Group #16820403 — subgroups

Subgroups — #16820403

Order 3712.

316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11745167	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271168	C₂	1	2	yes	maximal, complemented
3	C₂×#11745181	C₂	1	2	yes	maximal, complemented
4	#14271118	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
7	C₂×D₈×C₂₉	—	2	1	no	—
8	C₂×D₈×C₂₉	—	2	1	no	—
9	C₂×D₈×C₂₉	—	2	2	no	—
10	C₂×D₈×C₂₉	C₄	1	4	yes	complemented
11	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745288	C₂²	1	1	yes	characteristic
13	C₂×#90777	C₂²	1	2	yes	—
14	C₂×#90777	C₂²	1	1	yes	characteristic
15	#11745181	—	2	4	no	—
16	#11745180	—	2	4	no	—
17	#11745167	—	2	2	no	—
18	#11745163	—	2	1	no	—
19	C₈×Dic₂₉	—	2	1	no	—
20	C₂⁴×C₂₉	—	2	2	no	—
21	C₂×D₄×C₂₉	—	2	2	no	—
22	C₂×D₄×C₂₉	—	2	2	no	—
23	C₂×D₄×C₂₉	—	2	2	no	—
24	C₂×D₄×C₂₉	—	2	2	no	—
25	C₂×D₄×C₂₉	—	2	2	no	—
26	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
27	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
28	D₈×C₂₉	—	2	4	no	—
29	D₈×C₂₉	—	2	4	no	—
30	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₂₉	D₄	1	2	yes	—
34	C₂²⋊Dic₂₉	—	2	1	no	—
35	C₄⋊Dic₂₉	D₄	1	2	yes	—
36	C₄×Dic₂₉	—	2	1	no	—
37	#90777	—	2	1	no	—
38	#90777	—	2	2	no	—
39	#90777	—	2	2	no	—
40	#90777	D₄	1	2	yes	—
41	C₂×#6597	—	2	1	no	—
42	C₂×#6597	—	2	2	no	—
43	C₂³×C₂₉	—	2	4	no	—
44	C₂³×C₂₉	—	4	2	no	—
45	C₂³×C₂₉	—	4	2	no	—
46	C₂³×C₂₉	—	8	4	no	—
47	C₂³×C₂₉	#41	1	1	yes	characteristic
48	D₄×C₂₉	—	2	4	no	—
49	D₄×C₂₉	—	2	4	no	—
50	D₄×C₂₉	—	4	2	no	—
51	D₄×C₂₉	—	4	2	no	—
52	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
58	C₂×Dic₂₉	—	2	2	no	—
59	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
60	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
61	#6597	—	2	2	no	—
62	#6597	—	4	2	no	—
63	#1978	—	29	1	no	maximal, Sylow
64	C₂²×C₂₉	—	2	2	no	—
65	C₂²×C₂₉	—	4	4	no	—
66	C₂²×C₂₉	—	8	4	no	—
67	C₂²×C₂₉	—	8	4	no	—
68	C₂²×C₂₉	—	8	4	no	—
69	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
70	C₂²×C₂₉	#121	1	1	yes	characteristic
71	C₂²×C₂₉	#124	1	1	yes	characteristic
72	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
74	C₄×C₂₉	#121	1	1	yes	characteristic
75	C₄×C₂₉	#127	1	1	yes	characteristic
76	Dic₂₉	—	4	2	no	—
77	C₂²×D₈	D₂₉	1	1	yes	characteristic
78	C₂×#108	—	29	1	no	—
79	#418	—	29	2	no	—
80	C₂×#100	—	29	2	no	—
81	#405	—	29	1	no	—
82	C₂×C₂₉	—	2	1	no	—
83	C₂×C₂₉	—	2	1	no	—
84	C₂×C₂₉	—	8	4	no	—
85	C₂×C₂₉	#390	1	1	yes	characteristic
86	C₂×C₂₉	#472	1	2	yes	—
87	C₂²×D₄	C₂×D₂₉	1	2	yes	—
88	C₂×D₈	—	2	1	no	—
89	C₂×D₈	—	2	1	no	—
90	C₂×D₈	—	2	2	no	—
91	C₂×D₈	Dic₂₉	1	4	yes	complemented
92	C₂×M₁₆	—	29	1	no	—
93	C₂×M₁₆	—	29	2	no	—
94	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
95	#117	—	29	1	no	—
96	#108	—	58	2	no	—
97	#102	—	58	4	no	—
98	#100	—	58	4	no	—
99	#97	—	58	1	no	—
100	C₄×C₈	—	58	1	no	—
101	C₂₉	#1978	1	1	yes	characteristic, complemented, Sylow
102	C₂⁴	—	2	2	no	—
103	C₂×D₄	—	2	2	no	—
104	C₂×D₄	—	2	2	no	—
105	C₂×D₄	—	2	2	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	2	2	no	—
108	C₂×D₄	C₂×Dic₂₉	1	4	yes	—
109	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
110	D₈	—	2	4	no	—
111	D₈	—	2	4	no	—
112	M₁₆	—	29	2	no	—
113	M₁₆	—	58	1	no	—
114	M₁₆	—	58	2	no	—
115	M₁₆	—	58	2	no	—
116	C₂×C₈	—	58	1	no	—
117	C₂×C₈	—	58	2	no	—
118	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
119	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
120	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
121	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
122	C₄⋊C₄	—	29	2	no	—
123	C₂²⋊C₄	—	58	1	no	—
124	C₄²	—	58	1	no	—
125	C₂³	—	2	4	no	—
126	C₂³	—	4	2	no	—
127	C₂³	—	4	2	no	—
128	C₂³	—	8	4	no	—
129	C₂³	#90807	1	1	yes	characteristic
130	D₄	—	2	4	no	—
131	D₄	—	2	4	no	—
132	D₄	—	4	2	no	—
133	D₄	—	4	2	no	—
134	C₂×C₄	—	58	2	no	—
135	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
136	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
137	C₂×C₄	#90807	1	1	yes	characteristic
138	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
139	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
140	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
141	C₈	—	58	2	no	—
142	C₈	—	116	2	no	—
143	C₈	C₂²⋊Dic₂₉	1	2	yes	—
144	C₈	C₂²⋊Dic₂₉	1	2	yes	—
145	C₂²	—	2	2	no	—
146	C₂²	—	4	4	no	—
147	C₂²	—	8	4	no	—
148	C₂²	—	8	4	no	—
149	C₂²	—	8	4	no	—
150	C₂²	D₄×Dic₂₉	1	1	yes	characteristic
151	C₂²	#11745298	1	1	yes	characteristic
152	C₂²	#11745300	1	1	yes	characteristic
153	C₄	—	116	2	no	—
154	C₄	D₄×Dic₂₉	1	1	yes	characteristic
155	C₄	#11745300	1	1	yes	characteristic
156	C₄	#11745302	1	1	yes	characteristic
157	C₄	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	—	8	4	no	—
161	C₂	#14271066	1	1	yes	characteristic
162	C₂	#14271430	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745167

