Subgroups — C₈₃×#1332 #24903017

Order 10624.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
3	#335×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₈₃	C₄	1	1	yes	characteristic
5	C₄×Q₈×C₈₃	—	2	1	no	—
6	C₂×C₁₆×C₈₃	—	2	1	no	—
7	#107×C₈₃	C₄	1	1	yes	characteristic
8	C₄⋊C₈×C₈₃	—	2	1	no	—
9	#103×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₈₃	—	2	1	no	—
12	Q₁₆×C₈₃	—	2	1	no	—
13	Q₁₆×C₈₃	C₈	1	2	yes	complemented
14	C₂×C₈×C₈₃	—	4	1	no	—
15	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₈₃	—	2	1	no	—
18	C₄⋊C₄×C₈₃	—	4	1	no	—
19	C₄²×C₈₃	—	4	1	no	—
20	C₄²×C₈₃	D₄	1	1	yes	characteristic
21	C₁₆×C₈₃	—	2	2	no	—
22	Q₈×C₈₃	—	2	2	no	—
23	Q₈×C₈₃	—	4	1	no	—
24	C₂×C₄×C₈₃	—	4	1	no	—
25	C₂×C₄×C₈₃	—	4	1	no	—
26	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
29	C₈×C₈₃	—	2	1	no	—
30	C₈×C₈₃	—	8	1	no	—
31	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₈₃	M₁₆	1	1	yes	characteristic
33	C₂²×C₈₃	#102	1	1	yes	characteristic
34	C₄×C₈₃	—	2	1	no	—
35	C₄×C₈₃	—	4	2	no	—
36	C₄×C₈₃	—	8	1	no	—
37	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₈₃	#104	1	1	yes	characteristic
39	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
40	C₄×C₈₃	Q₃₂	1	1	yes	characteristic
41	C₂×C₈₃	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₈₃	#358	1	1	yes	characteristic
43	C₂×C₈₃	#359	1	1	yes	characteristic
44	#1332	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₈₃	#1332	1	1	yes	characteristic, direct product factor, Sylow
46	C₄×Q₁₆	C₂×C₈₃	1	1	yes	characteristic
47	C₄×C₁₆	C₂×C₈₃	1	1	yes	characteristic
48	#335	C₂×C₈₃	1	1	yes	characteristic
49	C₂×Q₁₆	C₄×C₈₃	1	1	yes	characteristic
50	C₄×Q₈	—	2	1	no	—
51	C₂×C₁₆	—	2	1	no	—
52	#107	C₄×C₈₃	1	1	yes	characteristic
53	C₄⋊C₈	—	2	1	no	—
54	#103	—	2	1	no	—
55	C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
56	C₂×Q₈	—	2	1	no	—
57	Q₁₆	—	2	1	no	—
58	Q₁₆	C₈×C₈₃	1	2	yes	complemented
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
61	C₂×C₈	D₄×C₈₃	1	1	yes	characteristic
62	C₄⋊C₄	—	2	1	no	—
63	C₄⋊C₄	—	4	1	no	—
64	C₄²	—	4	1	no	—
65	C₄²	D₄×C₈₃	1	1	yes	characteristic
66	C₁₆	—	2	2	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
72	C₂×C₄	D₈×C₈₃	1	1	yes	characteristic
73	C₂×C₄	SD₁₆×C₈₃	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	8	1	no	—
76	C₈	C₂×C₈×C₈₃	1	1	yes	characteristic
77	C₈	M₁₆×C₈₃	1	1	yes	characteristic
78	C₂²	#102×C₈₃	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	4	2	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊C₈×C₈₃	1	1	yes	characteristic
83	C₄	#104×C₈₃	1	1	yes	characteristic
84	C₄	SD₃₂×C₈₃	1	1	yes	characteristic
85	C₄	Q₃₂×C₈₃	1	1	yes	characteristic
86	C₂	D₄⋊C₈×C₈₃	1	1	yes	characteristic
87	C₂	#358×C₈₃	1	1	yes	characteristic
88	C₂	#359×C₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₃	D₈
commutator	C₈	C₂×C₈×C₈₃
Frattini, cosocle	C₄×C₈	C₂²×C₈₃
socle, prime radical	C₂²×C₈₃	#102
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ C₄²×C₈₃ ◁ C₄×C₈×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. Q₁₆×C₈₃	C₈	semidirect
44. #1332	C₈₃	direct (N × H)
45. C₈₃	#1332	direct (N × H)
58. Q₁₆	C₈×C₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₁₆×C₈₃	2
C₄×C₁₆×C₈₃	2
#335×C₈₃	2
#1332	83

Subgroups — C83×#1332 #24903017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#1332 #24903017