Subgroups — #19127751

Order 5312.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₈₃	C₂	1	1	yes	maximal, characteristic
2	Dic₈₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²⋊(C₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₈₃	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₈₃	C₄	1	1	yes	characteristic
8	C₂×C₈₃⋊C₈	C₂²	1	2	yes	—
9	C₄×Dic₈₃	C₄	1	1	yes	characteristic
10	C₄×Dic₈₃	C₄	1	1	yes	characteristic
11	C₄×Dic₈₃	C₂²	1	1	yes	characteristic
12	C₄×Dic₈₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₈₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₈₃	C₂²	1	2	yes	—
15	C₂³×C₈₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₈₃	—	2	2	no	—
17	C₂×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₈₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₈₃	—	2	2	no	—
20	C₂×Dic₈₃	C₈	1	4	yes	complemented
21	C₂×Dic₈₃	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₈₃	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₈₃	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₈₃	C₂×C₄	1	1	yes	characteristic
25	C₈×C₈₃	—	2	2	no	—
26	C₈₃⋊C₈	—	2	2	no	—
27	C₂²×C₈₃	—	2	1	no	—
28	C₂²×C₈₃	—	2	1	no	—
29	C₂²×C₈₃	C₂×C₈	1	2	yes	—
30	C₂²×C₈₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₈₃	—	2	1	no	—
32	C₄×C₈₃	#41	1	2	yes	—
33	Dic₈₃	—	2	1	no	—
34	Dic₈₃	C₂×C₈	1	2	yes	—
35	Dic₈₃	C₂×C₈	1	2	yes	—
36	Dic₈₃	M₁₆	1	2	yes	—
37	C₂×C₈₃	—	2	2	no	—
38	C₂×C₈₃	#117	1	1	yes	characteristic
39	C₂×C₈₃	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₈₃	C₂×M₁₆	1	1	yes	characteristic
41	C₈₃	#431	1	1	yes	characteristic, complemented, Sylow
42	#431	—	83	1	no	maximal, Sylow
43	C₂×C₄²	—	83	1	no	—
44	C₄⋊C₈	—	83	2	no	—
45	C₂²⋊C₈	—	83	1	no	—
46	C₂²⋊C₈	D₈₃	1	1	yes	characteristic
47	C₄×C₈	—	83	2	no	—
48	C₂²×C₄	—	83	1	no	—
49	C₂²×C₄	—	83	1	no	—
50	C₂²×C₄	C₂×D₈₃	1	1	yes	characteristic
51	C₂×C₈	—	83	2	no	—
52	C₂×C₈	C₂×D₈₃	1	2	yes	—
53	C₄²	—	83	1	no	—
54	C₄²	—	83	1	no	—
55	C₄²	—	83	1	no	—
56	C₄²	—	83	1	no	—
57	C₂³	C₄×D₈₃	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	83	4	no	—
60	C₂×C₄	—	83	1	no	—
61	C₂×C₄	—	83	1	no	—
62	C₂×C₄	—	83	1	no	—
63	C₂×C₄	—	83	1	no	—
64	C₂×C₄	—	166	2	no	—
65	C₂×C₄	C₄×D₈₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₈₃	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	166	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	C₈×D₈₃	1	2	yes	—
72	C₂²	C₂×C₄×D₈₃	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	83	2	no	—
75	C₄	—	83	2	no	—
76	C₄	—	83	2	no	—
77	C₄	—	166	1	no	—
78	C₄	#13050589	1	2	yes	—
79	C₂	—	2	2	no	—
80	C₂	#14581748	1	1	yes	characteristic
81	C₂	C₂×C₈×D₈₃	1	1	yes	characteristic
82	C₂	M₁₆×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₈₃
commutator	C₂×C₈₃	C₂²×C₈
Fitting	C₂²⋊C₈×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×C₄
hypercenter	C₂²⋊C₈	D₈₃
hypocenter	C₈₃	#431
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. Dic₈₃⋊C₈	C₂	semidirect
4. C₈×Dic₈₃	C₂	semidirect
20. C₂×Dic₈₃	C₈	semidirect
41. C₈₃	#431	semidirect