Group #23765454 — subgroups

Subgroups — #23765454

Order 10112.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14579106	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14579102	C₂	1	1	yes	maximal, characteristic
3	#19098946	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098645	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098366	C₂	1	1	yes	maximal, characteristic, complemented
7	#357×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#11929612	—	2	1	no	—
10	C₂×D₆₃₂	C₂²	1	1	yes	characteristic
11	#14579148	—	2	1	no	—
12	#14579123	—	2	1	no	—
13	#14579106	—	2	2	no	—
14	#14579102	—	2	2	no	—
15	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	#14579081	—	2	1	no	—
17	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	#107×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	2	1	no	—
22	C₂×D₃₁₆	—	2	1	no	—
23	C₂×C₄×D₇₉	—	4	1	no	—
24	Dic₃₁₆	—	2	1	no	—
25	Dic₃₁₆	—	2	1	no	—
26	#11929612	—	4	2	no	—
27	D₆₃₂	—	2	1	no	—
28	D₆₃₂	D₄	1	2	yes	—
29	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
30	C₂²⋊Dic₇₉	—	4	1	no	—
31	C₂²⋊Dic₇₉	—	4	1	no	—
32	(C₂×D₇₉)⋊C₄	—	4	1	no	—
33	C₄×Dic₇₉	D₄	1	1	yes	characteristic
34	C₇₉⋊C₁₆	—	2	1	no	—
35	C₂×D₄×C₇₉	—	2	1	no	—
36	D₈×C₇₉	—	2	1	no	—
37	D₈×C₇₉	—	2	1	no	—
38	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
39	C₄⋊C₄×C₇₉	—	2	1	no	—
40	C₁₆×C₇₉	—	2	1	no	—
41	C₂³×C₇₉	—	4	1	no	—
42	C₂²×D₇₉	—	4	1	no	—
43	D₄×C₇₉	—	4	1	no	—
44	D₄×C₇₉	—	4	1	no	—
45	C₂×C₄×C₇₉	—	4	1	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₇₉	—	4	1	no	—
48	C₂×Dic₇₉	D₈	1	1	yes	characteristic
49	C₂×Dic₇₉	D₈	1	1	yes	characteristic
50	D₃₁₆	—	2	2	no	—
51	D₃₁₆	—	4	1	no	—
52	C₄×D₇₉	—	8	2	no	—
53	Dic₁₅₈	—	4	1	no	—
54	Dic₁₅₈	—	4	1	no	—
55	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₇₉	#41	1	1	yes	characteristic
57	C₇₉⋊C₈	—	2	1	no	—
58	C₂²×C₇₉	—	8	1	no	—
59	C₂²×C₇₉	—	8	1	no	—
60	C₂²×C₇₉	—	8	1	no	—
61	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
62	C₂×D₇₉	—	4	2	no	—
63	C₂×D₇₉	—	8	1	no	—
64	C₂×D₇₉	—	8	1	no	—
65	C₄×C₇₉	—	8	1	no	—
66	C₄×C₇₉	#121	1	1	yes	characteristic
67	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
68	Dic₇₉	—	2	1	no	—
69	Dic₇₉	—	2	1	no	—
70	Dic₇₉	—	8	1	no	—
71	C₂×C₇₉	—	16	1	no	—
72	C₂×C₇₉	#459	1	1	yes	characteristic
73	C₂×C₇₉	#508	1	1	yes	characteristic
74	C₂×C₇₉	#509	1	1	yes	characteristic
75	D₇₉	—	8	2	no	—
76	#2210	—	79	1	no	maximal, Sylow
77	C₇₉	#2210	1	1	yes	characteristic, complemented, Sylow
78	C₂×SD₃₂	—	79	1	no	—
79	C₂×D₁₆	—	79	1	no	—
80	#495	—	79	1	no	—
81	C₄×D₈	—	79	1	no	—
82	C₄⋊C₁₆	—	79	1	no	—
83	#358	—	79	1	no	—
84	#357	D₇₉	1	1	yes	characteristic, complemented
85	C₂×Q₁₆	—	79	1	no	—
86	C₂×SD₁₆	—	158	1	no	—
87	C₂×D₈	—	79	1	no	—
88	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
89	#124	—	158	1	no	—
90	C₄×D₄	—	158	1	no	—
91	SD₃₂	—	158	2	no	—
92	D₁₆	—	158	2	no	—
93	C₂×C₁₆	—	79	1	no	—
94	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
95	#107	C₂×D₇₉	1	1	yes	characteristic
96	#102	—	158	1	no	—
97	C₄×C₈	—	79	1	no	—
98	C₂×Q₈	—	158	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	158	1	no	—
101	C₂²×C₄	—	316	1	no	—
102	Q₁₆	—	158	1	no	—
103	Q₁₆	—	158	1	no	—
104	SD₁₆	—	316	2	no	—
105	D₈	—	2	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	79	2	no	—
108	D₈	—	158	1	no	—
109	C₂×C₈	—	79	1	no	—
110	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
111	C₄⋊C₄	—	2	1	no	—
112	C₂²⋊C₄	—	316	1	no	—
113	C₂²⋊C₄	—	316	1	no	—
114	C₂²⋊C₄	—	316	1	no	—
115	C₄²	—	79	1	no	—
116	C₁₆	—	2	1	no	—
117	C₁₆	—	158	1	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	316	1	no	—
120	Q₈	—	316	1	no	—
121	Q₈	—	316	1	no	—
122	D₄	—	4	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	316	1	no	—
125	D₄	—	158	2	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	316	1	no	—
128	C₂×C₄	—	79	1	no	—
129	C₂×C₄	—	79	1	no	—
130	C₂×C₄	—	632	2	no	—
131	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
132	C₈	—	158	1	no	—
133	C₈	D₄×D₇₉	1	1	yes	characteristic
134	C₈	#11929624	1	1	yes	characteristic
135	C₂²	—	8	1	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	316	2	no	—
139	C₂²	—	632	1	no	—
140	C₂²	—	632	1	no	—
141	C₂²	D₈×D₇₉	1	1	yes	characteristic
142	C₄	—	8	1	no	—
143	C₄	—	632	1	no	—
144	C₄	—	158	1	no	—
145	C₄	—	158	1	no	—
146	C₄	#14579134	1	1	yes	characteristic
147	C₄	#14579188	1	1	yes	characteristic
148	C₂	—	16	1	no	—
149	C₂	—	632	2	no	—
150	C₂	#19098757	1	1	yes	characteristic
151	C₂	#19098994	1	1	yes	characteristic
152	C₂	#19098997	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579106

