Group #23764876 — subgroups

Subgroups — #23764876

Order 10112.

230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14579092	C₂	1	2	yes	maximal
2	#19098433	C₂	1	1	yes	maximal, characteristic
3	#19098325	C₂	1	2	yes	maximal
4	#19098318	C₂	1	1	yes	maximal, characteristic
5	#389×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₇₉	—	2	1	no	—
8	C₂×C₄⋊Dic₇₉	—	2	1	no	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
10	#14579092	—	2	4	no	—
11	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
12	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	#95×C₇₉	—	2	1	no	—
16	C₂²×Dic₇₉	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₂×C₇₉⋊C₈	—	2	2	no	—
19	C₂×C₇₉⋊C₈	Q₈	1	4	yes	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₄⋊Dic₇₉	—	2	2	no	—
22	C₄⋊Dic₇₉	—	4	2	no	—
23	C₄⋊Dic₇₉	—	4	2	no	—
24	C₂²×C₄×C₇₉	—	2	1	no	—
25	C₂²×C₄×C₇₉	—	2	1	no	—
26	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×C₇₉	—	2	1	no	—
30	C₄⋊C₄×C₇₉	—	2	2	no	—
31	C₄⋊C₄×C₇₉	—	4	2	no	—
32	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
33	C₄²×C₇₉	—	2	2	no	—
34	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₉	—	2	1	no	—
36	C₂×C₄×C₇₉	—	2	1	no	—
37	C₂×C₄×C₇₉	—	2	1	no	—
38	C₂×C₄×C₇₉	—	2	1	no	—
39	C₂×C₄×C₇₉	—	2	2	no	—
40	C₂×C₄×C₇₉	—	4	1	no	—
41	C₂×C₄×C₇₉	—	4	1	no	—
42	C₂×C₄×C₇₉	—	4	1	no	—
43	C₂×C₄×C₇₉	—	4	1	no	—
44	C₂×C₄×C₇₉	—	4	1	no	—
45	C₂×C₄×C₇₉	SD₁₆	1	2	yes	—
46	C₂×C₄×C₇₉	SD₁₆	1	2	yes	—
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₇₉	#41	1	2	yes	—
50	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
51	C₂×Dic₇₉	—	4	2	no	—
52	C₂×Dic₇₉	—	4	2	no	—
53	C₂×Dic₇₉	—	4	2	no	—
54	C₇₉⋊C₈	—	2	4	no	—
55	C₂²×C₇₉	#121	1	1	yes	characteristic
56	C₂²×C₇₉	#123	1	1	yes	characteristic
57	C₂²×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
58	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
59	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
60	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂²×C₇₉	#137	1	1	yes	characteristic
62	C₄×C₇₉	—	2	2	no	—
63	C₄×C₇₉	—	2	2	no	—
64	C₄×C₇₉	—	4	2	no	—
65	C₄×C₇₉	—	8	1	no	—
66	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
67	C₄×C₇₉	#125	1	2	yes	—
68	Dic₇₉	—	8	2	no	—
69	C₂×C₇₉	#398	1	1	yes	characteristic
70	C₂×C₇₉	#460	1	1	yes	characteristic
71	C₂×C₇₉	#461	1	1	yes	characteristic
72	C₂×C₇₉	#481	1	1	yes	characteristic
73	C₂×C₇₉	#483	1	1	yes	characteristic
74	C₂×C₇₉	#498	1	1	yes	characteristic
75	C₂×C₇₉	#501	1	1	yes	characteristic
76	#2084	—	79	1	no	maximal, Sylow
77	C₇₉	#2084	1	1	yes	characteristic, complemented, Sylow
78	C₂×#106	—	79	2	no	—
79	#389	D₇₉	1	1	yes	characteristic
80	#384	—	79	1	no	—
81	#340	—	79	2	no	—
82	#336	—	79	1	no	—
83	C₂²×C₈	—	79	2	no	—
84	C₂×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄⋊C₄	—	79	2	no	—
86	C₂×C₄⋊C₄	—	158	1	no	—
87	C₂×C₄⋊C₄	—	158	1	no	—
88	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
89	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
90	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
91	#106	—	158	4	no	—
92	#95	—	2	1	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	158	2	no	—
96	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
99	C₂×C₈	—	79	4	no	—
100	C₂×C₈	—	158	2	no	—
101	C₂×C₈	—	158	2	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	4	2	no	—
105	C₄⋊C₄	—	316	2	no	—
106	C₄⋊C₄	—	316	2	no	—
107	C₄⋊C₄	—	158	2	no	—
108	C₄⋊C₄	—	158	2	no	—
109	C₄⋊C₄	D₃₁₆	1	2	yes	—
110	C₄²	—	2	2	no	—
111	C₂³	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	316	2	no	—
123	C₂×C₄	—	316	2	no	—
124	C₂×C₄	—	316	2	no	—
125	C₂×C₄	#11929611	1	2	yes	—
126	C₂×C₄	#11929612	1	2	yes	—
127	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
128	C₂×C₄	Q₈×D₇₉	1	2	yes	—
129	C₂×C₄	#11929623	1	2	yes	—
130	C₂×C₄	#11929624	1	1	yes	characteristic
131	C₈	—	158	4	no	—
132	C₂²	#14579135	1	1	yes	characteristic
133	C₂²	#14579142	1	1	yes	characteristic
134	C₂²	#14579159	1	1	yes	characteristic
135	C₂²	C₂×#11929611	1	1	yes	characteristic
136	C₂²	C₂×#11929612	1	1	yes	characteristic
137	C₂²	#14579186	1	1	yes	characteristic
138	C₂²	#14579191	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	2	2	no	—
141	C₄	—	4	2	no	—
142	C₄	—	8	1	no	—
143	C₄	—	632	2	no	—
144	C₄	#14579141	1	2	yes	—
145	C₄	#14579151	1	2	yes	—
146	C₂	#19098493	1	1	yes	characteristic
147	C₂	#19098763	1	1	yes	characteristic
148	C₂	#19098768	1	1	yes	characteristic
149	C₂	#19098879	1	1	yes	characteristic
150	C₂	#19098891	1	1	yes	characteristic
151	C₂	#19098959	1	1	yes	characteristic
152	C₂	#19098973	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579092

