Group #23765495 — subgroups

Subgroups — #23765495

Order 10112.

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

normal subgroups only

This group has 164 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×#14579105	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098805	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098796	C₂	1	1	yes	maximal, characteristic
5	#19098390	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098368	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×C₈×D₇₉	C₂²	1	1	yes	characteristic
10	#14579141	—	2	1	no	—
11	#14579132	—	2	1	no	—
12	#14579105	—	2	2	no	—
13	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₁₆×D₇₉	—	2	2	no	—
15	#14579095	C₂²	1	1	yes	characteristic
16	#14579084	—	2	1	no	—
17	#14579082	—	2	1	no	—
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×C₂²⋊D₇₉	—	4	1	no	—
23	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
24	Dic₃₁₆	—	2	1	no	—
25	Dic₃₁₆	—	2	1	no	—
26	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
27	C₈×D₇₉	—	2	1	no	—
28	C₈×D₇₉	—	2	1	no	—
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	4	1	no	—
31	C₂²⋊Dic₇₉	—	4	1	no	—
32	(C₂×D₇₉)⋊C₄	—	4	1	no	—
33	C₇₉⋊C₁₆	D₄	1	2	yes	complemented
34	C₂×D₄×C₇₉	—	2	1	no	—
35	D₈×C₇₉	—	2	1	no	—
36	D₈×C₇₉	—	2	1	no	—
37	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₇₉	—	2	1	no	—
39	C₁₆×C₇₉	—	2	1	no	—
40	C₂³×C₇₉	—	4	1	no	—
41	C₂²×D₇₉	D₈	1	1	yes	characteristic
42	D₄×C₇₉	—	4	1	no	—
43	D₄×C₇₉	—	4	1	no	—
44	C₂×C₄×C₇₉	—	4	1	no	—
45	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
46	C₂²⋊D₇₉	—	8	2	no	—
47	C₂×Dic₇₉	—	4	1	no	—
48	C₂×Dic₇₉	—	4	1	no	—
49	C₂×Dic₇₉	D₈	1	1	yes	characteristic
50	C₄×D₇₉	—	2	1	no	—
51	C₄×D₇₉	—	2	1	no	—
52	Dic₁₅₈	—	4	1	no	—
53	Dic₁₅₈	—	4	1	no	—
54	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₇₉	#41	1	1	yes	characteristic
56	C₇₉⋊C₈	—	2	1	no	—
57	C₂²×C₇₉	—	8	1	no	—
58	C₂²×C₇₉	—	8	1	no	—
59	C₂²×C₇₉	—	8	1	no	—
60	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
61	C₂×D₇₉	—	2	1	no	—
62	C₂×D₇₉	—	2	1	no	—
63	C₂×D₇₉	SD₃₂	1	2	yes	complemented
64	C₄×C₇₉	—	8	1	no	—
65	C₄×C₇₉	#121	1	1	yes	characteristic
66	C₄×C₇₉	#135	1	1	yes	characteristic
67	Dic₇₉	—	2	1	no	—
68	Dic₇₉	—	8	1	no	—
69	Dic₇₉	—	8	1	no	—
70	C₂×C₇₉	—	16	1	no	—
71	C₂×C₇₉	#466	1	1	yes	characteristic
72	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
73	C₂×C₇₉	#508	1	1	yes	characteristic
74	D₇₉	—	2	2	no	—
75	#2217	—	79	1	no	maximal, Sylow
76	C₇₉	#2217	1	1	yes	characteristic, complemented, Sylow
77	C₂×SD₃₂	—	79	1	no	—
78	C₂²×C₁₆	—	79	1	no	—
79	#467	—	79	1	no	—
80	#466	—	79	1	no	—
81	#367	—	79	1	no	—
82	#358	—	79	1	no	—
83	#357	D₇₉	1	1	yes	characteristic, complemented
84	C₂×Q₁₆	—	79	1	no	—
85	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
86	C₂²×C₈	—	79	1	no	—
87	C₂²⋊Q₈	—	158	1	no	—
88	#121	—	158	1	no	—
89	SD₃₂	—	158	2	no	—
90	C₂×C₁₆	—	79	1	no	—
91	C₂×C₁₆	—	158	2	no	—
92	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
93	#107	—	79	1	no	—
94	#107	C₂×D₇₉	1	1	yes	characteristic
95	#103	—	158	1	no	—
96	#102	—	158	1	no	—
97	C₂×Q₈	—	158	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	316	1	no	—
100	C₂²×C₄	—	79	1	no	—
101	Q₁₆	—	158	1	no	—
102	Q₁₆	—	158	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	C₂×C₈	—	79	1	no	—
106	C₂×C₈	—	158	1	no	—
107	C₂×C₈	—	158	1	no	—
108	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	316	1	no	—
111	C₄⋊C₄	—	158	1	no	—
112	C₂²⋊C₄	—	316	1	no	—
113	C₂²⋊C₄	—	316	1	no	—
114	C₁₆	—	2	1	no	—
115	C₁₆	—	79	2	no	—
116	C₂³	—	4	1	no	—
117	C₂³	—	79	1	no	—
118	Q₈	—	316	1	no	—
119	Q₈	—	316	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	632	2	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	316	1	no	—
125	C₂×C₄	—	316	1	no	—
126	C₂×C₄	—	79	1	no	—
127	C₂×C₄	—	158	1	no	—
128	C₂×C₄	—	158	1	no	—
129	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
130	C₈	—	158	1	no	—
131	C₈	D₄×D₇₉	1	1	yes	characteristic
132	C₈	#11929624	1	1	yes	characteristic
133	C₂²	—	8	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	8	1	no	—
136	C₂²	—	79	2	no	—
137	C₂²	—	158	1	no	—
138	C₂²	—	158	1	no	—
139	C₂²	D₈×D₇₉	1	1	yes	characteristic
140	C₄	—	8	1	no	—
141	C₄	—	632	1	no	—
142	C₄	—	632	1	no	—
143	C₄	—	158	1	no	—
144	C₄	#14579134	1	1	yes	characteristic
145	C₄	#14579182	1	1	yes	characteristic
146	C₂	—	16	1	no	—
147	C₂	—	158	2	no	—
148	C₂	#19098798	1	1	yes	characteristic
149	C₂	SD₃₂×D₇₉	1	1	yes	characteristic
150	C₂	#19098992	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579105

