Group #23762949 — subgroups

Subgroups — #23762949

Order 10112.

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

normal subgroups only

This group has 160 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	#19098915	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098843	C₂	1	1	yes	maximal, characteristic
3	#19098641	C₂	1	1	yes	maximal, characteristic
4	#19098315	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098309	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098308	C₂	1	1	yes	maximal, characteristic, complemented
7	#461×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#11929608	—	2	1	no	—
9	#14579161	C₂²	1	1	yes	characteristic
10	#14579094	—	2	1	no	—
11	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	#14579084	—	2	1	no	—
14	#14579084	—	2	1	no	—
15	#14579082	—	2	1	no	—
16	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
17	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×SD₁₆×C₇₉	—	2	1	no	—
19	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
22	#103×C₇₉	—	2	1	no	—
23	C₂×Dic₁₅₈	—	2	1	no	—
24	#11929608	—	4	2	no	—
25	C₂×C₇₉⋊C₈	—	2	1	no	—
26	C₂×C₇₉⋊C₈	—	2	1	no	—
27	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
28	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	C₂×Q₈×C₇₉	—	2	1	no	—
32	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	—	2	1	no	—
34	SD₁₆×C₇₉	—	4	2	no	—
35	C₂×C₈×C₇₉	—	2	1	no	—
36	C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₄⋊C₄×C₇₉	—	2	1	no	—
38	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
39	C₂²⋊C₄×C₇₉	—	2	1	no	—
40	C₄²×C₇₉	C₂³	1	1	yes	characteristic
41	C₂³×C₇₉	—	2	1	no	—
42	Q₈×C₇₉	—	4	1	no	—
43	Q₈×C₇₉	—	4	1	no	—
44	D₄×C₇₉	—	2	1	no	—
45	D₄×C₇₉	—	2	1	no	—
46	C₂×C₄×C₇₉	—	2	1	no	—
47	C₂×C₄×C₇₉	—	4	1	no	—
48	C₂×C₄×C₇₉	—	4	1	no	—
49	C₂×C₄×C₇₉	—	4	1	no	—
50	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
53	C₂×Dic₇₉	—	4	1	no	—
54	Dic₁₅₈	—	4	1	no	—
55	Dic₁₅₈	—	4	1	no	—
56	C₈×C₇₉	—	4	1	no	—
57	C₇₉⋊C₈	—	2	1	no	—
58	C₇₉⋊C₈	—	2	1	no	—
59	C₇₉⋊C₈	—	4	1	no	—
60	C₇₉⋊C₈	—	4	1	no	—
61	C₂²×C₇₉	—	4	1	no	—
62	C₂²×C₇₉	—	4	1	no	—
63	C₂²×C₇₉	—	4	1	no	—
64	C₂²×C₇₉	#121	1	1	yes	characteristic
65	C₄×C₇₉	—	2	1	no	—
66	C₄×C₇₉	—	4	1	no	—
67	C₄×C₇₉	—	8	1	no	—
68	C₄×C₇₉	#135	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	—	8	1	no	—
73	C₂×C₇₉	—	8	1	no	—
74	C₂×C₇₉	#463	1	1	yes	characteristic
75	C₂×C₇₉	#468	1	1	yes	characteristic
76	C₂×C₇₉	#473	1	1	yes	characteristic
77	#1699	—	79	1	no	maximal, Sylow
78	C₇₉	#1699	1	1	yes	characteristic, complemented, Sylow
79	#487	—	79	1	no	—
80	#474	—	79	1	no	—
81	#461	D₇₉	1	1	yes	characteristic
82	#436	—	79	1	no	—
83	#335	—	79	1	no	—
84	#332	—	79	1	no	—
85	#332	—	79	1	no	—
86	C₂×SD₁₆	—	2	1	no	—
87	C₂×M₁₆	—	158	1	no	—
88	C₄⋊Q₈	—	79	1	no	—
89	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
90	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
91	#107	—	158	1	no	—
92	C₄⋊C₈	—	79	1	no	—
93	C₄⋊C₈	—	79	1	no	—
94	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
95	#103	—	2	1	no	—
96	#103	—	158	1	no	—
97	#103	—	158	1	no	—
98	#102	—	158	1	no	—
99	C₂²⋊C₈	—	158	1	no	—
100	C₄×C₈	—	79	1	no	—
101	C₂×Q₈	—	2	1	no	—
102	C₂×Q₈	—	158	1	no	—
103	C₂×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
104	C₂²×C₄	—	2	1	no	—
105	SD₁₆	—	4	2	no	—
106	M₁₆	—	316	2	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	79	1	no	—
109	C₂×C₈	—	79	1	no	—
110	C₂×C₈	—	158	1	no	—
111	C₂×C₈	—	158	1	no	—
112	C₄⋊C₄	—	2	1	no	—
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	—	158	1	no	—
115	C₄⋊C₄	—	158	1	no	—
116	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
117	C₂²⋊C₄	—	2	1	no	—
118	C₄²	C₂²×D₇₉	1	1	yes	characteristic
119	C₂³	—	2	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	4	1	no	—
122	Q₈	—	316	1	no	—
123	Q₈	—	316	1	no	—
124	D₄	—	2	1	no	—
125	D₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	316	1	no	—
131	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
132	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
133	C₂×C₄	#11929623	1	1	yes	characteristic
134	C₈	—	4	1	no	—
135	C₈	—	316	1	no	—
136	C₈	—	316	1	no	—
137	C₈	—	158	1	no	—
138	C₈	—	158	1	no	—
139	C₂²	—	4	1	no	—
140	C₂²	—	4	1	no	—
141	C₂²	—	4	1	no	—
142	C₂²	#14579133	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	4	1	no	—
145	C₄	—	8	1	no	—
146	C₄	—	632	1	no	—
147	C₄	#14579182	1	1	yes	characteristic
148	C₄	#14579187	1	1	yes	characteristic
149	C₄	#14579188	1	1	yes	characteristic
150	C₄	#14579191	1	1	yes	characteristic
151	C₂	—	8	1	no	—
152	C₂	#19098780	1	1	yes	characteristic
153	C₂	#19098807	1	1	yes	characteristic
154	C₂	#19098836	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098915