C₂

yes

maximal

#19098433

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal

#19098318

C₂

yes

maximal, characteristic

#389×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

#14579092

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#95×C₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

Q₈

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

SD₁₆

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₄⋊Q₈

yes

characteristic

C₂²×C₇₉

C₂×SD₁₆

yes

characteristic

C₂²×C₇₉

C₂×SD₁₆

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

#125

yes

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×#106

—

#389

D₇₉

yes

—

—

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₇₉

yes

characteristic

C₂×C₄²

C₂×D₇₉

yes

characteristic

#106

—

158

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

158

—

101

C₂×C₈

—

158

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

316

—

106

C₄⋊C₄

—

316

—

107

C₄⋊C₄

—

158

—

108

C₄⋊C₄

—

158

—

109

C₄⋊C₄

D₃₁₆

yes

—

110

C₄²

—

111

C₂³

C₂×C₂²⋊D₇₉

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

316

—

123

C₂×C₄

—

316

—

124

C₂×C₄

—

316

—

125

C₂×C₄

#11929611

yes

—

126

C₂×C₄

#11929612

yes

—

127

C₂×C₄

C₂×D₃₁₆

yes

characteristic

128

C₂×C₄

Q₈×D₇₉

yes

—

129

C₂×C₄

#11929623

yes

—

130

C₂×C₄

#11929624

yes

characteristic

131

C₈

—

158

—

132

C₂²

#14579135

yes

characteristic

133

C₂²

#14579142

yes

characteristic

134

C₂²

#14579159

yes

characteristic

135

C₂²

C₂×#11929611

yes

characteristic

136

C₂²

C₂×#11929612

yes

characteristic

137

C₂²

#14579186

yes

characteristic

138

C₂²

#14579191

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

632

—

144

C₄

#14579141

yes

—

145

C₄

#14579151

yes

—

146

C₂

#19098493

yes

characteristic

147

C₂

#19098763

yes

characteristic

148

C₂

#19098768

yes

characteristic

149

C₂

#19098879

yes

characteristic

150

C₂

#19098891

yes

characteristic

151

C₂

#19098959

yes

characteristic

152

C₂

#19098973

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#389×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	#389	D₇₉
hypocenter	C₇₉	#2084
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₉

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#389×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

N	H ≅ G/N	type
77. C₇₉	#2084	semidirect

H ≅ G/N

type

77. C₇₉

#2084

semidirect

Subgroups — #23764876

Conjugacy classes of subgroups

Complements