Subgroups — #49093370

Order 35968.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823284	C₂	1	1	yes	maximal, characteristic
2	#31823239	C₂	1	1	yes	maximal, characteristic
3	#364×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#22582819	—	2	1	no	—
5	C₂×#17985113	C₄	1	1	yes	characteristic
6	C₂×#17985113	C₄	1	1	yes	characteristic
7	M₃₂×C₂₈₁	—	2	1	no	—
8	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
9	#17985113	—	2	1	no	—
10	#17985113	—	4	1	no	—
11	#17985113	C₈	1	2	yes	—
12	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
14	C₄²×C₂₈₁	Q₈	1	1	yes	characteristic
15	C₁₆×C₂₈₁	—	4	1	no	—
16	C₂×C₄×C₂₈₁	—	2	1	no	—
17	C₂×C₄×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₈₁	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₈₁	M₁₆	1	1	yes	characteristic
20	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
22	C₂²×C₂₈₁	#108	1	1	yes	characteristic
23	C₄×C₂₈₁	—	4	1	no	—
24	C₄×C₂₈₁	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₂₈₁	#106	1	1	yes	characteristic
26	C₂×C₂₈₁	—	2	1	no	—
27	C₂×C₂₈₁	#334	1	1	yes	characteristic
28	C₂₈₁	#1369	1	1	yes	characteristic, complemented, Sylow
29	#1369	—	281	1	no	maximal, Sylow
30	#364	—	281	1	no	—
31	#364	D₂₈₁	1	1	yes	characteristic
32	#346	—	281	1	no	—
33	M₃₂	—	2	1	no	—
34	M₃₂	—	562	1	no	—
35	C₂×C₁₆	—	281	1	no	—
36	C₂×C₁₆	—	281	1	no	—
37	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
38	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
40	C₄²	Dic₅₆₂	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	281	2	no	—
43	C₁₆	—	562	1	no	—
44	C₁₆	—	1124	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	#17985117	1	1	yes	characteristic
47	C₈	C₈×D₂₈₁	1	1	yes	characteristic
48	C₈	#17985121	1	1	yes	characteristic
49	C₈	#17985125	1	1	yes	characteristic
50	C₈	#17985126	1	1	yes	characteristic
51	C₂²	#22582814	1	1	yes	characteristic
52	C₄	—	4	1	no	—
53	C₄	#22582808	1	1	yes	characteristic
54	C₄	#22582810	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#31823213	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22582810
commutator	C₈×C₂₈₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#364×C₂₈₁	C₂
socle	C₂×C₂₈₁	#334
prime radical	C₂²×C₂₈₁	#108
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#364	D₂₈₁
hypocenter	C₂₈₁	#1369
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
28. C₂₈₁	#1369	semidirect

Maximal subgroups

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

subgroup	index
#31823284	2
#31823239	2
#364×C₂₈₁	2
#1369	281