Group #23764873 — subgroups

Subgroups — #23764873

Order 10112.

230 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₂×#14579095	C₂	1	2	yes	maximal
2	#19098461	C₂	1	1	yes	maximal, characteristic
3	#19098433	C₂	1	1	yes	maximal, characteristic
4	#19098326	C₂	1	2	yes	maximal
5	#336×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₉	—	2	1	no	—
7	C₂×C₄⋊Dic₇₉	—	2	1	no	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₉⋊C₄	—	2	1	no	—
12	#14579095	—	2	4	no	—
13	C₇₉⋊#95	—	2	1	no	—
14	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×Dic₇₉	—	2	1	no	—
17	C₂²×Dic₇₉	—	2	1	no	—
18	C₂²×Dic₇₉	—	2	2	no	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	1	no	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	—	4	2	no	—
24	C₄⋊Dic₇₉	—	4	2	no	—
25	C₄⋊Dic₇₉	D₄	1	2	yes	—
26	Dic₇₉⋊C₄	—	4	2	no	—
27	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₇₉	—	2	2	no	—
31	C₂×C₈×C₇₉	—	2	2	no	—
32	C₂×C₈×C₇₉	Q₈	1	4	yes	—
33	C₄²×C₇₉	—	2	2	no	—
34	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	—	2	1	no	—
36	C₂×C₄×C₇₉	—	2	1	no	—
37	C₂×C₄×C₇₉	—	2	1	no	—
38	C₂×C₄×C₇₉	—	2	1	no	—
39	C₂×C₄×C₇₉	D₈	1	2	yes	—
40	C₂×C₄×C₇₉	Q₁₆	1	2	yes	—
41	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
43	C₂×C₄×C₇₉	#41	1	2	yes	—
44	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
45	C₂×Dic₇₉	—	2	2	no	—
46	C₂×Dic₇₉	—	4	1	no	—
47	C₂×Dic₇₉	—	4	1	no	—
48	C₂×Dic₇₉	—	4	2	no	—
49	C₂×Dic₇₉	—	4	1	no	—
50	C₂×Dic₇₉	—	4	1	no	—
51	C₂×Dic₇₉	—	4	2	no	—
52	C₂×Dic₇₉	—	4	2	no	—
53	C₂×Dic₇₉	—	4	1	no	—
54	C₈×C₇₉	—	2	4	no	—
55	C₂²×C₇₉	#121	1	1	yes	characteristic
56	C₂²×C₇₉	#123	1	1	yes	characteristic
57	C₂²×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
58	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
59	C₂²×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
60	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂²×C₇₉	#137	1	1	yes	characteristic
62	C₄×C₇₉	—	2	2	no	—
63	C₄×C₇₉	—	2	2	no	—
64	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₇₉	#125	1	2	yes	—
66	Dic₇₉	—	4	2	no	—
67	Dic₇₉	—	8	2	no	—
68	Dic₇₉	—	8	1	no	—
69	C₂×C₇₉	#398	1	1	yes	characteristic
70	C₂×C₇₉	#459	1	1	yes	characteristic
71	C₂×C₇₉	#462	1	1	yes	characteristic
72	C₂×C₇₉	#480	1	1	yes	characteristic
73	C₂×C₇₉	#484	1	1	yes	characteristic
74	C₂×C₇₉	#500	1	1	yes	characteristic
75	C₂×C₇₉	#501	1	1	yes	characteristic
76	#2083	—	79	1	no	maximal, Sylow
77	C₇₉	#2083	1	1	yes	characteristic, complemented, Sylow
78	C₂×#107	—	79	2	no	—
79	#389	—	79	1	no	—
80	#384	—	79	1	no	—
81	#340	—	79	2	no	—
82	#336	D₇₉	1	1	yes	characteristic
83	C₂²×C₈	C₂×D₇₉	1	2	yes	—
84	C₂×C₄⋊C₄	—	79	1	no	—
85	C₂×C₄⋊C₄	—	79	1	no	—
86	C₂×C₄⋊C₄	—	79	2	no	—
87	C₂×C₄⋊C₄	—	158	1	no	—
88	C₂×C₄⋊C₄	—	158	1	no	—
89	C₂×C₄⋊C₄	—	158	1	no	—
90	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
91	#107	—	158	4	no	—
92	#95	—	158	1	no	—
93	C₂²×C₄	—	158	1	no	—
94	C₂²×C₄	—	158	2	no	—
95	C₂²×C₄	—	158	1	no	—
96	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
97	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	Dic₁₅₈	1	4	yes	—
102	C₄⋊C₄	—	316	2	no	—
103	C₄⋊C₄	—	316	2	no	—
104	C₄⋊C₄	—	316	2	no	—
105	C₄⋊C₄	—	79	2	no	—
106	C₄⋊C₄	—	158	2	no	—
107	C₄⋊C₄	—	158	2	no	—
108	C₄⋊C₄	—	158	2	no	—
109	C₄⋊C₄	—	158	1	no	—
110	C₄²	—	2	2	no	—
111	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	316	1	no	—
117	C₂×C₄	—	316	1	no	—
118	C₂×C₄	—	316	2	no	—
119	C₂×C₄	—	316	1	no	—
120	C₂×C₄	—	316	2	no	—
121	C₂×C₄	—	316	1	no	—
122	C₂×C₄	—	316	2	no	—
123	C₂×C₄	—	316	1	no	—
124	C₂×C₄	—	158	2	no	—
125	C₂×C₄	D₆₃₂	1	2	yes	—
126	C₂×C₄	Dic₃₁₆	1	2	yes	—
127	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
128	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
129	C₂×C₄	#11929623	1	2	yes	—
130	C₂×C₄	#11929625	1	1	yes	characteristic
131	C₈	—	2	4	no	—
132	C₂²	#14579136	1	1	yes	characteristic
133	C₂²	#14579145	1	1	yes	characteristic
134	C₂²	#14579161	1	1	yes	characteristic
135	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
136	C₂²	C₂×Dic₃₁₆	1	1	yes	characteristic
137	C₂²	#14579189	1	1	yes	characteristic
138	C₂²	#14579194	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	2	2	no	—
141	C₄	—	316	2	no	—
142	C₄	—	632	2	no	—
143	C₄	—	632	1	no	—
144	C₄	#14579138	1	2	yes	—
145	C₄	#14579152	1	2	yes	—
146	C₂	#19098495	1	1	yes	characteristic
147	C₂	#19098759	1	1	yes	characteristic
148	C₂	#19098774	1	1	yes	characteristic
149	C₂	#19098877	1	1	yes	characteristic
150	C₂	#19098899	1	1	yes	characteristic
151	C₂	#19098968	1	1	yes	characteristic
152	C₂	#19098972	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579095