C₂

yes

maximal, characteristic, complemented

#19098843

C₂

yes

maximal, characteristic

#19098641

C₂

yes

maximal, characteristic

#19098315

C₂

yes

maximal, characteristic, complemented

#19098309

C₂

yes

maximal, characteristic, complemented

#19098308

C₂

yes

maximal, characteristic, complemented

#461×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

—

#14579161

C₂²

yes

characteristic

#14579094

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

—

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×SD₁₆×C₇₉

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#103×C₇₉

—

C₂×Dic₁₅₈

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

—

SD₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×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

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#487

—

#474

—

#461

D₇₉

yes

—

—

—

—

C₂×SD₁₆

—

C₂×M₁₆

—

158

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

C₄×D₄

C₂×D₇₉

yes

characteristic

#107

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#103

—

#103

—

158

—

#103

—

158

—

#102

—

158

—

C₂²⋊C₈

—

158

—

100

C₄×C₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

158

—

103

C₂×D₄

C₂²⋊D₇₉

yes

characteristic

104

C₂²×C₄

—

105

SD₁₆

—

106

M₁₆

—

316

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

158

—

111

C₂×C₈

—

158

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

158

—

115

C₄⋊C₄

—

158

—

116

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

117

C₂²⋊C₄

—

118

C₄²

C₂²×D₇₉

yes

characteristic

119

C₂³

—

120

Q₈

—

121

Q₈

—

122

Q₈

—

316

—

123

Q₈

—

316

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

316

—

131

C₂×C₄

D₄×D₇₉

yes

characteristic

132

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

133

C₂×C₄

#11929623

yes

characteristic

134

C₈

—

135

C₈

—

316

—

136

C₈

—

316

—

137

C₈

—

158

—

138

C₈

—

158

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

#14579133

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

632

—

147

C₄

#14579182

yes

characteristic

148

C₄

#14579187

yes

characteristic

149

C₄

#14579188

yes

characteristic

150

C₄

#14579191

yes

characteristic

151

C₂

—

152

C₂

#19098780

yes

characteristic

153

C₂

#19098807

yes

characteristic

154

C₂

#19098836

yes

characteristic

	subgroup	G/H
center	C₂²	#14579133
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#461×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×D₄×C₇₉	D₄
hypercenter	#461	D₇₉
hypocenter	C₇₉	#1699
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #461

subgroup

G/H

center

C₂²

#14579133

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#461×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂×D₄×C₇₉

D₄

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #461

N	H ≅ G/N	type
1. #19098915	C₂	semidirect
4. #19098315	C₂	semidirect
5. #19098309	C₂	semidirect
6. #19098308	C₂	semidirect
78. C₇₉	#1699	semidirect

H ≅ G/N

type

1. #19098915

C₂

semidirect

4. #19098315

C₂

semidirect

5. #19098309

C₂

semidirect

6. #19098308

C₂

semidirect

78. C₇₉

#1699

semidirect

Subgroups — #23762949

Conjugacy classes of subgroups

Complements