Subgroups — #24909692

Order 10624.

140 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	#19127504	C₂	1	4	yes	maximal
3	C₄×C₈₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#500×C₈₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₃₂	—	2	1	no	—
6	C₂×Dic₃₃₂	C₂²	1	2	yes	—
7	#14581792	—	2	1	no	—
8	C₂×C₈₃⋊C₁₆	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₈₃	—	2	1	no	—
10	#107×C₈₃	—	2	1	no	—
11	#107×C₈₃	C₂²	1	2	yes	—
12	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₆₆	—	2	2	no	—
14	Dic₃₃₂	—	2	4	no	—
15	Dic₃₃₂	—	4	2	no	—
16	C₄⋊Dic₈₃	—	4	1	no	—
17	C₄⋊Dic₈₃	—	4	1	no	—
18	C₈₃⋊C₁₆	—	2	2	no	—
19	C₂×Q₈×C₈₃	—	4	1	no	—
20	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₈₃	—	2	2	no	—
23	C₄⋊C₄×C₈₃	—	4	1	no	—
24	C₄²×C₈₃	D₄	1	1	yes	characteristic
25	Q₈×C₈₃	—	8	2	no	—
26	C₂×C₄×C₈₃	—	4	2	no	—
27	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₈₃	—	4	2	no	—
31	Dic₁₆₆	—	4	2	no	—
32	Dic₁₆₆	—	4	2	no	—
33	C₈×C₈₃	SD₁₆	1	2	yes	—
34	C₈×C₈₃	#41	1	2	yes	—
35	C₂²×C₈₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₈₃	—	8	2	no	—
37	C₄×C₈₃	SD₃₂	1	2	yes	—
38	C₄×C₈₃	Q₃₂	1	2	yes	—
39	C₄×C₈₃	#124	1	1	yes	characteristic
40	C₄×C₈₃	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₈₃	—	8	2	no	—
42	C₂×C₈₃	#486	1	1	yes	characteristic
43	C₂×C₈₃	C₂×SD₃₂	1	1	yes	characteristic
44	C₂×C₈₃	C₂×Q₃₂	1	1	yes	characteristic
45	#2241	—	83	1	no	maximal, Sylow
46	C₈₃	#2241	1	1	yes	characteristic, complemented, Sylow
47	#500	D₈₃	1	1	yes	characteristic
48	#494	—	83	1	no	—
49	#358	—	83	4	no	—
50	C₄×C₁₆	—	83	1	no	—
51	C₂×Q₁₆	—	83	2	no	—
52	C₂×Q₁₆	—	166	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	166	1	no	—
55	C₂×C₁₆	—	83	2	no	—
56	#107	—	2	1	no	—
57	#107	C₂×D₈₃	1	2	yes	—
58	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
59	C₂×Q₈	—	4	1	no	—
60	C₂×Q₈	—	166	2	no	—
61	Q₁₆	—	332	2	no	—
62	Q₁₆	—	166	4	no	—
63	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	332	1	no	—
68	C₄⋊C₄	—	332	1	no	—
69	C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
70	C₁₆	—	166	2	no	—
71	Q₈	—	8	2	no	—
72	Q₈	—	332	2	no	—
73	Q₈	—	332	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	332	2	no	—
76	C₂×C₄	#13050575	1	1	yes	characteristic
77	C₂×C₄	#13050575	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
79	C₈	#13050577	1	2	yes	—
80	C₈	#13050591	1	2	yes	—
81	C₂²	C₂×#13050575	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	664	2	no	—
84	C₄	#14581736	1	2	yes	—
85	C₄	#14581738	1	2	yes	—
86	C₄	#14581781	1	1	yes	characteristic
87	C₄	C₂×#13050577	1	1	yes	characteristic
88	C₂	#19128049	1	1	yes	characteristic
89	C₂	C₂×#14581736	1	1	yes	characteristic
90	C₂	C₂×#14581738	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13050575
commutator, cosocle	C₂×C₈×C₈₃	C₂³
Frattini	C₂×C₈	C₂²×D₈₃
Fitting	#500×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	C₂×D₈
hypercenter	#500	D₈₃
hypocenter	C₈₃	#2241
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
46. C₈₃	#2241	semidirect

Maximal subgroups

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

subgroup	index
#19128081	2
#19127504	2
C₄×C₈₃⋊C₁₆	2
#500×C₈₃	2
#2241	83