C₂

yes

maximal, characteristic, complemented

#14271168

C₂

yes

maximal, complemented

C₂×#11745181

C₂

yes

maximal, complemented

#14271118

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₂₉

C₂

yes

maximal, characteristic

C₂²×D₄×C₂₉

C₂²

yes

—

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

C₄

yes

complemented

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂×#90777

C₂²

yes

—

—

—

—

C₈×Dic₂₉

—

C₂⁴×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

D₈×C₂₉

—

D₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

—

—

—

D₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

#41

yes

characteristic

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₈×C₂₉

C₂²⋊C₄

yes

—

C₈×C₂₉

C₂²⋊C₄

yes

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₄×D₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

C₂²×D₈

D₂₉

yes

—

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#390

yes

characteristic

C₂×C₂₉

#472

yes

—

C₂²×D₄

C₂×D₂₉

yes

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

Dic₂₉

yes

complemented

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₂₉

yes

—

—

—

—

—

100

C₄×C₈

—

101

C₂₉

#1978

yes

characteristic, complemented, Sylow

102

C₂⁴

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

C₂×Dic₂₉

yes

—

109

C₂²×C₄

C₂²×D₂₉

yes

characteristic

110

D₈

—

111

D₈

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

C₂×Dic₂₉

yes

—

119

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

120

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

121

C₂×C₈

C₂²⋊D₂₉

yes

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

#90807

yes

characteristic

130

D₄

—

131

D₄

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

D₄×D₂₉

yes

characteristic

136

C₂×C₄

D₄×D₂₉

yes

characteristic

137

C₂×C₄

#90807

yes

characteristic

138

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

139

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

140

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

141

C₈

—

142

C₈

—

116

—

143

C₈

C₂²⋊Dic₂₉

yes

—

144

C₈

C₂²⋊Dic₂₉

yes

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

D₄×Dic₂₉

yes

characteristic

151

C₂²

#11745298

yes

characteristic

152

C₂²

#11745300

yes

characteristic

153

C₄

—

116

—

154

C₄

D₄×Dic₂₉

yes

characteristic

155

C₄

#11745300

yes

characteristic

156

C₄

#11745302

yes

characteristic

157

C₄

C₂×C₂²⋊Dic₂₉

yes

characteristic

158

C₂

—

159

C₂

—

160

C₂

—

161

C₂

#14271066

yes

characteristic

162

C₂

#14271430

yes

—

	subgroup	G/H
center	C₂²	#11745300
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting, prime radical	C₂²×D₈×C₂₉	C₂
socle	C₂²×C₂₉	#121
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂²×D₈	D₂₉
hypocenter	C₂₉	#1978
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₈

subgroup

G/H

center

C₂²

#11745300

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting, prime radical

C₂²×D₈×C₂₉

C₂

socle

C₂²×C₂₉

#121

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂²×D₈

D₂₉

hypocenter

C₂₉

#1978

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₈

N	H ≅ G/N	type
1. C₂×#11745167	C₂	semidirect
2. #14271168	C₂	semidirect
3. C₂×#11745181	C₂	semidirect
4. #14271118	C₂	semidirect
10. C₂×D₈×C₂₉	C₄	semidirect
91. C₂×D₈	Dic₂₉	semidirect
101. C₂₉	#1978	semidirect

H ≅ G/N

type

1. C₂×#11745167

C₂

semidirect

2. #14271168

C₂

semidirect

3. C₂×#11745181

C₂

semidirect

4. #14271118

C₂

semidirect

10. C₂×D₈×C₂₉

C₄

semidirect

91. C₂×D₈

Dic₂₉

semidirect

101. C₂₉

#1978

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11745167	2
#14271168	2
C₂×#11745181	2
#14271118	2
C₂²×D₈×C₂₉	2
#1978	29

subgroup

index

C₂²×D₈×C₂₉

Subgroups — #16820403

Conjugacy classes of subgroups

Complements

Maximal subgroups