Group #24907607 — subgroups

Subgroups — #24907607

Order 10624.

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127547	C₂	1	1	yes	maximal, characteristic
2	#19127456	C₂	1	1	yes	maximal, characteristic
3	#19127455	C₂	1	2	yes	maximal
4	#19127455	C₂	1	2	yes	maximal
5	#336×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₈₃	C₂²	1	1	yes	characteristic
9	C₈₃⋊#95	C₄	1	2	yes	—
10	C₈₃⋊#95	C₄	1	2	yes	—
11	C₂²×C₈×C₈₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
13	C₂²×Dic₈₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₈₃	C₂×C₄	1	2	yes	—
15	C₂²×Dic₈₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈₃⋊C₈	—	2	2	no	—
17	C₂×C₈₃⋊C₈	—	2	2	no	—
18	C₂×C₈₃⋊C₈	—	2	2	no	—
19	C₄×Dic₈₃	—	2	1	no	—
20	C₄×Dic₈₃	—	2	2	no	—
21	C₄×Dic₈₃	—	2	1	no	—
22	C₂²×C₄×C₈₃	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₈₃	—	2	2	no	—
25	C₂×C₈×C₈₃	—	2	2	no	—
26	C₂×C₈×C₈₃	—	2	2	no	—
27	C₄²×C₈₃	—	2	2	no	—
28	C₂³×C₈₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₈₃	—	2	2	no	—
30	C₂×C₄×C₈₃	—	2	2	no	—
31	C₂×C₄×C₈₃	—	2	2	no	—
32	C₂×C₄×C₈₃	#41	1	2	yes	—
33	C₂×C₄×C₈₃	#41	1	1	yes	characteristic
34	C₂×C₄×C₈₃	#41	1	2	yes	—
35	C₂×C₄×C₈₃	#41	1	1	yes	characteristic
36	C₂×Dic₈₃	—	2	1	no	—
37	C₂×Dic₈₃	—	2	1	no	—
38	C₂×Dic₈₃	—	2	2	no	—
39	C₂×Dic₈₃	—	2	2	no	—
40	C₂×Dic₈₃	—	2	2	no	—
41	C₂×Dic₈₃	—	2	2	no	—
42	C₂×Dic₈₃	—	2	2	no	—
43	C₈×C₈₃	—	4	2	no	—
44	C₈₃⋊C₈	—	4	2	no	—
45	C₂²×C₈₃	#117	1	1	yes	characteristic
46	C₂²×C₈₃	#117	1	1	yes	characteristic
47	C₂²×C₈₃	#117	1	1	yes	characteristic
48	C₂²×C₈₃	#131	1	2	yes	—
49	C₂²×C₈₃	#131	1	2	yes	—
50	C₄×C₈₃	—	4	2	no	—
51	C₄×C₈₃	#126	1	2	yes	—
52	C₄×C₈₃	#126	1	2	yes	—
53	Dic₈₃	—	4	1	no	—
54	Dic₈₃	—	4	2	no	—
55	Dic₈₃	—	4	1	no	—
56	C₂×C₈₃	#383	1	1	yes	characteristic
57	C₂×C₈₃	#433	1	2	yes	—
58	C₂×C₈₃	#433	1	1	yes	characteristic
59	C₂×C₈₃	#433	1	2	yes	—
60	C₂×C₈₃	#433	1	1	yes	characteristic
61	#1840	—	83	1	no	maximal, Sylow
62	C₈₃	#1840	1	1	yes	characteristic, complemented, Sylow
63	#376	—	83	1	no	—
64	#336	—	83	2	no	—
65	#336	—	83	2	no	—
66	#336	—	83	1	no	—
67	#336	D₈₃	1	1	yes	characteristic
68	C₂²×C₈	—	83	2	no	—
69	C₂²×C₈	C₂×D₈₃	1	2	yes	—
70	C₂×C₄²	—	83	1	no	—
71	C₂×C₄²	—	83	1	no	—
72	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
73	#95	—	83	2	no	—
74	#95	—	83	2	no	—
75	C₂²×C₄	—	83	1	no	—
76	C₂²×C₄	—	83	2	no	—
77	C₂²×C₄	—	83	1	no	—
78	C₂²×C₄	C₄×D₈₃	1	2	yes	—
79	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	166	2	no	—
84	C₂×C₈	—	166	2	no	—
85	C₂×C₈	—	166	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	—	166	1	no	—
88	C₄²	—	166	2	no	—
89	C₄²	—	166	1	no	—
90	C₂³	C₂×C₄×D₈₃	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	166	2	no	—
95	C₂×C₄	—	166	2	no	—
96	C₂×C₄	—	166	2	no	—
97	C₂×C₄	—	166	2	no	—
98	C₂×C₄	—	166	1	no	—
99	C₂×C₄	—	166	1	no	—
100	C₂×C₄	—	166	2	no	—
101	C₂×C₄	#13050589	1	1	yes	characteristic
102	C₂×C₄	#13050589	1	2	yes	—
103	C₂×C₄	#13050590	1	2	yes	—
104	C₂×C₄	#13050591	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	332	2	no	—
107	C₂²	#14581748	1	1	yes	characteristic
108	C₂²	#14581749	1	1	yes	characteristic
109	C₂²	#14581750	1	1	yes	characteristic
110	C₂²	#14581798	1	2	yes	—
111	C₂²	#14581800	1	2	yes	—
112	C₄	—	4	2	no	—
113	C₄	—	332	1	no	—
114	C₄	—	332	2	no	—
115	C₄	—	332	1	no	—
116	C₄	#14581785	1	2	yes	—
117	C₄	#14581787	1	2	yes	—
118	C₂	#19127568	1	1	yes	characteristic
119	C₂	#19127759	1	2	yes	—
120	C₂	#19127760	1	1	yes	characteristic
121	C₂	#19127761	1	2	yes	—
122	C₂	#19127763	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19127547

