Group #23765439 — subgroups

Subgroups — #23765439

Order 10112.

174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14579105	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098938	C₂	1	1	yes	maximal, characteristic
4	#19098657	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098363	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×D₆₃₂	C₂²	1	1	yes	characteristic
10	C₂×#11929609	—	2	1	no	—
11	#14579157	—	2	1	no	—
12	#14579126	—	2	1	no	—
13	#14579106	—	2	2	no	—
14	#14579105	—	2	2	no	—
15	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	#14579084	—	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×C₂²⋊D₇₉	—	4	1	no	—
24	C₂×C₂²⋊D₇₉	—	4	1	no	—
25	Dic₃₁₆	—	2	1	no	—
26	Dic₃₁₆	D₄	1	2	yes	complemented
27	D₆₃₂	—	2	1	no	—
28	D₆₃₂	—	2	1	no	—
29	#11929609	—	4	2	no	—
30	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
31	Dic₇₉⋊C₄	—	4	1	no	—
32	C₄×Dic₇₉	—	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	C₂²⋊D₇₉	—	8	2	no	—
48	C₂²⋊D₇₉	—	8	2	no	—
49	C₂×Dic₇₉	—	4	1	no	—
50	C₂×Dic₇₉	D₈	1	1	yes	characteristic
51	C₂×Dic₇₉	D₈	1	1	yes	characteristic
52	D₃₁₆	—	4	1	no	—
53	D₃₁₆	—	4	1	no	—
54	Dic₁₅₈	—	2	2	no	—
55	Dic₁₅₈	—	4	1	no	—
56	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
57	C₈×C₇₉	#41	1	1	yes	characteristic
58	C₇₉⋊C₈	—	2	1	no	—
59	C₂²×C₇₉	—	8	1	no	—
60	C₂²×C₇₉	—	8	1	no	—
61	C₂²×C₇₉	—	8	1	no	—
62	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
63	C₂×D₇₉	—	8	1	no	—
64	C₂×D₇₉	—	8	1	no	—
65	C₂×D₇₉	—	8	1	no	—
66	C₄×C₇₉	—	8	1	no	—
67	C₄×C₇₉	#121	1	1	yes	characteristic
68	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	Dic₇₉	—	2	1	no	—
70	Dic₇₉	—	4	2	no	—
71	Dic₇₉	SD₃₂	1	2	yes	complemented
72	C₂×C₇₉	—	16	1	no	—
73	C₂×C₇₉	#459	1	1	yes	characteristic
74	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
75	C₂×C₇₉	#509	1	1	yes	characteristic
76	D₇₉	—	16	1	no	—
77	#2207	—	79	1	no	maximal, Sylow
78	C₇₉	#2207	1	1	yes	characteristic, complemented, Sylow
79	C₂×SD₃₂	—	79	1	no	—
80	C₂×SD₃₂	—	79	1	no	—
81	#493	—	79	1	no	—
82	C₄×Q₁₆	—	79	1	no	—
83	C₄⋊C₁₆	—	79	1	no	—
84	#357	—	79	1	no	—
85	#357	D₇₉	1	1	yes	characteristic, complemented
86	C₂×Q₁₆	—	79	1	no	—
87	C₂×D₈	—	79	1	no	—
88	C₂×D₈	—	158	1	no	—
89	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
90	#127	—	158	1	no	—
91	C₄×Q₈	—	158	1	no	—
92	SD₃₂	—	158	2	no	—
93	SD₃₂	—	158	2	no	—
94	C₂×C₁₆	—	79	1	no	—
95	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
96	#107	C₂×D₇₉	1	1	yes	characteristic
97	#103	—	158	1	no	—
98	C₄×C₈	—	79	1	no	—
99	C₂×Q₈	—	158	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	316	1	no	—
102	C₂×D₄	—	316	1	no	—
103	C₂×D₄	—	158	1	no	—
104	Q₁₆	—	79	2	no	—
105	Q₁₆	—	158	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	316	2	no	—
109	D₈	—	158	1	no	—
110	D₈	—	158	1	no	—
111	C₂×C₈	—	79	1	no	—
112	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	—	316	1	no	—
115	C₄²	—	316	1	no	—
116	C₄²	—	79	1	no	—
117	C₁₆	—	2	1	no	—
118	C₁₆	—	158	1	no	—
119	C₂³	—	4	1	no	—
120	C₂³	—	316	1	no	—
121	Q₈	—	316	1	no	—
122	Q₈	—	158	2	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	316	1	no	—
126	D₄	—	316	1	no	—
127	D₄	—	632	2	no	—
128	D₄	—	632	2	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	316	1	no	—
131	C₂×C₄	—	79	1	no	—
132	C₂×C₄	—	79	1	no	—
133	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
134	C₈	—	158	1	no	—
135	C₈	D₄×D₇₉	1	1	yes	characteristic
136	C₈	#11929624	1	1	yes	characteristic
137	C₂²	—	8	1	no	—
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	—	632	1	no	—
141	C₂²	—	632	1	no	—
142	C₂²	—	632	1	no	—
143	C₂²	D₈×D₇₉	1	1	yes	characteristic
144	C₄	—	8	1	no	—
145	C₄	—	316	2	no	—
146	C₄	—	79	2	no	—
147	C₄	—	158	1	no	—
148	C₄	#14579134	1	1	yes	characteristic
149	C₄	#14579188	1	1	yes	characteristic
150	C₂	—	16	1	no	—
151	C₂	—	1264	1	no	—
152	C₂	#19098757	1	1	yes	characteristic
153	C₂	SD₃₂×D₇₉	1	1	yes	characteristic
154	C₂	#19098997	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579106

