Subgroups — #19127828

Order 5312.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic
2	Dic₈₃⋊C₈	C₂	1	2	yes	maximal
3	#14581702	C₂	1	2	yes	maximal
4	C₄×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₆₆	C₄	1	1	yes	characteristic
7	C₂×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₈₃	C₄	1	1	yes	characteristic
10	Dic₈₃⋊C₄	C₄	1	2	yes	—
11	C₄×Dic₈₃	C₂²	1	2	yes	—
12	C₂×C₈×C₈₃	C₂²	1	2	yes	—
13	C₄²×C₈₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₈₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₈₃	C₂×C₄	1	2	yes	—
18	C₂×Dic₈₃	C₂×C₄	1	2	yes	—
19	Dic₁₆₆	—	2	2	no	—
20	C₈×C₈₃	—	2	2	no	—
21	C₈₃⋊C₈	—	2	1	no	—
22	C₈₃⋊C₈	Q₈	1	2	yes	complemented
23	C₂²×C₈₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₈₃	—	2	1	no	—
25	C₄×C₈₃	M₁₆	1	2	yes	—
26	C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₈₃	#41	1	1	yes	characteristic
28	Dic₈₃	—	2	2	no	—
29	Dic₈₃	—	2	2	no	—
30	C₂×C₈₃	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₈₃	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₈₃	#131	1	1	yes	characteristic
33	C₈₃	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	83	1	no	maximal, Sylow
35	C₄×Q₈	—	83	1	no	—
36	C₄⋊C₈	—	83	2	no	—
37	C₄⋊C₈	D₈₃	1	1	yes	characteristic
38	#97	—	83	2	no	—
39	C₄×C₈	—	83	1	no	—
40	C₂×Q₈	—	83	1	no	—
41	C₂×C₈	—	83	1	no	—
42	C₂×C₈	—	83	1	no	—
43	C₂×C₈	C₂×D₈₃	1	2	yes	—
44	C₄⋊C₄	—	83	2	no	—
45	C₄⋊C₄	—	83	1	no	—
46	C₄²	—	83	2	no	—
47	C₄²	C₂×D₈₃	1	1	yes	characteristic
48	Q₈	—	166	2	no	—
49	C₂×C₄	—	83	2	no	—
50	C₂×C₄	—	83	2	no	—
51	C₂×C₄	C₄×D₈₃	1	1	yes	characteristic
52	C₂×C₄	C₄×D₈₃	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₈₃	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	83	2	no	—
56	C₈	—	166	1	no	—
57	C₂²	C₂×C₄×D₈₃	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	166	2	no	—
60	C₄	—	166	2	no	—
61	C₄	#13050573	1	2	yes	—
62	C₄	Q₈×D₈₃	1	1	yes	characteristic
63	C₄	#13050589	1	1	yes	characteristic
64	C₂	#14581757	1	1	yes	characteristic
65	C₂	C₂×#13050573	1	1	yes	characteristic
66	C₂	#14581800	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₈₃
commutator, socle	C₂²×C₈₃	C₂²×C₄
Fitting	C₄⋊C₈×C₈₃	C₂
hypercenter	C₄⋊C₈	D₈₃
hypocenter	C₈₃	#446
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
22. C₈₃⋊C₈	Q₈	semidirect
33. C₈₃	#446	semidirect