Group #23765952 — subgroups

Subgroups — #126×Dic₇₉ #23765952

Order 10112.

516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 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	#19098456	C₂	1	3	yes	maximal
2	#19098449	C₂	1	3	yes	maximal, complemented
3	#19098431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊C₄×Dic₇₉	C₂	1	3	yes	maximal, complemented
5	C₂²⋊C₄×Dic₇₉	C₂	1	3	yes	maximal
6	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#126×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
10	C₂×C₂²⋊Dic₇₉	C₂²	1	3	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
13	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
14	C₇₉⋊#95	C₂²	1	3	yes	—
15	C₇₉⋊#95	C₂²	1	3	yes	—
16	C₇₉⋊#95	C₂²	1	3	yes	—
17	C₇₉⋊#95	C₂²	1	3	yes	—
18	#126×C₇₉	C₄	1	8	yes	complemented
19	C₂×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
20	C₂×C₂²⋊C₄×C₇₉	C₂²	1	3	yes	—
21	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×Dic₇₉	—	2	6	no	—
23	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₇₉	C₂³	1	3	yes	—
25	C₂²×Dic₇₉	C₂³	1	3	yes	—
26	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₇₉	—	2	6	no	—
28	C₂²⋊Dic₇₉	—	2	6	no	—
29	C₄×Dic₇₉	—	2	6	no	—
30	C₄×Dic₇₉	—	2	6	no	—
31	C₄×Dic₇₉	—	2	6	no	—
32	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
34	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
35	C₄⋊C₄×C₇₉	C₂×C₄	1	12	yes	complemented
36	C₂²⋊C₄×C₇₉	C₂×C₄	1	12	yes	—
37	C₄²×C₇₉	C₂×C₄	1	4	yes	complemented
38	C₂³×C₇₉	—	2	3	no	—
39	C₂³×C₇₉	—	2	3	no	—
40	C₂³×C₇₉	C₂²×C₄	1	2	yes	—
41	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
42	C₂×C₄×C₇₉	—	2	3	no	—
43	C₂×C₄×C₇₉	—	2	3	no	—
44	C₂×C₄×C₇₉	—	2	3	no	—
45	C₂×C₄×C₇₉	—	2	3	no	—
46	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
47	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
48	C₂×Dic₇₉	—	2	3	no	—
49	C₂×Dic₇₉	—	2	3	no	—
50	C₂×Dic₇₉	—	2	3	no	—
51	C₂×Dic₇₉	—	2	3	no	—
52	C₂×Dic₇₉	—	2	3	no	—
53	C₂×Dic₇₉	—	2	3	no	—
54	C₂×Dic₇₉	—	4	4	no	—
55	C₂×Dic₇₉	#41	1	6	yes	—
56	C₂×Dic₇₉	#41	1	6	yes	—
57	C₂²×C₇₉	—	2	6	no	—
58	C₂²×C₇₉	—	4	1	no	—
59	C₂²×C₇₉	—	4	3	no	—
60	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
61	C₂²×C₇₉	C₂×#41	1	3	yes	—
62	C₂²×C₇₉	C₂×#41	1	3	yes	—
63	C₄×C₇₉	—	2	6	no	—
64	C₄×C₇₉	—	2	6	no	—
65	Dic₇₉	—	2	6	no	—
