Group #23762871 — subgroups

Subgroups — #23762871

Order 10112.

168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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	#19098935	C₂	1	1	yes	maximal, characteristic
2	#19098849	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098760	C₂	1	1	yes	maximal, characteristic
4	#19098690	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098315	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098310	C₂	1	1	yes	maximal, characteristic, complemented
7	#331×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#11929612	—	2	1	no	—
9	C₂×#11929612	—	2	1	no	—
10	C₂×#11929612	—	2	1	no	—
11	#14579161	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
13	#14579093	—	2	1	no	—
14	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	Dic₇₉⋊C₈	—	2	1	no	—
16	#14579086	—	2	1	no	—
17	#14579082	—	2	1	no	—
18	#14579071	—	2	1	no	—
19	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	#127×C₇₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₅₈	—	2	1	no	—
24	C₂×Dic₁₅₈	D₄	1	1	yes	characteristic
25	#11929612	—	4	2	no	—
26	#11929612	—	4	2	no	—
27	#11929612	—	4	2	no	—
28	C₂×C₇₉⋊C₈	—	2	1	no	—
29	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
30	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
31	C₄⋊Dic₇₉	—	2	1	no	—
32	C₄⋊Dic₇₉	—	2	1	no	—
33	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
34	Dic₇₉⋊C₄	—	2	1	no	—
35	C₄×Dic₇₉	—	2	1	no	—
36	C₂×D₄×C₇₉	—	2	1	no	—
37	C₂×D₄×C₇₉	—	2	1	no	—
38	C₂×D₄×C₇₉	—	2	1	no	—
39	C₂×C₈×C₇₉	—	2	1	no	—
40	C₂×C₈×C₇₉	—	2	1	no	—
41	C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₂³×C₇₉	—	4	1	no	—
43	D₄×C₇₉	—	4	1	no	—
44	D₄×C₇₉	—	4	1	no	—
45	D₄×C₇₉	—	4	1	no	—
46	D₄×C₇₉	—	4	1	no	—
47	D₄×C₇₉	—	8	1	no	—
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
51	C₂×Dic₇₉	—	2	1	no	—
52	C₂×Dic₇₉	—	2	1	no	—
53	C₂×Dic₇₉	—	4	1	no	—
54	Dic₁₅₈	—	2	1	no	—
55	Dic₁₅₈	—	2	1	no	—
56	Dic₁₅₈	—	4	1	no	—
57	Dic₁₅₈	—	4	1	no	—
58	C₈×C₇₉	—	4	1	no	—
59	C₈×C₇₉	—	4	1	no	—
60	C₇₉⋊C₈	—	2	1	no	—
61	C₇₉⋊C₈	—	4	1	no	—
62	C₇₉⋊C₈	SD₁₆	1	2	yes	complemented
63	C₂²×C₇₉	—	8	1	no	—
64	C₂²×C₇₉	—	8	1	no	—
65	C₂²×C₇₉	—	8	1	no	—
66	C₂²×C₇₉	#121	1	1	yes	characteristic
67	C₄×C₇₉	—	2	1	no	—
68	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
69	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
71	C₄×C₇₉	#137	1	1	yes	characteristic
72	Dic₇₉	—	4	1	no	—
73	Dic₇₉	—	4	1	no	—
74	Dic₇₉	—	8	1	no	—
75	C₂×C₇₉	—	16	1	no	—
76	C₂×C₇₉	#460	1	1	yes	characteristic
77	C₂×C₇₉	#468	1	1	yes	characteristic
78	C₂×C₇₉	#471	1	1	yes	characteristic
79	#1686	—	79	1	no	maximal, Sylow
80	C₇₉	#1686	1	1	yes	characteristic, complemented, Sylow
81	#492	—	79	1	no	—
82	#475	—	79	1	no	—
83	#460	—	79	1	no	—
84	#446	—	79	1	no	—
85	#335	—	79	1	no	—
86	#332	—	79	1	no	—
87	#331	D₇₉	1	1	yes	characteristic
88	C₂×SD₁₆	—	158	1	no	—
89	C₂×SD₁₆	—	158	1	no	—
90	C₂×SD₁₆	—	158	1	no	—
91	C₄⋊Q₈	—	79	1	no	—
92	#127	C₂×D₇₉	1	1	yes	characteristic
93	C₄×Q₈	—	79	1	no	—
94	#106	—	158	1	no	—
95	C₄⋊C₈	—	79	1	no	—
96	C₄⋊C₈	—	158	1	no	—
97	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
98	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
99	#103	—	158	1	no	—
100	#102	—	158	1	no	—
101	#97	—	158	1	no	—
102	C₄×C₈	—	79	1	no	—
103	C₂×Q₈	—	79	1	no	—
104	C₂×Q₈	—	158	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	C₂×D₄	—	2	1	no	—
108	SD₁₆	—	316	2	no	—
109	SD₁₆	—	316	2	no	—
110	SD₁₆	—	316	2	no	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	79	1	no	—
114	C₂×C₈	—	79	1	no	—
115	C₂×C₈	—	158	1	no	—
116	C₄⋊C₄	—	79	1	no	—
117	C₄⋊C₄	—	158	1	no	—
118	C₄⋊C₄	—	158	1	no	—
119	C₄⋊C₄	—	158	1	no	—
120	C₄²	—	158	1	no	—
121	C₄²	C₂²×D₇₉	1	1	yes	characteristic
122	C₂³	—	4	1	no	—
123	Q₈	—	316	1	no	—
124	Q₈	—	316	1	no	—
125	Q₈	—	158	1	no	—
126	Q₈	—	158	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	4	1	no	—
129	D₄	—	4	1	no	—
130	D₄	—	4	1	no	—
131	D₄	—	8	1	no	—
132	C₂×C₄	—	316	1	no	—
133	C₂×C₄	—	158	1	no	—
134	C₂×C₄	—	158	1	no	—
135	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
136	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
137	C₂×C₄	#11929624	1	1	yes	characteristic
138	C₈	—	4	1	no	—
139	C₈	—	4	1	no	—
140	C₈	—	316	1	no	—
141	C₈	—	79	2	no	—
142	C₈	—	158	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	—	8	1	no	—
145	C₂²	—	8	1	no	—
146	C₂²	#14579134	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	316	1	no	—
149	C₄	—	316	1	no	—
150	C₄	—	632	1	no	—
151	C₄	SD₁₆×D₇₉	1	1	yes	characteristic
152	C₄	#14579185	1	1	yes	characteristic
153	C₄	#14579185	1	1	yes	characteristic
154	C₄	#14579190	1	1	yes	characteristic
155	C₂	—	16	1	no	—
156	C₂	#19098762	1	1	yes	characteristic
157	C₂	#19098808	1	1	yes	characteristic
158	C₂	#19098825	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098935

