Subgroups — #49097549

Order 35968.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823865	C₂	1	1	yes	maximal, characteristic
2	#31823843	C₂	1	1	yes	maximal, characteristic
3	#31823268	C₂	1	4	yes	maximal
4	#346×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₂₄	—	2	1	no	—
6	C₂×Dic₁₁₂₄	C₂²	1	2	yes	—
7	#22582879	—	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×Dic₅₆₂	—	2	2	no	—
14	Dic₁₁₂₄	—	2	4	no	—
15	Dic₁₁₂₄	—	4	2	no	—
16	C₄⋊Dic₂₈₁	—	2	2	no	—
17	C₄⋊Dic₂₈₁	—	4	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	Dic₅₆₂	—	4	2	no	—
24	Dic₅₆₂	—	4	2	no	—
25	C₂×Dic₂₈₁	—	4	2	no	—
26	C₂×Dic₂₈₁	—	4	2	no	—
27	C₂×C₄×C₂₈₁	D₈	1	2	yes	—
28	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₈₁	SD₁₆	1	2	yes	—
30	C₈×C₂₈₁	#41	1	2	yes	—
31	C₂²×C₂₈₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₂₈₁	—	2	2	no	—
33	C₄×C₂₈₁	#124	1	1	yes	characteristic
34	C₄×C₂₈₁	C₂×SD₁₆	1	1	yes	characteristic
35	Dic₂₈₁	—	8	2	no	—
36	Dic₂₈₁	—	8	2	no	—
37	C₂×C₂₈₁	#486	1	1	yes	characteristic
38	C₂×C₂₈₁	#510	1	2	yes	—
39	C₂₈₁	#2245	1	1	yes	characteristic, complemented, Sylow
40	#2245	—	281	1	no	maximal, Sylow
41	#499	—	281	1	no	—
42	#494	—	281	1	no	—
43	#358	—	281	4	no	—
44	#346	D₂₈₁	1	1	yes	characteristic
45	C₂×Q₁₆	—	281	2	no	—
46	C₂×Q₁₆	—	562	1	no	—
47	C₄⋊Q₈	—	562	1	no	—
48	#125	—	562	1	no	—
49	C₂×C₁₆	C₂×D₂₈₁	1	2	yes	—
50	#107	—	281	2	no	—
51	#106	—	562	1	no	—
52	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
53	C₂×Q₈	—	562	2	no	—
54	Q₁₆	—	562	4	no	—
55	Q₁₆	—	1124	2	no	—
56	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
58	C₄⋊C₄	—	562	2	no	—
59	C₄⋊C₄	—	1124	2	no	—
60	C₄⋊C₄	—	1124	2	no	—
61	C₄²	D₁₁₂₄	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	1124	2	no	—
64	Q₈	—	1124	2	no	—
65	C₂×C₄	—	1124	2	no	—
66	C₂×C₄	—	1124	2	no	—
67	C₂×C₄	D₂₂₄₈	1	2	yes	—
68	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
69	C₈	#17985127	1	2	yes	—
70	C₈	#17985138	1	2	yes	—
71	C₂²	C₂×D₂₂₄₈	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	2248	2	no	—
74	C₄	—	2248	2	no	—
75	C₄	#22582867	1	1	yes	characteristic
76	C₄	C₂×#17985127	1	1	yes	characteristic
77	C₂	#31823810	1	1	yes	characteristic
78	C₂	#31823906	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, prime radical	C₂²×C₂₈₁	C₂×D₈
hypercenter	#346	D₂₈₁
hypocenter	C₂₈₁	#2245
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
39. C₂₈₁	#2245	semidirect

Maximal subgroups

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

subgroup	index
#31823865	2
#31823843	2
#31823268	2
#346×C₂₈₁	2
#2245	281