Subgroups — #49093351

Order 35968.

98 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	C₄⋊#17985113	C₂	1	1	yes	maximal, characteristic
3	#335×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₂₄	—	2	1	no	—
5	C₂×Dic₁₁₂₄	C₄	1	2	yes	—
6	#22582879	—	2	1	no	—
7	C₂×#17985113	—	2	1	no	—
8	C₄⋊C₈×C₂₈₁	—	2	1	no	—
9	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₆₂	—	2	2	no	—
11	Dic₁₁₂₄	—	4	2	no	—
12	Dic₁₁₂₄	—	4	1	no	—
13	Dic₁₁₂₄	—	4	1	no	—
14	C₄⋊Dic₂₈₁	—	4	1	no	—
15	C₄⋊Dic₂₈₁	—	4	1	no	—
16	#17985113	—	4	1	no	—
17	C₂×C₈×C₂₈₁	—	4	1	no	—
18	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
20	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
21	Dic₅₆₂	—	4	2	no	—
22	Dic₅₆₂	—	4	2	no	—
23	C₂×Dic₂₈₁	—	4	2	no	—
24	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₈₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₂₈₁	—	2	1	no	—
28	C₈×C₂₈₁	—	8	1	no	—
29	C₈×C₂₈₁	D₈	1	1	yes	characteristic
30	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
31	C₂²×C₂₈₁	#102	1	1	yes	characteristic
32	C₄×C₂₈₁	—	2	1	no	—
33	C₄×C₂₈₁	#100	1	1	yes	characteristic
34	C₄×C₂₈₁	#102	1	1	yes	characteristic
35	C₄×C₂₈₁	SD₃₂	1	1	yes	characteristic
36	C₄×C₂₈₁	Q₃₂	1	1	yes	characteristic
37	Dic₂₈₁	—	8	2	no	—
38	C₂×C₂₈₁	#331	1	1	yes	characteristic
39	C₂×C₂₈₁	#358	1	1	yes	characteristic
40	C₂×C₂₈₁	#362	1	1	yes	characteristic
41	C₂₈₁	#1362	1	1	yes	characteristic, complemented, Sylow
42	#1362	—	281	1	no	maximal, Sylow
43	#494	—	281	1	no	—
44	C₄⋊C₁₆	—	281	1	no	—
45	#335	D₂₈₁	1	1	yes	characteristic
46	C₂×Q₁₆	—	281	2	no	—
47	C₂×Q₁₆	—	562	1	no	—
48	C₄⋊Q₈	—	562	1	no	—
49	C₂×C₁₆	—	562	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
52	C₂×Q₈	—	562	2	no	—
53	Q₁₆	—	1124	2	no	—
54	Q₁₆	—	1124	1	no	—
55	Q₁₆	—	1124	1	no	—
56	C₂×C₈	—	4	1	no	—
57	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
58	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
59	C₄⋊C₄	—	1124	1	no	—
60	C₄⋊C₄	—	1124	1	no	—
61	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
62	C₁₆	—	1124	1	no	—
63	Q₈	—	1124	2	no	—
64	Q₈	—	1124	2	no	—
65	C₂×C₄	—	1124	2	no	—
66	C₂×C₄	#17985115	1	1	yes	characteristic
67	C₂×C₄	#17985123	1	1	yes	characteristic
68	C₂×C₄	#17985125	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	D₂₂₄₈	1	1	yes	characteristic
72	C₈	#17985127	1	1	yes	characteristic
73	C₂²	#22582799	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2248	2	no	—
76	C₄	#22582795	1	1	yes	characteristic
77	C₄	#22582801	1	1	yes	characteristic
78	C₄	#22582823	1	1	yes	characteristic
79	C₄	#22582825	1	1	yes	characteristic
80	C₂	#31823206	1	1	yes	characteristic
81	C₂	#31823266	1	1	yes	characteristic
82	C₂	#31823278	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22582799
commutator	C₂×C₈×C₂₈₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#335×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	#102
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#335	D₂₈₁
hypocenter	C₂₈₁	#1362
LCS	G ▷ C₂×C₈×C₂₈₁ ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
41. C₂₈₁	#1362	semidirect

Maximal subgroups

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

subgroup	index
#31823843	2
C₄⋊#17985113	2
#335×C₂₈₁	2
#1362	281