Group #16819674 — subgroups

Subgroups — #16819674

Order 3712.

324 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂²×#90777	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745162	C₂	1	2	yes	maximal, complemented
3	C₄×C₂²⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270917	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊Dic₂₉	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
11	C₂×#90777	—	2	2	no	—
12	C₂×#90777	—	2	4	no	—
13	C₂²×#6597	C₂²	1	2	yes	—
14	C₂₉×C₂²⋊C₈	—	2	2	no	—
15	#11745179	C₄	1	1	yes	characteristic
16	#11745179	C₄	1	1	yes	characteristic
17	#11745162	—	2	4	no	—
18	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₉	—	2	2	no	—
20	C₂²×C₄×C₂₉	—	2	2	no	—
21	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₂₉	D₄	1	2	yes	—
23	C₂²×C₄×C₂₉	Q₈	1	2	yes	—
24	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
26	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
27	C₂×C₈×C₂₉	—	2	2	no	—
28	C₂×C₈×C₂₉	—	2	1	no	—
29	C₂×C₈×C₂₉	—	2	1	no	—
30	C₂×C₈×C₂₉	—	2	2	no	—
31	C₂²⋊Dic₂₉	—	2	4	no	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₄×Dic₂₉	—	2	2	no	—
34	#90777	—	2	8	no	—
35	C₂×#6597	—	2	2	no	—
36	C₂×#6597	—	2	2	no	—
37	C₂×#6597	D₄	1	4	yes	—
38	C₂³×C₂₉	—	2	2	no	—
39	C₂³×C₂₉	—	2	2	no	—
40	C₂³×C₂₉	—	2	1	no	—
41	C₂³×C₂₉	—	2	1	no	—
42	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
43	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	—	2	4	no	—
47	C₂×C₄×C₂₉	—	2	2	no	—
48	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
49	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₂₉	#41	1	2	yes	—
53	C₂×Dic₂₉	—	2	2	no	—
54	C₂×Dic₂₉	—	2	2	no	—
55	C₂×Dic₂₉	—	2	2	no	—
56	C₂×Dic₂₉	—	2	2	no	—
57	C₂×Dic₂₉	—	2	2	no	—
58	C₂×Dic₂₉	M₁₆	1	4	yes	complemented
59	C₈×C₂₉	—	4	1	no	—
60	C₈×C₂₉	—	4	1	no	—
61	#6597	—	2	4	no	—
62	#1851	—	29	1	no	maximal, Sylow
63	C₂²×C₂₉	—	2	2	no	—
64	C₂²×C₂₉	—	2	2	no	—
65	C₂²×C₂₉	—	2	2	no	—
66	C₂²×C₂₉	—	4	2	no	—
67	C₂²×C₂₉	—	4	2	no	—
68	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₂₉	C₄×D₄	1	2	yes	—
70	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
71	C₂²×C₂₉	#131	1	1	yes	characteristic
72	C₂²×C₂₉	#131	1	1	yes	characteristic
73	C₄×C₂₉	—	2	2	no	—
74	C₄×C₂₉	#120	1	1	yes	characteristic
75	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
76	C₄×C₂₉	#123	1	1	yes	characteristic
77	Dic₂₉	—	2	4	no	—
78	Dic₂₉	—	4	2	no	—
79	C₂²×M₁₆	—	29	1	no	—
80	C₂×C₄⋊C₈	—	29	2	no	—
81	C₂×C₂²⋊C₈	D₂₉	1	1	yes	characteristic
82	C₄×C₂²⋊C₄	—	29	1	no	—
83	#336	—	29	2	no	—
84	C₂×C₂₉	—	4	2	no	—
85	C₂×C₂₉	#385	1	1	yes	characteristic
86	C₂×C₂₉	#423	1	1	yes	characteristic
87	C₂×C₂₉	#424	1	1	yes	characteristic
88	C₂×C₂₉	#435	1	2	yes	—
89	C₂×C₂₉	#436	1	2	yes	—
90	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
91	C₂×M₁₆	—	58	4	no	—
92	C₂×M₁₆	—	58	2	no	—
93	C₂²×C₈	—	29	2	no	—
94	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
95	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
96	C₂×C₂²⋊C₄	—	29	2	no	—
97	C₂×C₄²	—	29	2	no	—
98	C₄⋊C₈	—	58	4	no	—
99	C₂²⋊C₈	—	2	2	no	—
100	#95	—	29	1	no	—
101	#95	—	29	1	no	—
102	C₂₉	#1851	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	C₄×D₂₉	1	1	yes	characteristic
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	29	2	no	—
107	C₂²×C₄	—	29	2	no	—
108	C₂²×C₄	Dic₅₈	1	2	yes	—
109	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
110	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
111	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
112	M₁₆	—	58	8	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	29	4	no	—
118	C₂×C₈	—	58	2	no	—
119	C₂×C₈	—	58	2	no	—
120	C₂²⋊C₄	—	58	4	no	—
121	C₄²	—	58	2	no	—
122	C₄²	—	58	2	no	—
123	C₂³	—	2	2	no	—
124	C₂³	—	2	1	no	—
125	C₂³	—	2	1	no	—
126	C₂³	—	2	2	no	—
127	C₂³	#90779	1	2	yes	—
128	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	29	4	no	—
134	C₂×C₄	—	58	2	no	—
135	C₂×C₄	—	58	2	no	—
136	C₂×C₄	—	58	2	no	—
137	C₂×C₄	—	58	2	no	—
138	C₂×C₄	—	58	2	no	—
139	C₂×C₄	#90779	1	2	yes	—
140	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
141	C₂×C₄	D₄×D₂₉	1	2	yes	—
142	C₂×C₄	#90807	1	2	yes	—
143	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
144	C₈	—	4	1	no	—
145	C₈	—	4	1	no	—
146	C₈	—	58	4	no	—
147	C₂²	—	2	2	no	—
148	C₂²	—	2	2	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	4	2	no	—
151	C₂²	—	4	2	no	—
152	C₂²	#11745243	1	2	yes	—
153	C₂²	#11745263	1	1	yes	characteristic
154	C₂²	#11745263	1	1	yes	characteristic
155	C₂²	M₁₆×D₂₉	1	2	yes	—
156	C₂²	C₂×#90779	1	1	yes	characteristic
157	C₄	—	2	2	no	—
158	C₄	—	58	4	no	—
159	C₄	—	116	2	no	—
160	C₄	#11745240	1	2	yes	—
161	C₄	#11745297	1	1	yes	characteristic
162	C₄	#11745299	1	1	yes	characteristic
163	C₂	—	4	2	no	—
164	C₂	#14271035	1	1	yes	characteristic
165	C₂	#14271186	1	1	yes	characteristic
166	C₂	#14271189	1	1	yes	characteristic
167	C₂	#14271237	1	2	yes	—
168	C₂	#14271238	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#90777