C₂

yes

maximal

#19098461

C₂

yes

maximal, characteristic

#19098433

C₂

yes

maximal, characteristic

#19098326

C₂

yes

maximal

#336×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×Dic₇₉⋊C₄

—

#14579095

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

Q₈

yes

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

—

C₂×C₄×C₇₉

Q₁₆

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₄⋊Q₈

yes

characteristic

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂²×C₇₉

C₂×Q₁₆

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

#125

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#107

—

158

—

#95

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

Dic₁₅₈

yes

—

102

C₄⋊C₄

—

316

—

103

C₄⋊C₄

—

316

—

104

C₄⋊C₄

—

316

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

158

—

107

C₄⋊C₄

—

158

—

108

C₄⋊C₄

—

158

—

109

C₄⋊C₄

—

158

—

110

C₄²

—

111

C₂³

C₂×D₃₁₆

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

316

—

117

C₂×C₄

—

316

—

118

C₂×C₄

—

316

—

119

C₂×C₄

—

316

—

120

C₂×C₄

—

316

—

121

C₂×C₄

—

316

—

122

C₂×C₄

—

316

—

123

C₂×C₄

—

316

—

124

C₂×C₄

—

158

—

125

C₂×C₄

D₆₃₂

yes

—

126

C₂×C₄

Dic₃₁₆

yes

—

127

C₂×C₄

D₄×D₇₉

yes

characteristic

128

C₂×C₄

C₂×Dic₁₅₈

yes

—

129

C₂×C₄

#11929623

yes

—

130

C₂×C₄

#11929625

yes

characteristic

131

C₈

—

132

C₂²

#14579136

yes

characteristic

133

C₂²

#14579145

yes

characteristic

134

C₂²

#14579161

yes

characteristic

135

C₂²

C₂×D₆₃₂

yes

characteristic

136

C₂²

C₂×Dic₃₁₆

yes

characteristic

137

C₂²

#14579189

yes

characteristic

138

C₂²

#14579194

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

316

—

142

C₄

—

632

—

143

C₄

—

632

—

144

C₄

#14579138

yes

—

145

C₄

#14579152

yes

—

146

C₂

#19098495

yes

characteristic

147

C₂

#19098759

yes

characteristic

148

C₂

#19098774

yes

characteristic

149

C₂

#19098877

yes

characteristic

150

C₂

#19098899

yes

characteristic

151

C₂

#19098968

yes

characteristic

152

C₂

#19098972

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₁₆
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#336×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	#336	D₇₉
hypocenter	C₇₉	#2083
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₃₁₆

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#336×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
77. C₇₉	#2083	semidirect

H ≅ G/N

type

77. C₇₉

#2083

semidirect

Subgroups — #23764873

Conjugacy classes of subgroups

Complements