Subgroups — #49119239

Order 36224.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₅₆₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₈₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₅₆₆	C₄	1	1	yes	characteristic
5	C₂×C₂₈₃⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₂₈₃⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₂₈₃⋊C₈	—	2	1	no	—
8	C₈×Dic₂₈₃	—	2	1	no	—
9	C₂×C₁₆×C₂₈₃	—	2	1	no	—
10	C₄×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₆₆	C₈	1	1	yes	characteristic
12	C₂×C₂₈₃⋊C₈	—	2	1	no	—
13	C₄⋊Dic₂₈₃	C₈	1	1	yes	characteristic
14	Dic₂₈₃⋊C₄	—	2	1	no	—
15	C₄×Dic₂₈₃	—	2	1	no	—
16	C₂₈₃⋊C₁₆	—	2	2	no	—
17	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
19	C₄²×C₂₈₃	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₂₈₃	—	4	1	no	—
21	Dic₅₆₆	—	2	1	no	—
22	Dic₅₆₆	C₁₆	1	2	yes	complemented
23	C₂×Dic₂₈₃	—	2	1	no	—
24	C₂×Dic₂₈₃	—	2	1	no	—
25	C₂₈₃⋊C₈	—	4	1	no	—
26	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₈₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₈₃	M₁₆	1	1	yes	characteristic
29	C₈×C₂₈₃	—	2	1	no	—
30	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
31	C₈×C₂₈₃	Q₁₆	1	1	yes	characteristic
32	C₂²×C₂₈₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₂₈₃	—	2	1	no	—
34	C₄×C₂₈₃	#103	1	1	yes	characteristic
35	C₄×C₂₈₃	#104	1	1	yes	characteristic
36	C₄×C₂₈₃	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₂₈₃	M₃₂	1	1	yes	characteristic
38	Dic₂₈₃	—	2	2	no	—
39	Dic₂₈₃	—	4	1	no	—
40	C₂×C₂₈₃	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₂₈₃	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₂₈₃	#350	1	1	yes	characteristic
43	C₂₈₃	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
44	Q₈⋊C₁₆	—	283	1	no	maximal, Sylow
45	C₈×Q₈	—	283	1	no	—
46	C₄⋊C₁₆	D₂₈₃	1	1	yes	characteristic
47	C₄×C₁₆	—	283	1	no	—
48	C₄×Q₈	—	283	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	566	1	no	—
51	C₄⋊C₈	—	283	1	no	—
52	C₄⋊C₈	—	566	1	no	—
53	C₄×C₈	—	566	1	no	—
54	C₄×C₈	C₂×D₂₈₃	1	1	yes	characteristic
55	C₂×Q₈	—	283	1	no	—
56	C₂×C₈	—	566	1	no	—
57	C₂×C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
58	C₂×C₈	D₁₁₃₂	1	1	yes	characteristic
59	C₄⋊C₄	—	283	1	no	—
60	C₄⋊C₄	—	566	1	no	—
61	C₄²	—	566	1	no	—
62	C₄²	C₄×D₂₈₃	1	1	yes	characteristic
63	C₁₆	—	4	1	no	—
64	C₁₆	—	566	2	no	—
65	Q₈	—	283	2	no	—
66	Q₈	—	566	1	no	—
67	C₂×C₄	—	566	1	no	—
68	C₂×C₄	—	566	1	no	—
69	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
70	C₂×C₄	C₈×D₂₈₃	1	1	yes	characteristic
71	C₂×C₄	#17985375	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	1132	1	no	—
74	C₈	#17985380	1	1	yes	characteristic
75	C₈	#17985382	1	1	yes	characteristic
76	C₂²	(C₂×D₂₈₃)⋊C₈	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	566	2	no	—
79	C₄	—	1132	1	no	—
80	C₄	#22583533	1	1	yes	characteristic
81	C₄	#22583536	1	1	yes	characteristic
82	C₄	C₁₆×D₂₈₃	1	1	yes	characteristic
83	C₄	#22583549	1	1	yes	characteristic
84	C₂	#31826195	1	1	yes	characteristic
85	C₂	(C₂×D₂₈₃)⋊C₁₆	1	1	yes	characteristic
86	C₂	#31826250	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₂₈₃
commutator	C₄×C₂₈₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₂₈₃
Fitting	C₄⋊C₁₆×C₂₈₃	C₂
socle, prime radical	C₂²×C₂₈₃	C₂²⋊C₈
cosocle	C₄×C₈×C₂₈₃	C₂²
hypercenter	C₄⋊C₁₆	D₂₈₃
hypocenter	C₂₈₃	Q₈⋊C₁₆
LCS	G ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
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. Dic₅₆₆	C₁₆	semidirect
43. C₂₈₃	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×Dic₅₆₆	2
C₄×C₂₈₃⋊C₁₆	2
C₄⋊C₁₆×C₂₈₃	2
Q₈⋊C₁₆	283