Subgroups — #49093341

Order 35968.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823843	C₂	1	1	yes	maximal, characteristic
2	#31823284	C₂	1	1	yes	maximal, characteristic
3	#364×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₂₄	—	2	1	no	—
5	C₂×Dic₁₁₂₄	—	2	1	no	—
6	#22582879	C₄	1	2	yes	—
7	#22582819	—	2	1	no	—
8	M₃₂×C₂₈₁	—	2	1	no	—
9	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₆₂	—	2	2	no	—
11	Dic₁₁₂₄	—	4	1	no	—
12	Dic₁₁₂₄	—	4	1	no	—
13	Dic₁₁₂₄	—	4	1	no	—
14	Dic₁₁₂₄	—	4	1	no	—
15	C₄⋊Dic₂₈₁	—	4	2	no	—
16	#17985113	—	4	1	no	—
17	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
19	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₂₈₁	—	4	1	no	—
21	Dic₅₆₂	—	4	2	no	—
22	Dic₅₆₂	—	4	2	no	—
23	C₂×Dic₂₈₁	—	4	2	no	—
24	C₂×C₄×C₂₈₁	—	2	1	no	—
25	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₈₁	D₈	1	1	yes	characteristic
27	C₈×C₂₈₁	D₈	1	1	yes	characteristic
28	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
29	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
30	C₂²×C₂₈₁	#100	1	1	yes	characteristic
31	C₄×C₂₈₁	—	2	2	no	—
32	C₄×C₂₈₁	#102	1	1	yes	characteristic
33	C₄×C₂₈₁	#102	1	1	yes	characteristic
34	Dic₂₈₁	—	8	2	no	—
35	C₂×C₂₈₁	—	2	1	no	—
36	C₂×C₂₈₁	#331	1	1	yes	characteristic
37	C₂₈₁	#1358	1	1	yes	characteristic, complemented, Sylow
38	#1358	—	281	1	no	maximal, Sylow
39	#494	—	281	1	no	—
40	#364	—	281	1	no	—
41	#364	D₂₈₁	1	1	yes	characteristic
42	C₂×Q₁₆	—	562	1	no	—
43	C₂×Q₁₆	—	562	1	no	—
44	C₄⋊Q₈	—	281	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	562	1	no	—
47	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
48	C₂×Q₈	—	562	2	no	—
49	Q₁₆	—	1124	1	no	—
50	Q₁₆	—	1124	1	no	—
51	Q₁₆	—	1124	1	no	—
52	Q₁₆	—	1124	1	no	—
53	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
54	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
55	C₄⋊C₄	—	1124	2	no	—
56	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	1124	1	no	—
59	Q₈	—	1124	2	no	—
60	Q₈	—	1124	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	1124	2	no	—
63	C₂×C₄	#17985115	1	1	yes	characteristic
64	C₈	#17985123	1	1	yes	characteristic
65	C₈	D₂₂₄₈	1	1	yes	characteristic
66	C₈	#17985125	1	1	yes	characteristic
67	C₈	#17985127	1	1	yes	characteristic
68	C₂²	#22582795	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	2248	2	no	—
71	C₄	#22582799	1	1	yes	characteristic
72	C₄	#22582801	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#31823206	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31823206
commutator	C₄²×C₂₈₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#364×C₂₈₁	C₂
socle	C₂×C₂₈₁	#331
prime radical	C₂²×C₂₈₁	#100
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#364	D₂₈₁
hypocenter	C₂₈₁	#1358
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
37. C₂₈₁	#1358	semidirect

Maximal subgroups

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

subgroup	index
#31823843	2
#31823284	2
#364×C₂₈₁	2
#1358	281