Subgroups — #49093368

Order 35968.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823239	C₂	1	1	yes	maximal, characteristic
2	#31823214	C₂	1	1	yes	maximal, characteristic
3	#334×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985113	C₄	1	1	yes	characteristic
5	C₂×#17985113	C₄	1	1	yes	characteristic
6	C₄⋊#14555886	—	2	1	no	—
7	C₄⋊C₈×C₂₈₁	—	2	1	no	—
8	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
9	C₂×#14555886	—	4	1	no	—
10	#17985113	—	2	1	no	—
11	#17985113	C₈	1	2	yes	complemented
12	C₂×C₈×C₂₈₁	—	4	1	no	—
13	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₈₁	Q₈	1	1	yes	characteristic
15	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
16	#14555886	—	8	1	no	—
17	C₂×C₄×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₈₁	SD₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₈₁	SD₁₆	1	1	yes	characteristic
20	C₈×C₂₈₁	—	2	1	no	—
21	C₈×C₂₈₁	—	8	1	no	—
22	C₈×C₂₈₁	C₂×C₈	1	1	yes	characteristic
23	C₈×C₂₈₁	M₁₆	1	1	yes	characteristic
24	C₂²×C₂₈₁	#106	1	1	yes	characteristic
25	C₄×C₂₈₁	—	2	1	no	—
26	C₄×C₂₈₁	—	2	1	no	—
27	C₄×C₂₈₁	C₄⋊C₈	1	1	yes	characteristic
28	C₄×C₂₈₁	#108	1	1	yes	characteristic
29	C₂×C₂₈₁	#334	1	1	yes	characteristic
30	C₂×C₂₈₁	#365	1	1	yes	characteristic
31	C₂×C₂₈₁	#365	1	1	yes	characteristic
32	C₂₈₁	#1368	1	1	yes	characteristic, complemented, Sylow
33	#1368	—	281	1	no	maximal, Sylow
34	#346	—	281	1	no	—
35	#334	—	281	1	no	—
36	#334	D₂₈₁	1	1	yes	characteristic
37	C₂×C₁₆	—	281	1	no	—
38	C₂×C₁₆	—	281	1	no	—
39	C₄⋊C₈	—	2	1	no	—
40	C₄⋊C₈	—	562	1	no	—
41	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
42	C₂×C₈	—	4	1	no	—
43	C₂×C₈	—	1124	1	no	—
44	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
45	C₂×C₈	Dic₅₆₂	1	1	yes	characteristic
46	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
47	C₁₆	—	281	2	no	—
48	C₁₆	—	562	1	no	—
49	C₂×C₄	#17985117	1	1	yes	characteristic
50	C₂×C₄	#17985125	1	1	yes	characteristic
51	C₂×C₄	#17985126	1	1	yes	characteristic
52	C₈	—	2	1	no	—
53	C₈	—	8	1	no	—
54	C₈	—	2248	1	no	—
55	C₈	C₈×D₂₈₁	1	1	yes	characteristic
56	C₈	#17985121	1	1	yes	characteristic
57	C₂²	#22582810	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	#22582808	1	1	yes	characteristic
61	C₄	#22582814	1	1	yes	characteristic
62	C₂	#31823213	1	1	yes	characteristic
63	C₂	#31823285	1	1	yes	characteristic
64	C₂	#31823287	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22582810
commutator	C₈×C₂₈₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#334×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	#106
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#334	D₂₈₁
hypocenter	C₂₈₁	#1368
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
11. #17985113	C₈	semidirect
32. C₂₈₁	#1368	semidirect

Maximal subgroups

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

subgroup	index
#31823239	2
#31823214	2
#334×C₂₈₁	2
#1368	281