66	Dic₇₉	—	4	1	no	—
67	Dic₇₉	—	4	3	no	—
68	Dic₇₉	#126	1	4	yes	direct product factor
69	C₂×C₇₉	—	4	2	no	—
70	C₂×C₇₉	C₄×#41	1	3	yes	—
71	C₂×C₇₉	C₂×#126	1	1	yes	characteristic
72	C₂×C₇₉	#529	1	3	yes	—
73	C₄×#126	—	79	1	no	maximal, Sylow
74	C₇₉	C₄×#126	1	1	yes	characteristic, complemented, Sylow
75	C₂×#126	D₇₉	1	1	yes	characteristic
76	#388	—	79	3	no	—
77	#387	—	79	3	no	—
78	#383	—	79	1	no	—
79	C₄×C₄⋊C₄	—	79	3	no	—
80	C₄×C₂²⋊C₄	—	79	3	no	—
81	C₄³	—	79	1	no	—
82	C₂³×C₄	—	79	1	no	—
83	#126	Dic₇₉	1	8	yes	direct product factor
84	C₂×C₄⋊C₄	—	79	3	no	—
85	C₂×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
86	C₂×C₂²⋊C₄	—	79	3	no	—
87	C₂×C₂²⋊C₄	C₂×D₇₉	1	3	yes	—
88	C₂×C₄²	—	79	3	no	—
89	C₂×C₄²	—	79	3	no	—
90	C₂×C₄²	—	79	3	no	—
91	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
92	#95	—	79	3	no	—
93	#95	—	79	3	no	—
94	#95	—	79	3	no	—
95	#95	—	79	3	no	—
96	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
97	C₂²×C₄	—	79	1	no	—
98	C₂²×C₄	—	79	3	no	—
99	C₂²×C₄	—	79	1	no	—
100	C₂²×C₄	—	79	3	no	—
101	C₂²×C₄	—	158	6	no	—
102	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
103	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
104	C₄⋊C₄	—	158	6	no	—
105	C₄⋊C₄	C₂×Dic₇₉	1	12	yes	complemented
106	C₂²⋊C₄	—	158	6	no	—
107	C₂²⋊C₄	C₂×Dic₇₉	1	12	yes	—
108	C₄²	—	158	6	no	—
109	C₄²	—	158	6	no	—
110	C₄²	—	158	6	no	—
111	C₄²	C₂×Dic₇₉	1	4	yes	complemented
112	C₂³	—	2	3	no	—
113	C₂³	—	2	3	no	—
114	C₂³	C₂²×Dic₇₉	1	2	yes	—
115	C₂³	C₂³×D₇₉	1	1	yes	characteristic
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	2	3	no	—
119	C₂×C₄	—	2	3	no	—
120	C₂×C₄	—	316	4	no	—
121	C₂×C₄	—	79	6	no	—
122	C₂×C₄	—	79	6	no	—
123	C₂×C₄	—	158	3	no	—
124	C₂×C₄	—	158	3	no	—
125	C₂×C₄	—	158	3	no	—
126	C₂×C₄	—	158	3	no	—
127	C₂×C₄	—	158	3	no	—
128	C₂×C₄	—	158	3	no	—
129	C₂×C₄	C₂²×Dic₇₉	1	6	yes	—
130	C₂×C₄	C₂²×Dic₇₉	1	6	yes	—
131	C₂²	—	2	6	no	—
132	C₂²	—	4	1	no	—
133	C₂²	—	4	3	no	—
134	C₂²	C₂³×Dic₇₉	1	1	yes	characteristic
135	C₂²	#41×D₇₉	1	3	yes	—
136	C₂²	#41×D₇₉	1	3	yes	—
137	C₄	—	2	6	no	—
138	C₄	—	2	6	no	—
139	C₄	—	316	1	no	—
140	C₄	—	316	3	no	—
141	C₄	—	79	4	no	—
142	C₄	—	158	6	no	—
143	C₂	—	4	2	no	—
144	C₂	#41×Dic₇₉	1	3	yes	—
145	C₂	#126×D₇₉	1	1	yes	characteristic
146	C₂	#19099096	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098456

