Group #23762828 — subgroups

Subgroups — #23762828

Order 10112.

150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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	#19098913	C₂	1	1	yes	maximal, characteristic
2	#19098773	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#19098313	C₂	1	1	yes	maximal, characteristic
5	#19098310	C₂	1	1	yes	maximal, characteristic
6	#19098309	C₂	1	1	yes	maximal, characteristic
7	#475×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#11929614	—	2	1	no	—
9	#14579161	C₂²	1	1	yes	characteristic
10	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
11	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	#14579085	—	2	1	no	—
14	#14579085	—	2	1	no	—
15	#14579084	—	2	1	no	—
16	C₄×C₇₉⋊C₈	—	2	1	no	—
17	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	#106×C₇₉	—	2	1	no	—
21	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
22	#103×C₇₉	—	2	1	no	—
23	C₂×Dic₁₅₈	—	2	1	no	—
24	#11929614	—	4	2	no	—
25	C₂×C₇₉⋊C₈	—	2	1	no	—
26	C₂×C₇₉⋊C₈	—	2	1	no	—
27	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
28	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	C₂×Q₈×C₇₉	—	2	1	no	—
32	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₇₉	—	2	1	no	—
34	C₄⋊C₄×C₇₉	—	2	1	no	—
35	C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
38	C₄²×C₇₉	—	2	1	no	—
39	C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	Q₈×C₇₉	—	2	1	no	—
41	Q₈×C₇₉	—	4	1	no	—
42	Q₈×C₇₉	—	4	1	no	—
43	Q₈×C₇₉	SD₁₆	1	2	yes	—
44	C₂×C₄×C₇₉	—	2	1	no	—
45	C₂×C₄×C₇₉	—	2	1	no	—
46	C₂×C₄×C₇₉	—	4	1	no	—
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
50	C₂×Dic₇₉	—	4	1	no	—
51	Dic₁₅₈	—	4	1	no	—
52	Dic₁₅₈	—	4	1	no	—
53	C₈×C₇₉	—	4	1	no	—
54	C₇₉⋊C₈	—	2	1	no	—
55	C₇₉⋊C₈	—	2	1	no	—
56	C₇₉⋊C₈	—	4	1	no	—
57	C₇₉⋊C₈	—	4	1	no	—
58	C₂²×C₇₉	#121	1	1	yes	characteristic
59	C₄×C₇₉	—	2	2	no	—
60	C₄×C₇₉	—	2	1	no	—
61	C₄×C₇₉	—	4	1	no	—
62	C₄×C₇₉	—	8	1	no	—
63	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
64	C₄×C₇₉	#135	1	1	yes	characteristic
65	C₄×C₇₉	#135	1	1	yes	characteristic
66	C₄×C₇₉	#137	1	1	yes	characteristic
67	Dic₇₉	—	8	1	no	—
68	C₂×C₇₉	#464	1	1	yes	characteristic
69	C₂×C₇₉	#465	1	1	yes	characteristic
70	C₂×C₇₉	#473	1	1	yes	characteristic
71	#1680	—	79	1	no	maximal, Sylow
72	C₇₉	#1680	1	1	yes	characteristic, complemented, Sylow
73	#487	—	79	1	no	—
74	#475	D₇₉	1	1	yes	characteristic
75	#462	—	79	1	no	—
76	C₈×Q₈	—	79	1	no	—
77	#334	—	79	1	no	—
78	#332	—	79	1	no	—
79	#332	—	79	1	no	—
80	C₂×Q₁₆	—	158	1	no	—
81	C₄⋊Q₈	—	79	1	no	—
82	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
83	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
84	#106	—	2	1	no	—
85	C₄⋊C₈	—	79	1	no	—
86	C₄⋊C₈	—	79	1	no	—
87	C₄⋊C₈	—	158	1	no	—
88	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
89	#103	—	2	1	no	—
90	#103	—	158	1	no	—
91	#103	—	158	1	no	—
92	#103	—	158	1	no	—
93	C₄×C₈	—	79	1	no	—
94	C₄×C₈	—	158	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	158	1	no	—
97	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
98	Q₁₆	—	316	2	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	79	1	no	—
101	C₂×C₈	—	79	1	no	—
102	C₂×C₈	—	158	1	no	—
103	C₂×C₈	—	158	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	158	1	no	—
108	C₄⋊C₄	—	158	1	no	—
109	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
110	C₄²	—	2	1	no	—
111	C₄²	C₂²×D₇₉	1	1	yes	characteristic
112	Q₈	—	2	1	no	—
113	Q₈	—	4	1	no	—
114	Q₈	—	4	1	no	—
115	Q₈	—	316	1	no	—
116	Q₈	—	316	1	no	—
117	Q₈	#11929611	1	2	yes	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	316	1	no	—
122	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
123	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
124	C₂×C₄	#11929623	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	316	1	no	—
127	C₈	—	316	1	no	—
128	C₈	—	158	1	no	—
129	C₈	—	158	1	no	—
130	C₂²	#14579133	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	8	1	no	—
135	C₄	—	632	1	no	—
136	C₄	C₂×#11929611	1	1	yes	characteristic
137	C₄	#14579181	1	1	yes	characteristic
138	C₄	#14579182	1	1	yes	characteristic
139	C₄	#14579190	1	1	yes	characteristic
140	C₂	#19098783	1	1	yes	characteristic
141	C₂	#19098794	1	1	yes	characteristic
142	C₂	#19098836	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098913