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₇₉

C₂

yes

maximal, characteristic, complemented

#19098805

C₂

yes

maximal, characteristic, complemented

#19098796

C₂

yes

maximal, characteristic

#19098390

C₂

yes

maximal, characteristic, complemented

#19098368

C₂

yes

maximal, characteristic, complemented

#357×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₂×C₈×D₇₉

C₂²

yes

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₇₉

—

#14579095

C₂²

yes

characteristic

#14579084

—

#14579082

—

C₂×D₈×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

D₄

yes

characteristic

Dic₃₁₆

—

Dic₃₁₆

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₈×D₇₉

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₇₉⋊C₁₆

D₄

yes

complemented

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

—

C₂²×D₇₉

D₈

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₄×D₇₉

—

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

SD₃₂

yes

complemented

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#466

yes

characteristic

C₂×C₇₉

C₂×SD₃₂

yes

characteristic

C₂×C₇₉

#508

yes

characteristic

D₇₉

—

#2217

—

maximal, Sylow

C₇₉

#2217

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₂²×C₁₆

—

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×D₈

C₂×D₇₉

yes

characteristic

C₂²×C₈

—

C₂²⋊Q₈

—

158

—

#121

—

158

—

SD₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

—

158

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#107

C₂×D₇₉

yes

characteristic

#103

—

158

—

#102

—

158

—

C₂×Q₈

—

158

—

C₂×D₄

—

C₂×D₄

—

316

—

100

C₂²×C₄

—

101

Q₁₆

—

158

—

102

Q₁₆

—

158

—

103

D₈

—

104

D₈

—

105

C₂×C₈

—

106

C₂×C₈

—

158

—

107

C₂×C₈

—

158

—

108

C₂×C₈

C₂²×D₇₉

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

316

—

111

C₄⋊C₄

—

158

—

112

C₂²⋊C₄

—

316

—

113

C₂²⋊C₄

—

316

—

114

C₁₆

—

115

C₁₆

—

116

C₂³

—

117

C₂³

—

118

Q₈

—

316

—

119

Q₈

—

316

—

120

D₄

—

121

D₄

—

122

D₄

—

632

—

123

C₂×C₄

—

124

C₂×C₄

—

316

—

125

C₂×C₄

—

316

—

126

C₂×C₄

—

127

C₂×C₄

—

158

—

128

C₂×C₄

—

158

—

129

C₂×C₄

D₄×D₇₉

yes

characteristic

130

C₈

—

158

—

131

C₈

D₄×D₇₉

yes

characteristic

132

C₈

#11929624

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

158

—

138

C₂²

—

158

—

139

C₂²

D₈×D₇₉

yes

characteristic

140

C₄

—

141

C₄

—

632

—

142

C₄

—

632

—

143

C₄

—

158

—

144

C₄

#14579134

yes

characteristic

145

C₄

#14579182

yes

characteristic

146

C₂

—

147

C₂

—

158

—

148

C₂

#19098798

yes

characteristic

149

C₂

SD₃₂×D₇₉

yes

characteristic

150

C₂

#19098992

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	#19098796	C₂
hypercenter	#357	D₇₉
hypocenter	C₇₉	#2217
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×#14579105	C₂	semidirect
2. C₂×C₁₆×D₇₉	C₂	semidirect
3. #19098805	C₂	semidirect
5. #19098390	C₂	semidirect
6. #19098368	C₂	semidirect
7. #357×C₇₉	C₂	semidirect
33. C₇₉⋊C₁₆	D₄	semidirect
63. C₂×D₇₉	SD₃₂	semidirect
76. C₇₉	#2217	semidirect
83. #357	D₇₉	semidirect

H ≅ G/N

type

1. C₂×#14579105

C₂

semidirect

2. C₂×C₁₆×D₇₉

C₂

semidirect

3. #19098805

C₂

semidirect

5. #19098390

C₂

semidirect

6. #19098368

C₂

semidirect

7. #357×C₇₉

C₂

semidirect

33. C₇₉⋊C₁₆

D₄

semidirect

63. C₂×D₇₉

SD₃₂

semidirect

76. C₇₉

#2217

semidirect

83. #357

D₇₉

semidirect

Subgroups — #23765495

Conjugacy classes of subgroups

Complements