Subgroups — #49097545

Order 35968.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823865	C₂	1	1	yes	maximal, characteristic, complemented
2	#31823840	C₂	1	1	yes	maximal, characteristic
3	#31823265	C₂	1	4	yes	maximal, complemented
4	#346×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₂₄₈	—	2	1	no	—
6	C₂×D₂₂₄₈	C₂²	1	2	yes	—
7	#22582876	—	2	1	no	—
8	#22582871	—	2	1	no	—
9	#22582813	C₂²	1	2	yes	—
10	#22582811	—	2	1	no	—
11	C₂×C₁₆×C₂₈₁	C₂²	1	2	yes	—
12	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₂×D₁₁₂₄	—	2	2	no	—
14	C₂×D₁₁₂₄	—	4	2	no	—
15	D₂₂₄₈	—	2	4	no	—
16	D₂₂₄₈	—	4	2	no	—
17	C₄⋊Dic₂₈₁	—	2	2	no	—
18	#17985117	—	4	2	no	—
19	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
21	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
22	C₁₆×C₂₈₁	—	2	2	no	—
23	C₂²×D₂₈₁	—	4	2	no	—
24	D₁₁₂₄	—	4	2	no	—
25	D₁₁₂₄	—	4	2	no	—
26	D₁₁₂₄	—	8	4	no	—
27	C₂×Dic₂₈₁	—	4	2	no	—
28	C₂×C₄×C₂₈₁	D₈	1	2	yes	—
29	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
30	C₈×C₂₈₁	SD₁₆	1	2	yes	—
31	C₈×C₂₈₁	#41	1	2	yes	—
32	C₂²×C₂₈₁	C₂×D₈	1	1	yes	characteristic
33	C₂×D₂₈₁	—	8	2	no	—
34	C₂×D₂₈₁	—	8	4	no	—
35	C₄×C₂₈₁	—	2	2	no	—
36	C₄×C₂₈₁	#124	1	1	yes	characteristic
37	C₄×C₂₈₁	C₂×SD₁₆	1	1	yes	characteristic
38	Dic₂₈₁	—	8	2	no	—
39	C₂×C₂₈₁	#486	1	1	yes	characteristic
40	C₂×C₂₈₁	#509	1	2	yes	—
41	D₂₈₁	—	16	2	no	—
42	C₂₈₁	#2244	1	1	yes	characteristic, complemented, Sylow
43	#2244	—	281	1	no	maximal, Sylow
44	#499	—	281	1	no	—
45	#493	—	281	1	no	—
46	#357	—	281	4	no	—
47	#346	D₂₈₁	1	1	yes	characteristic, complemented
48	C₂×D₈	—	281	2	no	—
49	C₂×D₈	—	562	1	no	—
50	#127	—	562	1	no	—
51	#125	—	562	1	no	—
52	C₂×C₁₆	C₂×D₂₈₁	1	2	yes	—
53	#107	—	281	2	no	—
54	#106	—	562	1	no	—
55	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
56	C₂×D₄	—	562	2	no	—
57	C₂×D₄	—	1124	2	no	—
58	D₈	—	562	4	no	—
59	D₈	—	1124	2	no	—
60	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
62	C₄⋊C₄	—	562	2	no	—
63	C₄⋊C₄	—	1124	2	no	—
64	C₄²	D₁₁₂₄	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	1124	2	no	—
67	D₄	—	1124	2	no	—
68	D₄	—	1124	2	no	—
69	D₄	—	2248	4	no	—
70	C₂×C₄	—	1124	2	no	—
71	C₂×C₄	D₂₂₄₈	1	2	yes	—
72	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
73	C₈	#17985127	1	2	yes	—
74	C₈	#17985138	1	2	yes	—
75	C₂²	—	2248	4	no	—
76	C₂²	—	2248	2	no	—
77	C₂²	C₂×D₂₂₄₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2248	2	no	—
80	C₄	#22582867	1	1	yes	characteristic
81	C₄	C₂×#17985127	1	1	yes	characteristic
82	C₂	—	4496	2	no	—
83	C₂	#31823810	1	1	yes	characteristic
84	C₂	#31823901	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₂₄₈
commutator, cosocle	C₂×C₈×C₂₈₁	C₂³
Frattini	C₂×C₈	C₂²×D₂₈₁
Fitting	#346×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×D₈
prime radical	#31823840	C₂
hypercenter	#346	D₂₈₁
hypocenter	C₂₈₁	#2244
LCS	G ▷ C₂×C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
1. #31823865	C₂	semidirect
3. #31823265	C₂	semidirect
4. #346×C₂₈₁	C₂	semidirect
42. C₂₈₁	#2244	semidirect
47. #346	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823865	2
#31823840	2
#31823265	2
#346×C₂₈₁	2
#2244	281