Subgroups — #24905415

Order 10624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127729	C₂	1	1	yes	maximal, characteristic
2	#19127483	C₂	1	1	yes	maximal, characteristic
3	#349×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈₃⋊C₈	C₄	1	1	yes	characteristic
5	#14581751	C₄	1	1	yes	characteristic
6	#14581732	—	2	1	no	—
7	Dic₈₃⋊C₈	—	2	1	no	—
8	Dic₈₃⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	M₃₂×C₈₃	—	2	1	no	—
11	C₂×C₈₃⋊C₈	—	2	1	no	—
12	C₂×C₈₃⋊C₈	—	4	1	no	—
13	C₄⋊Dic₈₃	—	2	1	no	—
14	C₂²⋊Dic₈₃	C₈	1	2	yes	—
15	C₄×Dic₈₃	—	2	1	no	—
16	C₈₃⋊C₁₆	—	4	1	no	—
17	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
18	M₁₆×C₈₃	—	4	1	no	—
19	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
21	C₁₆×C₈₃	—	4	1	no	—
22	C₂³×C₈₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₈₃	—	2	1	no	—
24	C₂×C₄×C₈₃	—	2	1	no	—
25	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₈₃	M₁₆	1	1	yes	characteristic
27	C₂×Dic₈₃	—	2	2	no	—
28	C₈×C₈₃	—	2	1	no	—
29	C₈×C₈₃	—	2	1	no	—
30	C₈₃⋊C₈	—	4	1	no	—
31	C₂²×C₈₃	—	2	1	no	—
32	C₂²×C₈₃	—	4	1	no	—
33	C₂²×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₈₃	—	2	1	no	—
35	C₄×C₈₃	#99	1	1	yes	characteristic
36	C₄×C₈₃	#101	1	1	yes	characteristic
37	Dic₈₃	—	4	2	no	—
38	C₂×C₈₃	—	2	1	no	—
39	C₂×C₈₃	—	4	1	no	—
40	C₂×C₈₃	#324	1	1	yes	characteristic
41	#1328	—	83	1	no	maximal, Sylow
42	C₈₃	#1328	1	1	yes	characteristic, complemented, Sylow
43	#424	—	83	1	no	—
44	#349	—	83	1	no	—
45	#349	D₈₃	1	1	yes	characteristic
46	C₂×M₁₆	C₂×D₈₃	1	1	yes	characteristic
47	C₂²×C₈	—	83	1	no	—
48	#117	—	83	1	no	—
49	M₃₂	—	2	1	no	—
50	M₃₂	—	166	1	no	—
51	C₄⋊C₈	—	166	1	no	—
52	C₄⋊C₈	—	166	1	no	—
53	C₂²×C₄	C₄×D₈₃	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	332	1	no	—
56	C₂×C₈	—	166	1	no	—
57	C₂×C₈	D₃₃₂	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
59	C₄⋊C₄	—	166	1	no	—
60	C₂²⋊C₄	—	83	2	no	—
61	C₄²	—	166	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	332	1	no	—
64	C₂³	C₈×D₈₃	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	166	2	no	—
68	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
69	C₂×C₄	#13050573	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	332	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	332	2	no	—
78	C₄	#14581706	1	1	yes	characteristic
79	C₄	#14581710	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#19127426	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14581706
commutator, prime radical	C₂³×C₈₃	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₈₃
Fitting	#349×C₈₃	C₂
socle	C₂×C₈₃	#324
cosocle	C₂×M₁₆×C₈₃	C₂²
hypercenter	#349	D₈₃
hypocenter	C₈₃	#1328
LCS	G ▷ C₂³×C₈₃ ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
42. C₈₃	#1328	semidirect