Subgroups — #24905404

Order 10624.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127727	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₈₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13050574	C₄	1	1	yes	characteristic
5	#14581751	C₄	1	1	yes	characteristic
6	C₂×C₈₃⋊C₁₆	—	2	1	no	—
7	Dic₈₃⋊C₈	—	2	1	no	—
8	Dic₈₃⋊C₈	—	2	1	no	—
9	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₈₃	—	2	1	no	—
11	#13050574	—	4	1	no	—
12	C₂×C₈₃⋊C₈	—	2	1	no	—
13	C₄⋊Dic₈₃	C₈	1	1	yes	characteristic
14	C₄⋊Dic₈₃	C₈	1	1	yes	characteristic
15	C₂²⋊Dic₈₃	—	2	1	no	—
16	C₄×Dic₈₃	—	2	1	no	—
17	C₈₃⋊C₁₆	—	4	1	no	—
18	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₈₃	—	4	1	no	—
20	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
22	C₁₆×C₈₃	—	4	1	no	—
23	C₂³×C₈₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₈₃	—	2	1	no	—
25	C₂×C₄×C₈₃	—	2	1	no	—
26	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₈₃	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₈₃	—	2	1	no	—
29	C₂×Dic₈₃	—	2	1	no	—
30	C₈×C₈₃	—	2	1	no	—
31	C₈×C₈₃	—	2	1	no	—
32	C₈₃⋊C₈	—	4	1	no	—
33	C₂²×C₈₃	—	2	1	no	—
34	C₂²×C₈₃	—	2	1	no	—
35	C₂²×C₈₃	—	2	1	no	—
36	C₂²×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₈₃	—	2	1	no	—
38	C₄×C₈₃	#99	1	1	yes	characteristic
39	C₄×C₈₃	#101	1	1	yes	characteristic
40	Dic₈₃	—	4	1	no	—
41	Dic₈₃	—	4	1	no	—
42	C₂×C₈₃	—	4	1	no	—
43	C₂×C₈₃	#324	1	1	yes	characteristic
44	C₂×C₈₃	#350	1	1	yes	characteristic
45	C₂×C₈₃	#350	1	1	yes	characteristic
46	#1323	—	83	1	no	maximal, Sylow
47	C₈₃	#1323	1	1	yes	characteristic, complemented, Sylow
48	#424	—	83	1	no	—
49	C₂²⋊C₁₆	—	83	1	no	—
50	C₂²⋊C₁₆	D₈₃	1	1	yes	characteristic
51	C₂×M₁₆	—	83	1	no	—
52	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
53	#117	—	83	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	—	166	1	no	—
56	C₄⋊C₈	—	166	1	no	—
57	C₄⋊C₈	—	166	1	no	—
58	C₂²×C₄	C₄×D₈₃	1	1	yes	characteristic
59	M₁₆	—	332	1	no	—
60	C₂×C₈	—	4	1	no	—
61	C₂×C₈	—	166	1	no	—
62	C₂×C₈	D₃₃₂	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
64	C₄⋊C₄	—	83	1	no	—
65	C₄⋊C₄	—	83	1	no	—
66	C₂²⋊C₄	—	166	1	no	—
67	C₄²	—	166	1	no	—
68	C₁₆	—	4	1	no	—
69	C₁₆	—	332	1	no	—
70	C₂³	#13050573	1	1	yes	characteristic
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	166	1	no	—
74	C₂×C₄	—	166	1	no	—
75	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
76	C₂×C₄	C₈×D₈₃	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	332	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	332	1	no	—
86	C₄	—	332	1	no	—
87	C₄	#14581706	1	1	yes	characteristic
88	C₄	#14581710	1	1	yes	characteristic
89	C₂	—	4	1	no	—
90	C₂	#19127426	1	1	yes	characteristic
91	C₂	#19127484	1	1	yes	characteristic
92	C₂	#19127486	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₈₃)⋊C₄
commutator	C₂×C₄×C₈₃	C₂×C₈
Frattini	C₂²×C₈	C₂×D₈₃
Fitting	C₂²⋊C₁₆×C₈₃	C₂
socle	C₂²×C₈₃	C₂²⋊C₈
prime radical	C₂³×C₈₃	M₁₆
cosocle	C₂²×C₈×C₈₃	C₂²
hypercenter	C₂²⋊C₁₆	D₈₃
hypocenter	C₈₃	#1323
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
47. C₈₃	#1323	semidirect