C₂

yes

maximal, characteristic

#19098849

C₂

yes

maximal, characteristic, complemented

#19098760

C₂

yes

maximal, characteristic

#19098690

C₂

yes

maximal, characteristic, complemented

#19098315

C₂

yes

maximal, characteristic, complemented

#19098310

C₂

yes

maximal, characteristic, complemented

#331×C₇₉

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

characteristic

#14579093

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

#14579086

—

#14579082

—

#14579071

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

#127×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

—

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

characteristic

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

SD₁₆

yes

complemented

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

D₇₉

yes

characteristic

C₂×SD₁₆

—

158

—

C₂×SD₁₆

—

158

—

C₂×SD₁₆

—

158

—

C₄⋊Q₈

—

#127

C₂×D₇₉

yes

characteristic

C₄×Q₈

—

#106

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#103

—

158

—

100

#102

—

158

—

101

#97

—

158

—

102

C₄×C₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

158

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

SD₁₆

—

316

—

109

SD₁₆

—

316

—

110

SD₁₆

—

316

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

158

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

158

—

118

C₄⋊C₄

—

158

—

119

C₄⋊C₄

—

158

—

120

C₄²

—

158

—

121

C₄²

C₂²×D₇₉

yes

characteristic

122

C₂³

—

123

Q₈

—

316

—

124

Q₈

—

316

—

125

Q₈

—

158

—

126

Q₈

—

158

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

316

—

133

C₂×C₄

—

158

—

134

C₂×C₄

—

158

—

135

C₂×C₄

D₄×D₇₉

yes

characteristic

136

C₂×C₄

D₄×D₇₉

yes

characteristic

137

C₂×C₄

#11929624

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

316

—

141

C₈

—

142

C₈

—

158

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

#14579134

yes

characteristic

147

C₄

—

148

C₄

—

316

—

149

C₄

—

316

—

150

C₄

—

632

—

151

C₄

SD₁₆×D₇₉

yes

characteristic

152

C₄

#14579185

yes

characteristic

153

C₄

#14579185

yes

characteristic

154

C₄

#14579190

yes

characteristic

155

C₂

—

156

C₂

#19098762

yes

characteristic

157

C₂

#19098808

yes

characteristic

158

C₂

#19098825

yes

characteristic

	subgroup	G/H
center	C₂²	#14579134
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#331×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	#127×C₇₉	C₂²
hypercenter	#331	D₇₉
hypocenter	C₇₉	#1686
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#14579134

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#331×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

#127×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
2. #19098849	C₂	semidirect
4. #19098690	C₂	semidirect
5. #19098315	C₂	semidirect
6. #19098310	C₂	semidirect
62. C₇₉⋊C₈	SD₁₆	semidirect
80. C₇₉	#1686	semidirect

H ≅ G/N

type

2. #19098849

C₂

semidirect

4. #19098690

C₂

semidirect

5. #19098315

C₂

semidirect

6. #19098310

C₂

semidirect

62. C₇₉⋊C₈

SD₁₆

semidirect

80. C₇₉

#1686

semidirect

Subgroups — #23762871

Conjugacy classes of subgroups

Complements