Subgroups — #49093286

Order 35968.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823593	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#17985113	C₂	1	1	yes	maximal, characteristic
3	#346×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₅₆₂	C₄	1	1	yes	characteristic
5	C₂×#17985113	—	2	1	no	—
6	C₄⋊#14555886	C₄	1	1	yes	characteristic
7	#22582808	—	2	1	no	—
8	#22582789	—	2	1	no	—
9	C₂×C₁₆×C₂₈₁	—	2	1	no	—
10	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₆₂	C₈	1	1	yes	characteristic
12	C₂×#14555886	—	2	1	no	—
13	C₄⋊Dic₂₈₁	C₈	1	1	yes	characteristic
14	#17985117	—	2	1	no	—
15	C₄×Dic₂₈₁	—	2	1	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	—	2	2	no	—
21	Dic₅₆₂	—	4	1	no	—
22	C₂×Dic₂₈₁	—	2	1	no	—
23	C₂×Dic₂₈₁	—	2	1	no	—
24	#14555886	—	4	1	no	—
25	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₈₁	M₁₆	1	1	yes	characteristic
28	C₈×C₂₈₁	—	2	1	no	—
29	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₈₁	Q₁₆	1	1	yes	characteristic
31	C₂²×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₂₈₁	—	2	1	no	—
33	C₄×C₂₈₁	—	2	1	no	—
34	C₄×C₂₈₁	#103	1	1	yes	characteristic
35	C₄×C₂₈₁	#104	1	1	yes	characteristic
36	Dic₂₈₁	—	4	1	no	—
37	Dic₂₈₁	—	4	1	no	—
38	C₂×C₂₈₁	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₂₈₁	#349	1	1	yes	characteristic
40	C₂×C₂₈₁	#350	1	1	yes	characteristic
41	C₂₈₁	#1338	1	1	yes	characteristic, complemented, Sylow
42	#1338	—	281	1	no	maximal, Sylow
43	#446	—	281	1	no	—
44	C₄⋊C₁₆	—	281	1	no	—
45	#346	D₂₈₁	1	1	yes	characteristic
46	C₄×Q₈	—	281	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	562	1	no	—
49	C₄⋊C₈	—	281	1	no	—
50	C₄⋊C₈	—	562	1	no	—
51	#97	—	562	1	no	—
52	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
53	C₂×Q₈	—	281	1	no	—
54	C₂×C₈	—	562	1	no	—
55	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
56	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
57	C₄⋊C₄	—	281	1	no	—
58	C₄⋊C₄	—	562	1	no	—
59	C₄²	—	562	1	no	—
60	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	1124	1	no	—
63	Q₈	—	1124	1	no	—
64	C₂×C₄	—	562	1	no	—
65	C₂×C₄	—	562	1	no	—
66	C₂×C₄	#17985115	1	1	yes	characteristic
67	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
68	C₂×C₄	#17985121	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	1124	1	no	—
71	C₈	#17985127	1	1	yes	characteristic
72	C₈	Dic₁₁₂₄	1	1	yes	characteristic
73	C₂²	#22582791	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	1124	1	no	—
77	C₄	—	1124	1	no	—
78	C₄	#22582804	1	1	yes	characteristic
79	C₄	#22582807	1	1	yes	characteristic
80	C₂	#31823195	1	1	yes	characteristic
81	C₂	#31823244	1	1	yes	characteristic
82	C₂	#31823248	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#17985115
commutator	C₂×C₄×C₂₈₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#346×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂²⋊C₈
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#346	D₂₈₁
hypocenter	C₂₈₁	#1338
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
41. C₂₈₁	#1338	semidirect

Maximal subgroups

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

subgroup	index
#31823593	2
C₄⋊#17985113	2
#346×C₂₈₁	2
#1338	281