Group #23765118 — subgroups

Subgroups — #23765118

Order 10112.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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×Q₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579100	C₂	1	1	yes	maximal, characteristic
3	#19098600	C₂	1	1	yes	maximal, characteristic
4	#19098368	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098367	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098366	C₂	1	1	yes	maximal, characteristic, complemented
7	#358×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₇₉	—	2	1	no	—
9	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
10	C₂×#11929614	—	2	1	no	—
11	Q₁₆×D₇₉	—	2	2	no	—
12	Q₁₆×D₇₉	C₄	1	4	yes	complemented
13	C₂×C₈×D₇₉	C₂²	1	1	yes	characteristic
14	#14579119	—	2	1	no	—
15	#14579100	—	2	2	no	—
16	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
17	#14579095	C₂²	1	1	yes	characteristic
18	#14579092	—	2	1	no	—
19	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
21	#107×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×Dic₁₅₈	—	2	1	no	—
23	C₂×Dic₁₅₈	—	4	1	no	—
24	Q₈×D₇₉	—	2	4	no	—
25	Q₈×D₇₉	—	4	2	no	—
26	C₂×C₄×D₇₉	—	4	1	no	—
27	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
28	Dic₃₁₆	—	2	1	no	—
29	Dic₃₁₆	C₂×C₄	1	2	yes	—
30	#11929614	—	2	4	no	—
31	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
32	C₈×D₇₉	C₂×C₄	1	2	yes	—
33	C₈×D₇₉	D₄	1	2	yes	—
34	C₄⋊Dic₇₉	—	2	1	no	—
35	(C₂×D₇₉)⋊C₄	—	4	1	no	—
36	C₄×Dic₇₉	—	4	1	no	—
37	C₇₉⋊C₁₆	—	2	1	no	—
38	C₂×Q₈×C₇₉	—	2	1	no	—
39	Q₁₆×C₇₉	—	2	1	no	—
40	Q₁₆×C₇₉	C₂×C₄	1	2	yes	—
41	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₄×C₇₉	—	2	1	no	—
43	C₁₆×C₇₉	—	2	1	no	—
44	C₂²×D₇₉	D₈	1	1	yes	characteristic
45	Q₈×C₇₉	—	2	2	no	—
46	Q₈×C₇₉	—	4	1	no	—
47	C₂×C₄×C₇₉	—	4	1	no	—
48	C₂×C₄×C₇₉	—	4	1	no	—
49	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₇₉	—	4	1	no	—
51	C₂×Dic₇₉	—	4	1	no	—
52	C₂×Dic₇₉	D₈	1	1	yes	characteristic
53	C₄×D₇₉	—	4	4	no	—
54	C₄×D₇₉	C₂²⋊C₄	1	2	yes	—
55	C₄×D₇₉	SD₁₆	1	2	yes	—
56	Dic₁₅₈	—	2	2	no	—
57	Dic₁₅₈	—	4	1	no	—
58	Dic₁₅₈	—	4	4	no	—
59	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
60	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
61	C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
63	C₂×D₇₉	—	2	1	no	—
64	C₂×D₇₉	—	2	1	no	—
65	C₂×D₇₉	#102	1	2	yes	—
66	C₄×C₇₉	—	4	2	no	—
67	C₄×C₇₉	—	8	1	no	—
68	C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
70	Dic₇₉	—	4	2	no	—
71	Dic₇₉	—	8	1	no	—
72	Dic₇₉	#102	1	2	yes	—
73	C₂×C₇₉	C₂×#102	1	1	yes	characteristic
74	C₂×C₇₉	#510	1	1	yes	characteristic
75	C₂×C₇₉	#510	1	1	yes	characteristic
76	D₇₉	—	2	2	no	—
77	#2141	—	79	1	no	maximal, Sylow
78	C₇₉	#2141	1	1	yes	characteristic, complemented, Sylow
79	C₂²×Q₁₆	—	79	1	no	—
80	C₂×M₃₂	—	79	1	no	—
81	#427	—	79	1	no	—
82	#358	—	79	1	no	—
83	#358	—	79	1	no	—
84	#358	—	79	1	no	—
85	#358	D₇₉	1	1	yes	characteristic, complemented
86	C₂²×Q₈	—	158	1	no	—
87	C₂×Q₁₆	—	79	4	no	—
88	C₂×Q₁₆	—	79	1	no	—
89	C₂×Q₁₆	—	158	2	no	—
90	C₂×Q₁₆	—	158	1	no	—
91	C₂×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
92	C₂²×C₈	—	79	1	no	—
93	#117	—	158	1	no	—
94	M₃₂	—	158	2	no	—
95	C₂×C₁₆	—	79	1	no	—
96	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
97	#107	—	79	1	no	—
98	#107	C₂×D₇₉	1	1	yes	characteristic
99	#106	—	158	1	no	—
100	C₂×Q₈	—	2	1	no	—
101	C₂×Q₈	—	316	1	no	—
102	C₂×Q₈	—	316	2	no	—
103	C₂×Q₈	—	158	4	no	—
104	C₂×Q₈	—	158	1	no	—
105	C₂²×C₄	—	316	1	no	—
106	C₂²×C₄	—	79	1	no	—
107	Q₁₆	—	2	1	no	—
108	Q₁₆	—	79	2	no	—
109	Q₁₆	—	158	4	no	—
110	Q₁₆	—	158	1	no	—
111	Q₁₆	C₄×D₇₉	1	2	yes	—
112	C₂×C₈	—	79	1	no	—
113	C₂×C₈	—	79	2	no	—
114	C₂×C₈	—	79	2	no	—
115	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	158	1	no	—
118	C₂²⋊C₄	—	316	1	no	—
119	C₄²	—	316	1	no	—
120	C₁₆	—	2	1	no	—
121	C₁₆	—	158	1	no	—
122	C₂³	—	79	1	no	—
123	Q₈	—	2	2	no	—
124	Q₈	—	4	1	no	—
125	Q₈	—	316	4	no	—
126	Q₈	—	316	1	no	—
127	Q₈	—	158	2	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	316	4	no	—
131	C₂×C₄	—	316	1	no	—
132	C₂×C₄	—	316	1	no	—
133	C₂×C₄	—	79	1	no	—
134	C₂×C₄	—	79	2	no	—
135	C₂×C₄	—	79	2	no	—
136	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
137	C₈	—	79	2	no	—
138	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
139	C₈	D₄×D₇₉	1	1	yes	characteristic
140	C₂²	—	79	2	no	—
141	C₂²	—	158	1	no	—
142	C₂²	—	158	1	no	—
143	C₂²	D₈×D₇₉	1	1	yes	characteristic
144	C₄	—	4	2	no	—
145	C₄	—	8	1	no	—
146	C₄	—	316	2	no	—
147	C₄	—	79	2	no	—
148	C₄	—	632	1	no	—
149	C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
150	C₄	SD₁₆×D₇₉	1	1	yes	characteristic
151	C₂	—	158	2	no	—
152	C₂	#102×D₇₉	1	1	yes	characteristic
153	C₂	#19099002	1	1	yes	characteristic
154	C₂	#19099005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₇₉