C₂

yes

maximal, characteristic

C₂×#11745162

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₂₉

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal, complemented

C₂×C₂₉×C₂²⋊C₈

C₂

yes

maximal, characteristic

C₂³×C₄×C₂₉

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×#90777

—

C₂×#90777

—

C₂²×#6597

C₂²

yes

—

C₂₉×C₂²⋊C₈

—

#11745179

C₄

yes

characteristic

#11745179

C₄

yes

characteristic

#11745162

—

C₂⁴×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

Q₈

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂²⋊Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

—

—

—

D₄

yes

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₄⋊C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

M₁₆

yes

complemented

C₈×C₂₉

—

C₈×C₂₉

—

#6597

—

#1851

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×D₄

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

#120

yes

characteristic

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#123

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂²×M₁₆

—

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

D₂₉

yes

characteristic

C₄×C₂²⋊C₄

—

#336

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#436

yes

—

C₂³×C₄

C₂×D₂₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

#95

—

101

#95

—

102

C₂₉

#1851

yes

characteristic, complemented, Sylow

103

C₂⁴

C₄×D₂₉

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

Dic₅₈

yes

—

109

C₂²×C₄

C₄×D₂₉

yes

characteristic

110

C₂²×C₄

C₂²⋊D₂₉

yes

—

111

C₂²×C₄

C₂²×D₂₉

yes

characteristic

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

#90779

yes

—

128

C₂³

C₂×C₄×D₂₉

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#90779

yes

—

140

C₂×C₄

C₂×Dic₅₈

yes

characteristic

141

C₂×C₄

D₄×D₂₉

yes

—

142

C₂×C₄

#90807

yes

—

143

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

#11745243

yes

—

153

C₂²

#11745263

yes

characteristic

154

C₂²

#11745263

yes

characteristic

155

C₂²

M₁₆×D₂₉

yes

—

156

C₂²

C₂×#90779

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

116

—

160

C₄

#11745240

yes

—

161

C₄

#11745297

yes

characteristic

162

C₄

#11745299

yes

characteristic

163

C₂

—

164

C₂

#14271035

yes

characteristic

165

C₂

#14271186

yes

characteristic

166

C₂

#14271189

yes

characteristic

167

C₂

#14271237

yes

—

168

C₂

#14271238

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator, socle	C₂³×C₂₉	C₂²×C₄
Fitting	C₂×C₂₉×C₂²⋊C₈	C₂
prime radical	C₂⁴×C₂₉	C₂×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₂²⋊C₈	D₂₉
hypocenter	C₂₉	#1851
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator, socle

C₂³×C₂₉

C₂²×C₄

Fitting

C₂×C₂₉×C₂²⋊C₈

C₂

prime radical

C₂⁴×C₂₉

C₂×C₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×C₂²⋊C₈

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
2. C₂×#11745162	C₂	semidirect
4. #14270917	C₂	semidirect
58. C₂×Dic₂₉	M₁₆	semidirect
102. C₂₉	#1851	semidirect

H ≅ G/N

type

2. C₂×#11745162

C₂

semidirect

4. #14270917

C₂

semidirect

58. C₂×Dic₂₉

M₁₆

semidirect

102. C₂₉

#1851

semidirect

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

subgroup	index
C₂²×#90777	2
C₂×#11745162	2
C₄×C₂²⋊Dic₂₉	2
#14270917	2
C₂×C₂₉×C₂²⋊C₈	2
#1851	29

subgroup

index

C₂²×#90777

C₂×#11745162

C₄×C₂²⋊Dic₂₉

#14270917

C₂×C₂₉×C₂²⋊C₈

#1851

Subgroups — #16819674

Conjugacy classes of subgroups

Complements

Maximal subgroups