Subgroups — #49093281

Order 35968.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₅₆₂	C₂	1	1	yes	maximal, characteristic
2	C₄×#17985113	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×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	C₈×Dic₂₈₁	—	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	—	2	2	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	—	2	1	no	—
22	Dic₅₆₂	C₁₆	1	2	yes	complemented
23	C₂×Dic₂₈₁	—	2	1	no	—
24	C₂×Dic₂₈₁	—	2	1	no	—
25	#14555886	—	4	1	no	—
26	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₈₁	M₁₆	1	1	yes	characteristic
29	C₈×C₂₈₁	—	2	1	no	—
30	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
31	C₈×C₂₈₁	Q₁₆	1	1	yes	characteristic
32	C₂²×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₂₈₁	—	2	1	no	—
34	C₄×C₂₈₁	#103	1	1	yes	characteristic
35	C₄×C₂₈₁	#104	1	1	yes	characteristic
36	C₄×C₂₈₁	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₂₈₁	M₃₂	1	1	yes	characteristic
38	Dic₂₈₁	—	2	2	no	—
39	Dic₂₈₁	—	4	1	no	—
40	C₂×C₂₈₁	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₂₈₁	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₂₈₁	#350	1	1	yes	characteristic
43	C₂₈₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
44	Q₈⋊C₁₆	—	281	1	no	maximal, Sylow
45	C₈×Q₈	—	281	1	no	—
46	C₄⋊C₁₆	D₂₈₁	1	1	yes	characteristic
47	C₄×C₁₆	—	281	1	no	—
48	C₄×Q₈	—	281	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	562	1	no	—
51	C₄⋊C₈	—	281	1	no	—
52	C₄⋊C₈	—	562	1	no	—
53	C₄×C₈	—	562	1	no	—
54	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
55	C₂×Q₈	—	281	1	no	—
56	C₂×C₈	—	562	1	no	—
57	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
58	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
59	C₄⋊C₄	—	281	1	no	—
60	C₄⋊C₄	—	562	1	no	—
61	C₄²	—	562	1	no	—
62	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
63	C₁₆	—	4	1	no	—
64	C₁₆	—	562	2	no	—
65	Q₈	—	281	2	no	—
66	Q₈	—	562	1	no	—
67	C₂×C₄	—	562	1	no	—
68	C₂×C₄	—	562	1	no	—
69	C₂×C₄	#17985115	1	1	yes	characteristic
70	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
71	C₂×C₄	#17985121	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	1124	1	no	—
74	C₈	#17985126	1	1	yes	characteristic
75	C₈	#17985128	1	1	yes	characteristic
76	C₂²	#22582791	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	562	2	no	—
79	C₄	—	1124	1	no	—
80	C₄	#22582802	1	1	yes	characteristic
81	C₄	#22582805	1	1	yes	characteristic
82	C₄	C₁₆×D₂₈₁	1	1	yes	characteristic
83	C₄	#22582818	1	1	yes	characteristic
84	C₂	#31823193	1	1	yes	characteristic
85	C₂	#31823242	1	1	yes	characteristic
86	C₂	#31823248	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₂₈₁
commutator	C₄×C₂₈₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	C₄⋊C₁₆×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂²⋊C₈
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	C₄⋊C₁₆	D₂₈₁
hypocenter	C₂₈₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
22. Dic₅₆₂	C₁₆	semidirect
43. C₂₈₁	Q₈⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×Dic₅₆₂	2
C₄×#17985113	2
C₄⋊C₁₆×C₂₈₁	2
Q₈⋊C₁₆	281