C₂

yes

maximal, characteristic

C₂×#14579100

C₂

yes

maximal, characteristic

#19098600

C₂

yes

maximal, characteristic

#19098368

C₂

yes

maximal, characteristic, complemented

#19098367

C₂

yes

maximal, characteristic, complemented

#19098366

C₂

yes

maximal, characteristic, complemented

#358×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₇₉

—

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₂×#11929614

—

Q₁₆×D₇₉

—

Q₁₆×D₇₉

C₄

yes

complemented

C₂×C₈×D₇₉

C₂²

yes

characteristic

#14579119

—

#14579100

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579092

—

C₂×Q₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Q₈×D₇₉

—

Q₈×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

D₄

yes

characteristic

Dic₃₁₆

—

Dic₃₁₆

C₂×C₄

yes

—

#11929614

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₈×D₇₉

C₂×C₄

yes

—

C₈×D₇₉

D₄

yes

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₂²×D₇₉

D₈

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

C₂²⋊C₄

yes

—

C₄×D₇₉

SD₁₆

yes

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

C₂×D₄

yes

characteristic

C₇₉⋊C₈

C₂²⋊C₄

yes

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

#102

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

#102

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#2141

—

maximal, Sylow

C₇₉

#2141

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×M₃₂

—

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂²×Q₈

—

158

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

C₂×D₇₉

yes

characteristic

C₂²×C₈

—

#117

—

158

—

M₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#107

C₂×D₇₉

yes

characteristic

#106

—

158

—

100

C₂×Q₈

—

101

C₂×Q₈

—

316

—

102

C₂×Q₈

—

316

—

103

C₂×Q₈

—

158

—

104

C₂×Q₈

—

158

—

105

C₂²×C₄

—

316

—

106

C₂²×C₄

—

107

Q₁₆

—

108

Q₁₆

—

109

Q₁₆

—

158

—

110

Q₁₆

—

158

—

111

Q₁₆

C₄×D₇₉

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂²×D₇₉

yes

characteristic

116

C₄⋊C₄

—

117

C₄⋊C₄

—

158

—

118

C₂²⋊C₄

—

316

—

119

C₄²

—

316

—

120

C₁₆

—

121

C₁₆

—

158

—

122

C₂³

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

316

—

126

Q₈

—

316

—

127

Q₈

—

158

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

316

—

131

C₂×C₄

—

316

—

132

C₂×C₄

—

316

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

D₄×D₇₉

yes

characteristic

137

C₈

—

138

C₈

C₂×C₄×D₇₉

yes

characteristic

139

C₈

D₄×D₇₉

yes

characteristic

140

C₂²

—

141

C₂²

—

158

—

142

C₂²

—

158

—

143

C₂²

D₈×D₇₉

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

316

—

147

C₄

—

148

C₄

—

632

—

149

C₄

C₂²⋊C₄×D₇₉

yes

characteristic

150

C₄

SD₁₆×D₇₉

yes

characteristic

151

C₂

—

158

—

152

C₂

#102×D₇₉

yes

characteristic

153

C₂

#19099002

yes

characteristic

154

C₂

#19099005

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#358×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂²×D₇₉	D₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#358	D₇₉
hypocenter	C₇₉	#2141
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#358×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂²×D₇₉

D₈

cosocle

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
4. #19098368	C₂	semidirect
5. #19098367	C₂	semidirect
6. #19098366	C₂	semidirect
7. #358×C₇₉	C₂	semidirect
12. Q₁₆×D₇₉	C₄	semidirect
78. C₇₉	#2141	semidirect
85. #358	D₇₉	semidirect

H ≅ G/N

type

4. #19098368

C₂

semidirect

5. #19098367

C₂

semidirect

6. #19098366

C₂

semidirect

7. #358×C₇₉

C₂

semidirect

12. Q₁₆×D₇₉

C₄

semidirect

78. C₇₉

#2141

semidirect

85. #358

D₇₉

semidirect

Subgroups — #23765118

Conjugacy classes of subgroups

Complements