C₂

yes

maximal

#19098449

C₂

yes

maximal, complemented

#19098431

C₂

yes

maximal, characteristic, complemented

C₄⋊C₄×Dic₇₉

C₂

yes

maximal, complemented

C₂²⋊C₄×Dic₇₉

C₂

yes

maximal

C₄²×Dic₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#126×C₇₉

C₂

yes

maximal, characteristic

C₂³×Dic₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₂²⋊Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

#126×C₇₉

C₄

yes

complemented

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂×C₄

yes

complemented

C₂²⋊C₄×C₇₉

C₂×C₄

yes

—

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂²×C₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#41

yes

—

C₂×Dic₇₉

#41

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

#126

yes

direct product factor

C₂×C₇₉

—

C₂×C₇₉

C₄×#41

yes

—

C₂×C₇₉

C₂×#126

yes

characteristic

C₂×C₇₉

#529

yes

—

C₄×#126

—

maximal, Sylow

C₇₉

C₄×#126

yes

characteristic, complemented, Sylow

C₂×#126

D₇₉

yes

—

—

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

C₄³

—

C₂³×C₄

—

#126

Dic₇₉

yes

direct product factor

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

158

—

102

C₂²×C₄

C₂²×D₇₉

yes

—

103

C₂²×C₄

C₂²×D₇₉

yes

—

104

C₄⋊C₄

—

158

—

105

C₄⋊C₄

C₂×Dic₇₉

yes

complemented

106

C₂²⋊C₄

—

158

—

107

C₂²⋊C₄

C₂×Dic₇₉

yes

—

108

C₄²

—

158

—

109

C₄²

—

158

—

110

C₄²

—

158

—

111

C₄²

C₂×Dic₇₉

yes

complemented

112

C₂³

—

113

C₂³

—

114

C₂³

C₂²×Dic₇₉

yes

—

115

C₂³

C₂³×D₇₉

yes

characteristic

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

316

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

158

—

124

C₂×C₄

—

158

—

125

C₂×C₄

—

158

—

126

C₂×C₄

—

158

—

127

C₂×C₄

—

158

—

128

C₂×C₄

—

158

—

129

C₂×C₄

C₂²×Dic₇₉

yes

—

130

C₂×C₄

C₂²×Dic₇₉

yes

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₂³×Dic₇₉

yes

characteristic

135

C₂²

#41×D₇₉

yes

—

136

C₂²

#41×D₇₉

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

316

—

140

C₄

—

316

—

141

C₄

—

142

C₄

—

158

—

143

C₂

—

144

C₂

#41×Dic₇₉

yes

—

145

C₂

#126×D₇₉

yes

characteristic

146

C₂

#19099096

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Fitting	C₂×#126×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂⁴×C₇₉	C₂³
hypercenter	C₂×#126	D₇₉
hypocenter	C₇₉	C₄×#126
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#126

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Fitting

C₂×#126×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

prime radical

C₂⁴×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₂×#126

N	H ≅ G/N	type
2. #19098449	C₂	semidirect
3. #19098431	C₂	semidirect
4. C₄⋊C₄×Dic₇₉	C₂	semidirect
6. C₄²×Dic₇₉	C₂	semidirect
18. #126×C₇₉	C₄	semidirect
35. C₄⋊C₄×C₇₉	C₂×C₄	semidirect
37. C₄²×C₇₉	C₂×C₄	semidirect
68. Dic₇₉	#126	direct (N × H)
74. C₇₉	C₄×#126	semidirect
83. #126	Dic₇₉	direct (N × H)
105. C₄⋊C₄	C₂×Dic₇₉	semidirect
111. C₄²	C₂×Dic₇₉	semidirect

H ≅ G/N

type

2. #19098449

C₂

semidirect

3. #19098431

C₂

semidirect

4. C₄⋊C₄×Dic₇₉

C₂

semidirect

6. C₄²×Dic₇₉

C₂

semidirect

18. #126×C₇₉

C₄

semidirect

35. C₄⋊C₄×C₇₉

C₂×C₄

semidirect

37. C₄²×C₇₉

C₂×C₄

semidirect

68. Dic₇₉

#126

direct (N × H)

74. C₇₉

C₄×#126

semidirect

83. #126

Dic₇₉

direct (N × H)

105. C₄⋊C₄

C₂×Dic₇₉

semidirect

111. C₄²

C₂×Dic₇₉

semidirect

Subgroups — #126×Dic₇₉ #23765952

Conjugacy classes of subgroups

Complements

Subgroups — #126×Dic79 #23765952

Conjugacy classes of subgroups

Complements

Subgroups — #126×Dic₇₉ #23765952