C₂

yes

maximal, characteristic

#19098773

C₂

yes

maximal, characteristic

Q₈×C₇₉⋊C₈

C₂

yes

maximal, characteristic

#19098313

C₂

yes

maximal, characteristic

#19098310

C₂

yes

maximal, characteristic

#19098309

C₂

yes

maximal, characteristic

#475×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929614

—

#14579161

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

—

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄×Q₈×C₇₉

C₂²

yes

characteristic

#106×C₇₉

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#103×C₇₉

—

C₂×Dic₁₅₈

—

#11929614

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#487

—

#475

D₇₉

yes

characteristic

#462

—

C₈×Q₈

—

#334

—

#332

—

#332

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

C₄×Q₈

C₂×D₇₉

yes

characteristic

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#103

—

#103

—

158

—

#103

—

158

—

#103

—

158

—

C₄×C₈

—

C₄×C₈

—

158

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

Q₁₆

—

316

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

158

—

103

C₂×C₈

—

158

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

158

—

108

C₄⋊C₄

—

158

—

109

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

110

C₄²

—

111

C₄²

C₂²×D₇₉

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

316

—

116

Q₈

—

316

—

117

Q₈

#11929611

yes

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

316

—

122

C₂×C₄

D₄×D₇₉

yes

characteristic

123

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

124

C₂×C₄

#11929623

yes

characteristic

125

C₈

—

126

C₈

—

316

—

127

C₈

—

316

—

128

C₈

—

158

—

129

C₈

—

158

—

130

C₂²

#14579133

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

632

—

136

C₄

C₂×#11929611

yes

characteristic

137

C₄

#14579181

yes

characteristic

138

C₄

#14579182

yes

characteristic

139

C₄

#14579190

yes

characteristic

140

C₂

#19098783

yes

characteristic

141

C₂

#19098794

yes

characteristic

142

C₂

#19098836

yes

characteristic

	subgroup	G/H
center	C₂²	#14579133
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#475×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#121
hypercenter	#475	D₇₉
hypocenter	C₇₉	#1680
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

subgroup

G/H

center

C₂²

#14579133

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#475×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #475

N	H ≅ G/N	type
72. C₇₉	#1680	semidirect

H ≅ G/N

type

72. C₇₉

#1680

semidirect

Subgroups — #23762828

Conjugacy classes of subgroups

Complements