C₂

yes

maximal, characteristic, complemented

C₂×#14579102

C₂

yes

maximal, characteristic

#19098946

C₂

yes

maximal, characteristic, complemented

#19098645

C₂

yes

maximal, characteristic, complemented

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#19098366

C₂

yes

maximal, characteristic, complemented

#357×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₂×#11929612

—

C₂×D₆₃₂

C₂²

yes

—

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579081

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×D₈×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929612

—

D₆₃₂

—

D₆₃₂

D₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

—

C₂²×D₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#2210

—

maximal, Sylow

C₇₉

#2210

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×D₈

—

C₄⋊C₁₆

—

#358

—

#357

D₇₉

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×SD₁₆

—

158

—

C₂×D₈

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#124

—

158

—

C₄×D₄

—

158

—

SD₃₂

—

158

—

D₁₆

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

C₂×D₇₉

yes

characteristic

#102

—

158

—

C₄×C₈

—

C₂×Q₈

—

158

—

C₂×D₄

—

100

C₂×D₄

—

158

—

101

C₂²×C₄

—

316

—

102

Q₁₆

—

158

—

103

Q₁₆

—

158

—

104

SD₁₆

—

316

—

105

D₈

—

106

D₈

—

107

D₈

—

108

D₈

—

158

—

109

C₂×C₈

—

110

C₂×C₈

C₂²×D₇₉

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

316

—

113

C₂²⋊C₄

—

316

—

114

C₂²⋊C₄

—

316

—

115

C₄²

—

116

C₁₆

—

117

C₁₆

—

158

—

118

C₂³

—

119

C₂³

—

316

—

120

Q₈

—

316

—

121

Q₈

—

316

—

122

D₄

—

123

D₄

—

124

D₄

—

316

—

125

D₄

—

158

—

126

C₂×C₄

—

127

C₂×C₄

—

316

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

632

—

131

C₂×C₄

D₄×D₇₉

yes

characteristic

132

C₈

—

158

—

133

C₈

D₄×D₇₉

yes

characteristic

134

C₈

#11929624

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

316

—

139

C₂²

—

632

—

140

C₂²

—

632

—

141

C₂²

D₈×D₇₉

yes

characteristic

142

C₄

—

143

C₄

—

632

—

144

C₄

—

158

—

145

C₄

—

158

—

146

C₄

#14579134

yes

characteristic

147

C₄

#14579188

yes

characteristic

148

C₂

—

149

C₂

—

632

—

150

C₂

#19098757

yes

characteristic

151

C₂

#19098994

yes

characteristic

152

C₂

#19098997

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#357×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×#14579102	C₂
hypercenter	#357	D₇₉
hypocenter	C₇₉	#2210
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#357×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

C₂

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#14579106	C₂	semidirect
3. #19098946	C₂	semidirect
4. #19098645	C₂	semidirect
5. Dic₇₉⋊C₁₆	C₂	semidirect
6. #19098366	C₂	semidirect
7. #357×C₇₉	C₂	semidirect
77. C₇₉	#2210	semidirect
84. #357	D₇₉	semidirect

H ≅ G/N

type

1. C₂×#14579106

C₂

semidirect

3. #19098946

C₂

semidirect

4. #19098645

C₂

semidirect

5. Dic₇₉⋊C₁₆

C₂

semidirect

6. #19098366

C₂

semidirect

7. #357×C₇₉

C₂

semidirect

77. C₇₉

#2210

semidirect

84. #357

D₇₉

semidirect

Subgroups — #23765454

Conjugacy classes of subgroups

Complements