Subgroups — #24905511

Order 10624.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128081	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₈₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#335×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₂	—	2	1	no	—
5	C₂×Dic₃₃₂	C₄	1	2	yes	—
6	#14581792	—	2	1	no	—
7	C₂×C₈₃⋊C₁₆	—	2	1	no	—
8	C₄⋊C₈×C₈₃	—	2	1	no	—
9	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₆₆	—	2	2	no	—
11	Dic₃₃₂	—	4	2	no	—
12	Dic₃₃₂	—	4	1	no	—
13	Dic₃₃₂	—	4	1	no	—
14	C₄⋊Dic₈₃	—	4	1	no	—
15	C₄⋊Dic₈₃	—	4	1	no	—
16	C₈₃⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₈₃	—	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	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₈₃	—	4	2	no	—
25	Dic₁₆₆	—	4	2	no	—
26	Dic₁₆₆	—	4	2	no	—
27	C₈×C₈₃	—	2	1	no	—
28	C₈×C₈₃	—	8	1	no	—
29	C₈×C₈₃	D₈	1	1	yes	characteristic
30	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
31	C₂²×C₈₃	#102	1	1	yes	characteristic
32	C₄×C₈₃	—	2	1	no	—
33	C₄×C₈₃	#100	1	1	yes	characteristic
34	C₄×C₈₃	#102	1	1	yes	characteristic
35	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
36	C₄×C₈₃	Q₃₂	1	1	yes	characteristic
37	Dic₈₃	—	8	2	no	—
38	C₂×C₈₃	#331	1	1	yes	characteristic
39	C₂×C₈₃	#358	1	1	yes	characteristic
40	C₂×C₈₃	#362	1	1	yes	characteristic
41	#1362	—	83	1	no	maximal, Sylow
42	C₈₃	#1362	1	1	yes	characteristic, complemented, Sylow
43	#494	—	83	1	no	—
44	C₄⋊C₁₆	—	83	1	no	—
45	#335	D₈₃	1	1	yes	characteristic
46	C₂×Q₁₆	—	83	2	no	—
47	C₂×Q₁₆	—	166	1	no	—
48	C₄⋊Q₈	—	166	1	no	—
49	C₂×C₁₆	—	166	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
52	C₂×Q₈	—	166	2	no	—
53	Q₁₆	—	332	2	no	—
54	Q₁₆	—	332	1	no	—
55	Q₁₆	—	332	1	no	—
56	C₂×C₈	—	4	1	no	—
57	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
58	C₂×C₈	D₃₃₂	1	1	yes	characteristic
59	C₄⋊C₄	—	332	1	no	—
60	C₄⋊C₄	—	332	1	no	—
61	C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
62	C₁₆	—	332	1	no	—
63	Q₈	—	332	2	no	—
64	Q₈	—	332	2	no	—
65	C₂×C₄	—	332	2	no	—
66	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
67	C₂×C₄	#13050575	1	1	yes	characteristic
68	C₂×C₄	#13050577	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	D₆₆₄	1	1	yes	characteristic
72	C₈	#13050579	1	1	yes	characteristic
73	C₂²	#14581712	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	664	2	no	—
76	C₄	#14581708	1	1	yes	characteristic
77	C₄	#14581714	1	1	yes	characteristic
78	C₄	#14581736	1	1	yes	characteristic
79	C₄	#14581738	1	1	yes	characteristic
80	C₂	#19127444	1	1	yes	characteristic
81	C₂	#19127504	1	1	yes	characteristic
82	C₂	#19127516	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14581712
commutator	C₂×C₈×C₈₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₈₃
Fitting	#335×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#102
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	#335	D₈₃
hypocenter	C₈₃	#1362
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
42. C₈₃	#1362	semidirect