Group #16819348 — subgroups

Subgroups — #16819348

Order 3712.

260 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 121 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×#11745162	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745162	C₂	1	1	yes	maximal, characteristic
3	C₂×#11745163	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
5	#14271009	C₂	1	1	yes	maximal, characteristic
6	#14270918	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂²×#6597	C₂²	1	1	yes	characteristic
14	C₂²×#6597	C₂²	1	1	yes	characteristic
15	#11745179	C₄	1	2	yes	—
16	#11745179	C₄	1	2	yes	—
17	#11745163	—	2	2	no	—
18	#11745162	C₄	1	4	yes	complemented
19	#11745162	C₄	1	4	yes	complemented
20	C₈×Dic₂₉	—	2	2	no	—
21	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₂₉	—	2	1	no	—
27	C₂×C₈×C₂₉	—	2	1	no	—
28	C₂×C₈×C₂₉	—	2	1	no	—
29	C₂×C₈×C₂₉	—	2	1	no	—
30	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
32	C₄²×C₂₉	—	2	1	no	—
33	C₄²×C₂₉	—	2	1	no	—
34	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
35	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
36	C₄×Dic₂₉	D₄	1	2	yes	—
37	C₄×Dic₂₉	Q₈	1	2	yes	—
38	C₂×#6597	—	2	1	no	—
39	C₂×#6597	—	2	1	no	—
40	C₂×#6597	—	2	1	no	—
41	C₂×#6597	—	2	1	no	—
42	C₂×#6597	C₂×C₄	1	2	yes	—
43	C₂×#6597	C₂×C₄	1	2	yes	—
44	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	—	2	2	no	—
47	C₂×C₄×C₂₉	—	2	2	no	—
48	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
53	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
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	C₄²	1	2	yes	—
59	C₂×Dic₂₉	C₄²	1	2	yes	—
60	C₂×Dic₂₉	C₄⋊C₄	1	4	yes	—
61	C₈×C₂₉	—	2	2	no	—
62	C₈×C₂₉	—	2	2	no	—
63	#6597	—	2	2	no	—
64	#6597	—	2	2	no	—
65	#1768	—	29	1	no	maximal, Sylow
66	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
67	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₂₉	#117	1	1	yes	characteristic
69	C₂²×C₂₉	#131	1	2	yes	—
70	C₂²×C₂₉	#131	1	2	yes	—
71	C₄×C₂₉	—	4	2	no	—
72	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
73	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
74	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
75	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
76	Dic₂₉	—	2	2	no	—
77	Dic₂₉	—	2	2	no	—
78	Dic₂₉	—	2	4	no	—
79	C₂×C₄⋊C₈	—	29	1	no	—
80	C₂×C₄⋊C₈	—	29	1	no	—
81	C₂×#97	—	29	1	no	—
82	C₂×C₄×C₈	—	29	1	no	—
83	#376	—	29	1	no	—
84	#336	—	29	1	no	—
85	#336	D₂₉	1	1	yes	characteristic
86	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₂₉	#405	1	1	yes	characteristic
88	C₂×C₂₉	#405	1	1	yes	characteristic
89	C₂×C₂₉	#424	1	2	yes	—
90	C₂×C₂₉	#433	1	2	yes	—
91	C₂²×C₈	—	29	1	no	—
92	C₂²×C₈	—	29	1	no	—
93	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
94	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
95	C₂×C₄²	—	29	1	no	—
96	C₂×C₄²	—	29	1	no	—
97	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
98	C₄⋊C₈	—	29	4	no	—
99	C₄⋊C₈	—	29	4	no	—
100	#97	—	58	2	no	—
101	C₄×C₈	—	58	2	no	—
102	#95	—	29	2	no	—
103	#95	—	29	2	no	—
104	C₂₉	#1768	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₄	—	29	1	no	—
106	C₂²×C₄	—	29	1	no	—
107	C₂²×C₄	—	29	2	no	—
108	C₂²×C₄	C₄×D₂₉	1	2	yes	—
109	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	2	1	no	—
114	C₂×C₈	—	29	2	no	—
115	C₂×C₈	—	29	2	no	—
116	C₂×C₈	—	58	1	no	—
117	C₂×C₈	—	58	1	no	—
118	C₂×C₈	—	58	1	no	—
119	C₂×C₈	—	58	1	no	—
120	C₂×C₈	C₄×D₂₉	1	2	yes	—
121	C₂×C₈	C₄×D₂₉	1	2	yes	—
122	C₄²	—	2	1	no	—
123	C₄²	—	2	1	no	—
124	C₄²	—	29	2	no	—
125	C₄²	—	29	2	no	—
126	C₄²	—	29	2	no	—
127	C₄²	—	29	2	no	—
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	—	29	2	no	—
133	C₂×C₄	—	29	2	no	—
134	C₂×C₄	—	29	4	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	C₂×C₄×D₂₉	1	1	yes	characteristic
140	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
141	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
142	C₂×C₄	#90807	1	1	yes	characteristic
143	C₂×C₄	#90807	1	1	yes	characteristic
144	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
145	C₈	—	2	2	no	—
146	C₈	—	2	2	no	—
147	C₈	—	58	2	no	—
148	C₈	—	58	2	no	—
149	C₂²	C₄²×D₂₉	1	1	yes	characteristic
150	C₂²	#11745239	1	1	yes	characteristic
151	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
152	C₂²	#11745263	1	2	yes	—
153	C₂²	#11745269	1	2	yes	—
154	C₄	—	4	2	no	—
155	C₄	—	58	2	no	—
156	C₄	—	58	2	no	—
157	C₄	—	58	4	no	—
158	C₄	#11745243	1	1	yes	characteristic
159	C₄	#11745243	1	1	yes	characteristic
160	C₄	#11745249	1	1	yes	characteristic
161	C₄	#11745249	1	1	yes	characteristic
162	C₂	#14271014	1	1	yes	characteristic
163	C₂	#14271117	1	1	yes	characteristic
164	C₂	#14271120	1	1	yes	characteristic
165	C₂	#14271188	1	2	yes	—
166	C₂	#14271221	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745162

