Subgroups — C₈₃×#1333 #24903018

Order 10624.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic
2	#346×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#334×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₈₃	C₄	1	1	yes	characteristic
5	C₄×D₄×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	#102×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₈₃	—	2	1	no	—
12	C₂²×C₄×C₈₃	—	4	1	no	—
13	D₈×C₈₃	—	2	1	no	—
14	D₈×C₈₃	C₈	1	2	yes	complemented
15	C₂×C₈×C₈₃	—	4	1	no	—
16	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₈₃	—	2	1	no	—
19	C₂²⋊C₄×C₈₃	—	4	1	no	—
20	C₄²×C₈₃	D₄	1	1	yes	characteristic
21	C₁₆×C₈₃	—	2	2	no	—
22	C₂³×C₈₃	—	4	1	no	—
23	D₄×C₈₃	—	2	2	no	—
24	D₄×C₈₃	—	4	1	no	—
25	C₂×C₄×C₈₃	—	4	1	no	—
26	C₂×C₄×C₈₃	—	8	2	no	—
27	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₈₃	—	2	1	no	—
31	C₈×C₈₃	—	8	1	no	—
32	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₈₃	M₁₆	1	1	yes	characteristic
34	C₂²×C₈₃	—	4	2	no	—
35	C₂²×C₈₃	—	8	1	no	—
36	C₂²×C₈₃	—	8	1	no	—
37	C₂²×C₈₃	#102	1	1	yes	characteristic
38	C₄×C₈₃	—	2	1	no	—
39	C₄×C₈₃	—	2	1	no	—
40	C₄×C₈₃	—	8	1	no	—
41	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₈₃	#104	1	1	yes	characteristic
43	C₂×C₈₃	—	8	2	no	—
44	C₂×C₈₃	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₈₃	#360	1	1	yes	characteristic
46	C₂×C₈₃	#361	1	1	yes	characteristic
47	#1333	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₈₃	#1333	1	1	yes	characteristic, direct product factor, Sylow
49	C₄×D₈	C₂×C₈₃	1	1	yes	characteristic
50	#346	C₂×C₈₃	1	1	yes	characteristic, complemented
51	#334	C₂×C₈₃	1	1	yes	characteristic, complemented
52	C₂×D₈	C₄×C₈₃	1	1	yes	characteristic
53	C₄×D₄	—	2	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	#107	C₄×C₈₃	1	1	yes	characteristic
56	C₄⋊C₈	—	2	1	no	—
57	#102	—	2	1	no	—
58	C₄×C₈	C₂²×C₈₃	1	1	yes	characteristic
59	C₂×D₄	—	2	1	no	—
60	C₂²×C₄	—	4	1	no	—
61	D₈	—	2	1	no	—
62	D₈	C₈×C₈₃	1	2	yes	complemented
63	C₂×C₈	—	4	1	no	—
64	C₂×C₈	C₂×C₄×C₈₃	1	1	yes	characteristic
65	C₂×C₈	D₄×C₈₃	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₂²⋊C₄	—	4	1	no	—
68	C₄²	D₄×C₈₃	1	1	yes	characteristic
69	C₁₆	—	2	2	no	—
70	C₂³	—	4	1	no	—
71	D₄	—	2	2	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	8	2	no	—
75	C₂×C₄	C₂²⋊C₄×C₈₃	1	1	yes	characteristic
76	C₂×C₄	D₈×C₈₃	1	1	yes	characteristic
77	C₂×C₄	SD₁₆×C₈₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	8	1	no	—
80	C₈	C₂×C₈×C₈₃	1	1	yes	characteristic
81	C₈	M₁₆×C₈₃	1	1	yes	characteristic
82	C₂²	—	4	2	no	—
83	C₂²	—	8	1	no	—
84	C₂²	—	8	1	no	—
85	C₂²	#102×C₈₃	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	C₂²⋊C₈×C₈₃	1	1	yes	characteristic
90	C₄	#104×C₈₃	1	1	yes	characteristic
91	C₂	—	8	2	no	—
92	C₂	D₄⋊C₈×C₈₃	1	1	yes	characteristic
93	C₂	#360×C₈₃	1	1	yes	characteristic
94	C₂	#361×C₈₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #346×C₈₃	C₂	semidirect
3. #334×C₈₃	C₂	semidirect
14. D₈×C₈₃	C₈	semidirect
47. #1333	C₈₃	direct (N × H)
48. C₈₃	#1333	direct (N × H)
50. #346	C₂×C₈₃	semidirect
51. #334	C₂×C₈₃	semidirect
62. D₈	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×D₈×C₈₃	2
#346×C₈₃	2
#334×C₈₃	2
#1333	83

Subgroups — C83×#1333 #24903018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₃×#1333 #24903018