Subgroups — #35292066

Order 21248.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24909742	C₂	1	1	yes	maximal, characteristic
2	#24905539	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#1422	C₂	1	1	yes	maximal, characteristic
4	#19128103	—	2	1	no	—
5	#19127529	C₄	1	2	yes	—
6	#19127527	—	2	1	no	—
7	#19127522	—	2	1	no	—
8	M₆₄×C₈₃	—	2	1	no	—
9	C₄×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	#14581784	—	4	1	no	—
11	#14581732	—	4	1	no	—
12	#14581726	—	2	2	no	—
13	#14581724	—	4	1	no	—
14	C₂×C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₈₃	D₄	1	1	yes	characteristic
16	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
17	C₃₂×C₈₃	—	4	1	no	—
18	C₄⋊Dic₈₃	—	4	2	no	—
19	Dic₈₃⋊C₄	—	8	2	no	—
20	C₈₃⋊C₁₆	—	8	1	no	—
21	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₃	D₈	1	1	yes	characteristic
23	C₄²×C₈₃	SD₁₆	1	1	yes	characteristic
24	C₁₆×C₈₃	—	2	1	no	—
25	C₁₆×C₈₃	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₈₃	Q₁₆	1	1	yes	characteristic
27	C₂×C₄×C₈₃	—	2	1	no	—
28	C₂×C₄×C₈₃	#102	1	1	yes	characteristic
29	C₂×Dic₈₃	—	8	2	no	—
30	C₈×C₈₃	#101	1	1	yes	characteristic
31	C₈×C₈₃	#103	1	1	yes	characteristic
32	C₈×C₈₃	SD₃₂	1	1	yes	characteristic
33	C₈×C₈₃	Q₃₂	1	1	yes	characteristic
34	C₂²×C₈₃	#361	1	1	yes	characteristic
35	C₄×C₈₃	—	4	1	no	—
36	C₄×C₈₃	#332	1	1	yes	characteristic
37	C₄×C₈₃	#358	1	1	yes	characteristic
38	Dic₈₃	—	16	2	no	—
39	#7454	—	83	1	no	maximal, Sylow
40	C₂×C₈₃	—	2	1	no	—
41	C₂×C₈₃	#1365	1	1	yes	characteristic
42	#2253	—	83	1	no	—
43	#1422	D₈₃	1	1	yes	characteristic
44	#1373	—	83	1	no	—
45	C₈₃	#7454	1	1	yes	characteristic, complemented, Sylow
46	#499	—	166	1	no	—
47	M₆₄	—	2	1	no	—
48	#367	—	83	2	no	—
49	#366	—	166	1	no	—
50	#364	—	166	1	no	—
51	C₄×C₁₆	C₂×D₈₃	1	1	yes	characteristic
52	#125	—	332	1	no	—
53	M₃₂	—	332	1	no	—
54	C₂×C₁₆	C₄×D₈₃	1	1	yes	characteristic
55	C₂×C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
56	#107	—	166	2	no	—
57	#106	—	332	1	no	—
58	C₄×C₈	D₃₃₂	1	1	yes	characteristic
59	C₃₂	—	4	1	no	—
60	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
61	C₂×C₈	D₆₆₄	1	1	yes	characteristic
62	C₄⋊C₄	—	332	2	no	—
63	C₄⋊C₄	—	664	2	no	—
64	C₄²	#13050579	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	664	1	no	—
67	C₁₆	#13050578	1	1	yes	characteristic
68	C₁₆	#13050580	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	664	2	no	—
71	C₂×C₄	#14581714	1	1	yes	characteristic
72	C₈	#14581710	1	1	yes	characteristic
73	C₈	#14581715	1	1	yes	characteristic
74	C₈	#14581737	1	1	yes	characteristic
75	C₈	Dic₆₆₄	1	1	yes	characteristic
76	C₂²	#19127515	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	1328	2	no	—
79	C₄	#19127446	1	1	yes	characteristic
80	C₄	#19127506	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#24905520	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#24905520
commutator	C₂×C₁₆×C₈₃	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₃
Fitting	C₈₃×#1422	C₂
socle	C₂×C₈₃	#1365
prime radical	C₂²×C₈₃	#361
cosocle	C₄×C₁₆×C₈₃	C₂²
hypercenter	#1422	D₈₃
hypocenter	C₈₃	#7454
LCS	G ▷ C₂×C₁₆×C₈₃ ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
45. C₈₃	#7454	semidirect

Maximal subgroups

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

subgroup	index
#24909742	2
#24905539	2
C₈₃×#1422	2
#7454	83