Subgroups — #24905428

Order 10624.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₃₃₂	C₂	1	1	yes	maximal, characteristic
2	#19127454	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₂	C₄	1	1	yes	characteristic
5	C₄×Dic₁₆₆	—	2	1	no	—
6	#14581726	C₄	1	1	yes	characteristic
7	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
8	#14581717	—	2	1	no	—
9	C₂×C₁₆×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₆₆	—	2	1	no	—
12	Dic₃₃₂	—	2	1	no	—
13	Dic₃₃₂	C₈	1	2	yes	complemented
14	C₂×C₈₃⋊C₈	—	4	1	no	—
15	C₄⋊Dic₈₃	—	2	1	no	—
16	Dic₈₃⋊C₄	—	4	1	no	—
17	C₄×Dic₈₃	—	4	1	no	—
18	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
20	C₄²×C₈₃	D₄	1	1	yes	characteristic
21	C₁₆×C₈₃	—	2	2	no	—
22	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
24	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₈₃	—	4	1	no	—
26	C₂×Dic₈₃	—	4	1	no	—
27	Dic₁₆₆	—	2	2	no	—
28	Dic₁₆₆	—	4	1	no	—
29	C₈×C₈₃	—	2	1	no	—
30	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₈₃	M₁₆	1	1	yes	characteristic
32	C₈₃⋊C₈	—	8	1	no	—
33	C₂²×C₈₃	#102	1	1	yes	characteristic
34	C₄×C₈₃	—	2	1	no	—
35	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₈₃	#104	1	1	yes	characteristic
37	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
38	C₄×C₈₃	Q₃₂	1	1	yes	characteristic
39	Dic₈₃	—	4	2	no	—
40	Dic₈₃	—	8	1	no	—
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	—	83	1	no	maximal, Sylow
45	C₈₃	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	83	1	no	—
47	C₄×C₁₆	D₈₃	1	1	yes	characteristic
48	#335	—	83	1	no	—
49	C₂×Q₁₆	—	83	1	no	—
50	C₄×Q₈	—	166	1	no	—
51	C₂×C₁₆	—	2	1	no	—
52	#107	—	83	1	no	—
53	C₄⋊C₈	—	166	1	no	—
54	#103	—	166	1	no	—
55	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
56	C₂×Q₈	—	166	1	no	—
57	Q₁₆	—	83	2	no	—
58	Q₁₆	—	166	1	no	—
59	C₂×C₈	—	332	1	no	—
60	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
61	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
62	C₄⋊C₄	—	332	1	no	—
63	C₄⋊C₄	—	166	1	no	—
64	C₄²	—	332	1	no	—
65	C₄²	D₃₃₂	1	1	yes	characteristic
66	C₁₆	—	2	2	no	—
67	Q₈	—	332	1	no	—
68	Q₈	—	166	2	no	—
69	C₂×C₄	—	332	1	no	—
70	C₂×C₄	—	332	1	no	—
71	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
72	C₂×C₄	D₆₆₄	1	1	yes	characteristic
73	C₂×C₄	#13050579	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	664	1	no	—
76	C₈	C₈×D₈₃	1	1	yes	characteristic
77	C₈	#13050573	1	1	yes	characteristic
78	C₂²	#14581714	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	332	2	no	—
81	C₄	—	664	1	no	—
82	C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
83	C₄	#14581720	1	1	yes	characteristic
84	C₄	#14581737	1	1	yes	characteristic
85	C₄	Dic₆₆₄	1	1	yes	characteristic
86	C₂	#19127430	1	1	yes	characteristic
87	C₂	#19127506	1	1	yes	characteristic
88	C₂	#19127509	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₆₆₄
commutator	C₈×C₈₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₃
Fitting	C₄×C₁₆×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#102
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	C₄×C₁₆	D₈₃
hypocenter	C₈₃	#1332
LCS	G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
13. Dic₃₃₂	C₈	semidirect
45. C₈₃	#1332	semidirect