂₈₁	C₄×C₁₆
Fitting	C₄×C₁₆×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₄×C₈
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	C₄×C₁₆	D₂₈₁
hypocenter	C₂₈₁	#1312
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
17. #14555886	C₁₆	semidirect
31. C₂₈₁	#1312	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
#1312	281