C₂

yes

maximal, characteristic

#19127456

C₂

yes

maximal, characteristic

#19127455

C₂

yes

maximal

#19127455

C₂

yes

maximal

#336×C₈₃

C₂

yes

maximal, characteristic

C₂²×C₈₃⋊C₈

C₂²

yes

—

C₂×C₄×Dic₈₃

C₂²

yes

characteristic

C₂×C₄×Dic₈₃

C₂²

yes

characteristic

C₈₃⋊#95

C₄

yes

—

C₈₃⋊#95

C₄

yes

—

C₂²×C₈×C₈₃

C₂²

yes

—

C₂×C₄²×C₈₃

C₂²

yes

characteristic

C₂²×Dic₈₃

C₂×C₄

yes

characteristic

C₂²×Dic₈₃

C₂×C₄

yes

—

C₂²×Dic₈₃

C₂×C₄

yes

characteristic

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

C₂×C₄

yes

—

C₂²×C₄×C₈₃

C₂³

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₄²×C₈₃

—

C₂³×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#41

yes

—

C₂×C₄×C₈₃

#41

yes

characteristic

C₂×C₄×C₈₃

#41

yes

—

C₂×C₄×C₈₃

#41

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₂²×C₈₃

yes

C₂²×C₈₃

yes

—

C₂²×C₈₃

#131

yes

—

C₄×C₈₃

—

C₄×C₈₃

#126

yes

—

C₄×C₈₃

#126

yes

—

Dic₈₃

—

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

#383

yes

characteristic

C₂×C₈₃

#433

yes

—

C₂×C₈₃

#433

yes

characteristic

C₂×C₈₃

#433

yes

—

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

—

—

—

—

D₈₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₈₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₈₃

yes

characteristic

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₈₃

yes

—

C₂²×C₄

C₂²×D₈₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

166

—

C₂×C₈

—

166

—

C₂×C₈

—

166

—

C₄²

—

C₄²

—

166

—

C₄²

—

166

—

C₄²

—

166

—

C₂³

C₂×C₄×D₈₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

100

C₂×C₄

—

166

—

101

C₂×C₄

#13050589

yes

characteristic

102

C₂×C₄

#13050589

yes

—

103

C₂×C₄

#13050590

yes

—

104

C₂×C₄

#13050591

yes

characteristic

105

C₈

—

106

C₈

—

332

—

107

C₂²

#14581748

yes

characteristic

108

C₂²

#14581749

yes

characteristic

109

C₂²

#14581750

yes

characteristic

110

C₂²

#14581798

yes

—

111

C₂²

#14581800

yes

—

112

C₄

—

113

C₄

—

332

—

114

C₄

—

332

—

115

C₄

—

332

—

116

C₄

#14581785

yes

—

117

C₄

#14581787

yes

—

118

C₂

#19127568

yes

characteristic

119

C₂

#19127759

yes

—

120

C₂

#19127760

yes

characteristic

121

C₂

#19127761

yes

—

122

C₂

#19127763

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₈₃
commutator, socle, prime radical	C₂³×C₈₃	C₂²×C₄
Fitting	#336×C₈₃	C₂
cosocle	C₂²×C₄×C₈₃	C₂³
hypercenter	#336	D₈₃
hypocenter	C₈₃	#1840
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₈₃

commutator, socle, prime radical

C₂³×C₈₃

C₂²×C₄

Fitting

#336×C₈₃

C₂

cosocle

C₂²×C₄×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂³×C₈₃ ▷ C₈₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
62. C₈₃	#1840	semidirect

H ≅ G/N

type

62. C₈₃

#1840

semidirect

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

subgroup	index
#19127547	2
#19127456	2
#19127455	2
#336×C₈₃	2
#1840	83

subgroup

index

#336×C₈₃

Subgroups — #24907607

Conjugacy classes of subgroups

Complements

Maximal subgroups