Group #23762872 — subgroups

Subgroups — #23762872

Order 10112.

168 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19098936	C₂	1	1	yes	maximal, characteristic
2	#19098848	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098763	C₂	1	1	yes	maximal, characteristic
4	#19098316	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098310	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098306	C₂	1	1	yes	maximal, characteristic
7	#446×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11929613	—	2	1	no	—
9	C₂×#11929613	—	2	1	no	—
10	C₂×#11929611	—	2	1	no	—
11	#14579161	C₂²	1	1	yes	characteristic
12	#14579158	C₂²	1	1	yes	characteristic
13	#14579092	—	2	1	no	—
14	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	#14579085	—	2	1	no	—
17	#14579081	—	2	1	no	—
18	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₇₉	—	2	1	no	—
20	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
21	#97×C₇₉	—	2	1	no	—
22	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₅₈	—	2	1	no	—
24	C₂×D₃₁₆	—	2	1	no	—
25	C₂×D₃₁₆	—	2	1	no	—
26	C₂×D₃₁₆	—	2	1	no	—
27	#11929613	—	4	2	no	—
28	#11929613	—	4	2	no	—
29	#11929611	—	4	2	no	—
30	C₂×C₇₉⋊C₈	—	2	1	no	—
31	C₂×C₇₉⋊C₈	—	2	1	no	—
32	C₄⋊Dic₇₉	—	2	1	no	—
33	C₄⋊Dic₇₉	—	2	1	no	—
34	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
35	C₂×C₈×C₇₉	—	2	1	no	—
36	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
37	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
38	C₄⋊C₄×C₇₉	—	2	1	no	—
39	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
40	C₄²×C₇₉	—	2	1	no	—
41	C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₂²×D₇₉	—	4	1	no	—
43	Q₈×C₇₉	—	2	1	no	—
44	Q₈×C₇₉	—	2	1	no	—
45	C₂×C₄×C₇₉	—	2	1	no	—
46	C₂×C₄×C₇₉	—	2	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	D₃₁₆	—	4	1	no	—
52	D₃₁₆	—	4	1	no	—
53	D₃₁₆	—	4	1	no	—
54	D₃₁₆	—	4	1	no	—
55	D₃₁₆	—	8	1	no	—
56	Dic₁₅₈	—	4	1	no	—
57	Dic₁₅₈	—	4	1	no	—
58	C₈×C₇₉	—	2	1	no	—
59	C₈×C₇₉	—	4	1	no	—
60	C₈×C₇₉	SD₁₆	1	2	yes	complemented
61	C₇₉⋊C₈	—	4	1	no	—
62	C₇₉⋊C₈	—	4	1	no	—
63	C₂²×C₇₉	#121	1	1	yes	characteristic
64	C₂×D₇₉	—	8	1	no	—
65	C₂×D₇₉	—	8	1	no	—
66	C₂×D₇₉	—	8	1	no	—
67	C₄×C₇₉	—	2	1	no	—
68	C₄×C₇₉	—	4	1	no	—
69	C₄×C₇₉	—	4	1	no	—
70	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
71	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
72	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
73	C₄×C₇₉	#137	1	1	yes	characteristic
74	Dic₇₉	—	8	1	no	—
75	C₂×C₇₉	#460	1	1	yes	characteristic
76	C₂×C₇₉	#468	1	1	yes	characteristic
77	C₂×C₇₉	#471	1	1	yes	characteristic
78	D₇₉	—	16	1	no	—
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	D₇₉	1	1	yes	characteristic, complemented
85	#335	—	79	1	no	—
86	#332	—	79	1	no	—
87	#331	—	79	1	no	—
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	—	79	1	no	—
93	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
94	#106	—	158	1	no	—
95	C₄⋊C₈	—	2	1	no	—
96	C₄⋊C₈	—	79	1	no	—
97	C₄⋊C₈	—	79	1	no	—
98	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
99	#103	—	158	1	no	—
100	#102	—	158	1	no	—
101	#97	—	2	1	no	—
102	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
103	C₂×Q₈	—	158	1	no	—
104	C₂×Q₈	D₃₁₆	1	1	yes	characteristic
105	C₂×D₄	—	158	1	no	—
106	C₂×D₄	—	158	1	no	—
107	C₂×D₄	—	158	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	—	158	1	no	—
113	C₂×C₈	—	158	1	no	—
114	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
115	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	158	1	no	—
118	C₄⋊C₄	—	158	1	no	—
119	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
120	C₄²	—	2	1	no	—
121	C₄²	C₂²×D₇₉	1	1	yes	characteristic
122	C₂³	—	316	1	no	—
123	Q₈	—	2	1	no	—
124	Q₈	—	2	1	no	—
125	Q₈	—	316	1	no	—
126	Q₈	—	316	1	no	—
127	D₄	—	316	1	no	—
128	D₄	—	316	1	no	—
129	D₄	—	316	1	no	—
130	D₄	—	316	1	no	—
131	D₄	—	632	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	316	1	no	—
135	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
136	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
137	C₂×C₄	#11929624	1	1	yes	characteristic
138	C₈	—	2	1	no	—
139	C₈	—	4	1	no	—
140	C₈	—	316	1	no	—
141	C₈	—	316	1	no	—
142	C₈	#11929611	1	2	yes	complemented
143	C₂²	—	632	1	no	—
144	C₂²	—	632	1	no	—
145	C₂²	—	632	1	no	—
146	C₂²	#14579135	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	4	1	no	—
149	C₄	—	4	1	no	—
150	C₄	—	632	1	no	—
151	C₄	C₂×#11929611	1	1	yes	characteristic
152	C₄	#14579186	1	1	yes	characteristic
153	C₄	#14579189	1	1	yes	characteristic
154	C₄	#14579194	1	1	yes	characteristic
155	C₂	—	1264	1	no	—
156	C₂	#19098763	1	1	yes	characteristic
157	C₂	#19098809	1	1	yes	characteristic
158	C₂	#19098826	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098936