C₂

yes

maximal, characteristic

C₂×#11745162

C₂

yes

maximal, characteristic

C₂×#11745163

C₂

yes

maximal, characteristic

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14271009

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

C₂₉×#336

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

#11745179

C₄

yes

—

#11745179

C₄

yes

—

#11745163

—

#11745162

C₄

yes

complemented

#11745162

C₄

yes

complemented

C₈×Dic₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

yes

—

—

—

—

—

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₂²×C₂₉

#131

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

#336

D₂₉

yes

characteristic

C₂×C₂₉

C₄×C₄⋊C₄

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

100

#97

—

101

C₄×C₈

—

102

#95

—

103

#95

—

104

C₂₉

#1768

yes

characteristic, complemented, Sylow

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₄×D₂₉

yes

—

109

C₂²×C₄

C₂²×D₂₉

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₄×D₂₉

yes

—

121

C₂×C₈

C₄×D₂₉

yes

—

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₄²

—

126

C₄²

—

127

C₄²

—

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

C₂×C₄×D₂₉

yes

characteristic

140

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

141

C₂×C₄

D₄×D₂₉

yes

characteristic

142

C₂×C₄

#90807

yes

characteristic

143

C₂×C₄

#90807

yes

characteristic

144

C₂×C₄

Q₈×D₂₉

yes

characteristic

145

C₈

—

146

C₈

—

147

C₈

—

148

C₈

—

149

C₂²

C₄²×D₂₉

yes

characteristic

150

C₂²

#11745239

yes

characteristic

151

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

152

C₂²

#11745263

yes

—

153

C₂²

#11745269

yes

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#11745243

yes

characteristic

159

C₄

#11745243

yes

characteristic

160

C₄

#11745249

yes

characteristic

161

C₄

#11745249

yes

characteristic

162

C₂

#14271014

yes

characteristic

163

C₂

#14271117

yes

characteristic

164

C₂

#14271120

yes

characteristic

165

C₂

#14271188

yes

—

166

C₂

#14271221

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂×C₄²
Fitting	C₂₉×#336	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#336	D₂₉
hypocenter	C₂₉	#1768
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator

C₂²×C₂₉

C₂×C₄²

Fitting

C₂₉×#336

C₂

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
18. #11745162	C₄	semidirect
19. #11745162	C₄	semidirect
104. C₂₉	#1768	semidirect

H ≅ G/N

type

18. #11745162

C₄

semidirect

19. #11745162

C₄

semidirect

104. C₂₉

#1768

semidirect

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

subgroup	index
C₂×#11745162	2
C₂×#11745163	2
C₂×C₈×Dic₂₉	2
#14271009	2
#14270918	2
C₂₉×#336	2
#1768	29

subgroup

index

C₂×C₈×Dic₂₉

C₂₉×#336

Subgroups — #16819348

Conjugacy classes of subgroups

Complements

Maximal subgroups