Subgroups — #49093496

Order 35968.

70 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	#31823293	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₃₂×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#22582815	—	2	1	no	—
5	#22582785	—	2	1	no	—
6	C₂×Q₁₆×C₂₈₁	—	2	1	no	—
7	Q₃₂×C₂₈₁	—	2	1	no	—
8	Q₃₂×C₂₈₁	C₄	1	2	yes	—
9	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
10	#17985122	—	4	1	no	—
11	C₂×Q₈×C₂₈₁	—	4	1	no	—
12	Q₁₆×C₂₈₁	—	2	2	no	—
13	Q₁₆×C₂₈₁	—	4	1	no	—
14	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
15	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
17	#14555886	—	8	1	no	—
18	Q₈×C₂₈₁	—	4	2	no	—
19	Q₈×C₂₈₁	—	8	1	no	—
20	C₂×C₄×C₂₈₁	—	8	1	no	—
21	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
22	C₈×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₂₈₁	SD₃₂	1	1	yes	characteristic
25	C₄×C₂₈₁	—	8	2	no	—
26	C₄×C₂₈₁	#102	1	1	yes	characteristic
27	C₄×C₂₈₁	D₁₆	1	1	yes	characteristic
28	C₂×C₂₈₁	—	2	1	no	—
29	C₂×C₂₈₁	#357	1	1	yes	characteristic
30	C₂₈₁	#1420	1	1	yes	characteristic, complemented, Sylow
31	#1420	—	281	1	no	maximal, Sylow
32	C₂×Q₃₂	D₂₈₁	1	1	yes	characteristic
33	M₆₄	—	281	1	no	—
34	#368	—	281	1	no	—
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	Dic₂₈₁	1	2	yes	—
38	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
39	#108	—	562	1	no	—
40	C₃₂	—	562	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	1124	1	no	—
45	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
46	C₁₆	C₂×Dic₂₈₁	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₂₈₁	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#17985123	1	1	yes	characteristic
52	C₈	—	2248	1	no	—
53	C₈	C₂²⋊Dic₂₈₁	1	1	yes	characteristic
54	C₈	#17985126	1	1	yes	characteristic
55	C₂²	#22582823	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#22582800	1	1	yes	characteristic
58	C₄	#22582820	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#31823264	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31823264
commutator	C₁₆×C₂₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	C₂×Q₃₂×C₂₈₁	C₂
socle	C₂×C₂₈₁	#357
prime radical	C₂²×C₂₈₁	SD₃₂
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	C₂×Q₃₂	D₂₈₁
hypocenter	C₂₈₁	#1420
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
30. C₂₈₁	#1420	semidirect

Maximal subgroups

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

subgroup	index
#31823297	2
#31823293	2
C₂×Q₃₂×C₂₈₁	2
#1420	281