C₂

yes

maximal, characteristic

#19098848

C₂

yes

maximal, characteristic, complemented

#19098763

C₂

yes

maximal, characteristic

#19098316

C₂

yes

maximal, characteristic, complemented

#19098310

C₂

yes

maximal, characteristic, complemented

#19098306

C₂

yes

maximal, characteristic

#446×C₇₉

C₂

yes

maximal, characteristic, complemented

—

—

—

C₂²

yes

characteristic

#14579158

C₂²

yes

characteristic

#14579092

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

#14579085

—

#14579081

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#97×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

#11929613

—

#11929613

—

#11929611

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×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

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

SD₁₆

yes

complemented

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

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

D₇₉

—

#1686

—

maximal, Sylow

C₇₉

#1686

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

characteristic, complemented

#335

—

#332

—

#331

—

C₂×SD₁₆

—

158

—

C₂×SD₁₆

—

158

—

C₂×SD₁₆

—

158

—

C₄⋊Q₈

—

#127

—

C₄×Q₈

C₂×D₇₉

yes

characteristic

#106

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#103

—

158

—

100

#102

—

158

—

101

#97

—

102

C₄×C₈

C₂×D₇₉

yes

characteristic

103

C₂×Q₈

—

158

—

104

C₂×Q₈

D₃₁₆

yes

characteristic

105

C₂×D₄

—

158

—

106

C₂×D₄

—

158

—

107

C₂×D₄

—

158

—

108

SD₁₆

—

316

—

109

SD₁₆

—

316

—

110

SD₁₆

—

316

—

111

C₂×C₈

—

112

C₂×C₈

—

158

—

113

C₂×C₈

—

158

—

114

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

115

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

116

C₄⋊C₄

—

117

C₄⋊C₄

—

158

—

118

C₄⋊C₄

—

158

—

119

C₄⋊C₄

D₃₁₆

yes

characteristic

120

C₄²

—

121

C₄²

C₂²×D₇₉

yes

characteristic

122

C₂³

—

316

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

316

—

126

Q₈

—

316

—

127

D₄

—

316

—

128

D₄

—

316

—

129

D₄

—

316

—

130

D₄

—

316

—

131

D₄

—

632

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

316

—

135

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

136

C₂×C₄

C₂×D₃₁₆

yes

characteristic

137

C₂×C₄

#11929624

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

316

—

141

C₈

—

316

—

142

C₈

#11929611

yes

complemented

143

C₂²

—

632

—

144

C₂²

—

632

—

145

C₂²

—

632

—

146

C₂²

#14579135

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

632

—

151

C₄

C₂×#11929611

yes

characteristic

152

C₄

#14579186

yes

characteristic

153

C₄

#14579189

yes

characteristic

154

C₄

#14579194

yes

characteristic

155

C₂

—

1264

—

156

C₂

#19098763

yes

characteristic

157

C₂

#19098809

yes

characteristic

158

C₂

#19098826

yes

characteristic

	subgroup	G/H
center	C₂²	#14579135
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#446×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	#14579158	C₂²
hypercenter	#446	D₇₉
hypocenter	C₇₉	#1686
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#14579135

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#446×C₇₉

C₂

C₂²×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
2. #19098848	C₂	semidirect
4. #19098316	C₂	semidirect
5. #19098310	C₂	semidirect
7. #446×C₇₉	C₂	semidirect
60. C₈×C₇₉	SD₁₆	semidirect
80. C₇₉	#1686	semidirect
84. #446	D₇₉	semidirect
142. C₈	#11929611	semidirect

H ≅ G/N

type

2. #19098848

C₂

semidirect

4. #19098316

C₂

semidirect

5. #19098310

C₂

semidirect

7. #446×C₇₉

C₂

semidirect

60. C₈×C₇₉

SD₁₆

semidirect

80. C₇₉

#1686

semidirect

84. #446

D₇₉

semidirect

142. C₈

#11929611

semidirect

Subgroups — #23762872

Conjugacy classes of subgroups

Complements