C₂

yes

maximal, characteristic, complemented

C₂×#14579105

C₂

yes

maximal, characteristic, complemented

#19098938

C₂

yes

maximal, characteristic

#19098657

C₂

yes

maximal, characteristic, complemented

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#19098363

C₂

yes

maximal, characteristic, complemented

#357×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₂×D₆₃₂

C₂²

yes

—

—

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579084

—

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×C₂²⋊D₇₉

—

C₂×C₂²⋊D₇₉

—

Dic₃₁₆

—

Dic₃₁₆

D₄

yes

complemented

D₆₃₂

—

D₆₃₂

—

#11929609

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

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

C₂²⋊D₇₉

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

D₃₁₆

—

D₃₁₆

—

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

SD₃₂

yes

complemented

C₂×C₇₉

—

C₂×C₇₉

#459

yes

characteristic

C₂×C₇₉

C₂×SD₃₂

yes

characteristic

C₂×C₇₉

#509

yes

characteristic

D₇₉

—

#2207

—

maximal, Sylow

C₇₉

#2207

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₂×SD₃₂

—

#493

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#357

—

#357

D₇₉

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

—

158

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#127

—

158

—

C₄×Q₈

—

158

—

SD₃₂

—

158

—

SD₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

C₂×D₇₉

yes

characteristic

#103

—

158

—

C₄×C₈

—

C₂×Q₈

—

158

—

100

C₂×D₄

—

101

C₂×D₄

—

316

—

102

C₂×D₄

—

316

—

103

C₂×D₄

—

158

—

104

Q₁₆

—

105

Q₁₆

—

158

—

106

D₈

—

107

D₈

—

108

D₈

—

316

—

109

D₈

—

158

—

110

D₈

—

158

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₇₉

yes

characteristic

113

C₄⋊C₄

—

114

C₄⋊C₄

—

316

—

115

C₄²

—

316

—

116

C₄²

—

117

C₁₆

—

118

C₁₆

—

158

—

119

C₂³

—

120

C₂³

—

316

—

121

Q₈

—

316

—

122

Q₈

—

158

—

123

D₄

—

124

D₄

—

125

D₄

—

316

—

126

D₄

—

316

—

127

D₄

—

632

—

128

D₄

—

632

—

129

C₂×C₄

—

130

C₂×C₄

—

316

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

D₄×D₇₉

yes

characteristic

134

C₈

—

158

—

135

C₈

D₄×D₇₉

yes

characteristic

136

C₈

#11929624

yes

characteristic

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

632

—

141

C₂²

—

632

—

142

C₂²

—

632

—

143

C₂²

D₈×D₇₉

yes

characteristic

144

C₄

—

145

C₄

—

316

—

146

C₄

—

147

C₄

—

158

—

148

C₄

#14579134

yes

characteristic

149

C₄

#14579188

yes

characteristic

150

C₂

—

151

C₂

—

1264

—

152

C₂

#19098757

yes

characteristic

153

C₂

SD₃₂×D₇₉

yes

characteristic

154

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	#19098938	C₂
hypercenter	#357	D₇₉
hypocenter	C₇₉	#2207
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
2. C₂×#14579105	C₂	semidirect
4. #19098657	C₂	semidirect
5. Dic₇₉⋊C₁₆	C₂	semidirect
6. #19098363	C₂	semidirect
7. #357×C₇₉	C₂	semidirect
26. Dic₃₁₆	D₄	semidirect
71. Dic₇₉	SD₃₂	semidirect
78. C₇₉	#2207	semidirect
85. #357	D₇₉	semidirect

H ≅ G/N

type

1. C₂×#14579106

C₂

semidirect

2. C₂×#14579105

C₂

semidirect

4. #19098657

C₂

semidirect

5. Dic₇₉⋊C₁₆

C₂

semidirect

6. #19098363

C₂

semidirect

7. #357×C₇₉

C₂

semidirect

26. Dic₃₁₆

D₄

semidirect

71. Dic₇₉

SD₃₂

semidirect

78. C₇₉

#2207

semidirect

85. #357

D₇₉

semidirect

Subgroups — #23765439

Conjugacy classes of subgroups

Complements