Group #16819242 — subgroups

Subgroups — #16819242

Order 3712.

240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11745163	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	#14271009	C₂	1	1	yes	maximal, characteristic
4	#14270918	C₂	1	1	yes	maximal, characteristic
5	#14270917	C₂	1	1	yes	maximal, characteristic
6	#14270917	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	C₄	1	4	yes	complemented
18	C₈×Dic₂₉	C₄	1	4	yes	complemented
19	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
22	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	—	2	1	no	—
25	C₂×C₈×C₂₉	—	2	1	no	—
26	C₂×C₈×C₂₉	—	2	1	no	—
27	C₂×C₈×C₂₉	—	2	1	no	—
28	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
30	C₄²×C₂₉	—	2	1	no	—
31	C₄²×C₂₉	—	2	1	no	—
32	C₄×Dic₂₉	—	2	1	no	—
33	C₄×Dic₂₉	—	2	1	no	—
34	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
35	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
36	C₂×#6597	—	2	1	no	—
37	C₂×#6597	—	2	1	no	—
38	C₂×#6597	—	2	1	no	—
39	C₂×#6597	—	2	1	no	—
40	C₂×#6597	C₂×C₄	1	2	yes	—
41	C₂×#6597	C₂×C₄	1	2	yes	—
42	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
49	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
50	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
51	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
52	C₂×Dic₂₉	—	2	2	no	—
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	C₄²	1	2	yes	—
58	C₂×Dic₂₉	C₄²	1	2	yes	—
59	C₈×C₂₉	—	2	2	no	—
60	C₈×C₂₉	—	2	2	no	—
61	#6597	—	2	2	no	—
62	#6597	—	2	2	no	—
63	#1746	—	29	1	no	maximal, Sylow
64	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
65	C₂²×C₂₉	#117	1	1	yes	characteristic
66	C₂²×C₂₉	#117	1	1	yes	characteristic
67	C₂²×C₂₉	#131	1	2	yes	—
68	C₂²×C₂₉	#131	1	2	yes	—
69	C₄×C₂₉	—	4	2	no	—
70	C₄×C₂₉	#117	1	1	yes	characteristic
71	C₄×C₂₉	#117	1	1	yes	characteristic
72	C₄×C₂₉	#117	1	1	yes	characteristic
73	C₄×C₂₉	#117	1	1	yes	characteristic
74	Dic₂₉	—	2	2	no	—
75	Dic₂₉	—	2	2	no	—
76	Dic₂₉	—	4	2	no	—
77	C₂×#97	—	29	1	no	—
78	C₂×C₄×C₈	—	29	1	no	—
79	#376	—	29	1	no	—
80	#336	—	29	1	no	—
81	#336	—	29	1	no	—
82	#336	—	29	1	no	—
83	#336	D₂₉	1	1	yes	characteristic
84	C₂×C₂₉	#376	1	1	yes	characteristic
85	C₂×C₂₉	#405	1	1	yes	characteristic
86	C₂×C₂₉	#405	1	1	yes	characteristic
87	C₂×C₂₉	#433	1	2	yes	—
88	C₂×C₂₉	#433	1	2	yes	—
89	C₂²×C₈	—	29	1	no	—
90	C₂²×C₈	—	29	1	no	—
91	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
92	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
93	C₂×C₄²	—	29	1	no	—
94	C₂×C₄²	—	29	1	no	—
95	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
96	#97	—	29	4	no	—
97	C₄×C₈	—	29	4	no	—
98	#95	—	29	2	no	—
99	#95	—	29	2	no	—
100	C₂₉	#1746	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₄	—	29	1	no	—
102	C₂²×C₄	—	29	1	no	—
103	C₂²×C₄	—	29	2	no	—
104	C₂²×C₄	C₄×D₂₉	1	2	yes	—
105	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	29	2	no	—
111	C₂×C₈	—	29	2	no	—
112	C₂×C₈	—	58	1	no	—
113	C₂×C₈	—	58	1	no	—
114	C₂×C₈	—	58	1	no	—
115	C₂×C₈	—	58	1	no	—
116	C₂×C₈	C₄×D₂₉	1	2	yes	—
117	C₂×C₈	C₄×D₂₉	1	2	yes	—
118	C₄²	—	2	1	no	—
119	C₄²	—	2	1	no	—
120	C₄²	—	29	2	no	—
121	C₄²	—	29	2	no	—
122	C₄²	—	58	1	no	—
123	C₄²	—	58	1	no	—
124	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	29	2	no	—
129	C₂×C₄	—	29	2	no	—
130	C₂×C₄	—	58	2	no	—
131	C₂×C₄	—	58	2	no	—
132	C₂×C₄	—	58	2	no	—
133	C₂×C₄	—	58	2	no	—
134	C₂×C₄	—	58	2	no	—
135	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
136	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
137	C₂×C₄	#90807	1	1	yes	characteristic
138	C₂×C₄	#90807	1	1	yes	characteristic
139	C₂×C₄	#90807	1	1	yes	characteristic
140	C₂×C₄	#90809	1	1	yes	characteristic
141	C₈	—	2	2	no	—
142	C₈	—	2	2	no	—
143	C₈	—	58	2	no	—
144	C₈	—	58	2	no	—
145	C₂²	C₄²×D₂₉	1	1	yes	characteristic
146	C₂²	#11745239	1	1	yes	characteristic
147	C₂²	#11745254	1	1	yes	characteristic
148	C₂²	#11745263	1	2	yes	—
149	C₂²	#11745269	1	2	yes	—
150	C₄	—	4	2	no	—
151	C₄	—	58	2	no	—
152	C₄	—	58	2	no	—
153	C₄	—	116	2	no	—
154	C₄	#11745239	1	1	yes	characteristic
155	C₄	#11745239	1	1	yes	characteristic
156	C₄	#11745254	1	1	yes	characteristic
157	C₄	#11745254	1	1	yes	characteristic
158	C₂	#14271008	1	1	yes	characteristic
159	C₂	#14271117	1	1	yes	characteristic
160	C₂	#14271120	1	1	yes	characteristic
161	C₂	#14271221	1	2	yes	—
162	C₂	#14271223	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745163

C₂

yes

maximal, characteristic

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14271009

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal, characteristic

#14270917

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

C₄

yes

complemented

C₈×Dic₂₉

C₄

yes

complemented

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

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

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

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

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄²

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

C₂×C₄²

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₂²×C₂₉

#131

yes

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

C₂×#97

—

C₂×C₄×C₈

—

—

—

—

—

D₂₉

yes

C₂×C₂₉

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

#97

—

C₄×C₈

—

#95

—

#95

—

100

C₂₉

#1746

yes

characteristic, complemented, Sylow

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₄×D₂₉

yes

—

105

C₂²×C₄

C₂²×D₂₉

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₄×D₂₉

yes

—

117

C₂×C₈

C₄×D₂₉

yes

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₂³

C₂×C₄×D₂₉

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

136

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

137

C₂×C₄

#90807

yes

characteristic

138

C₂×C₄

#90807

yes

characteristic

139

C₂×C₄

#90807

yes

characteristic

140

C₂×C₄

#90809

yes

characteristic

141

C₈

—

142

C₈

—

143

C₈

—

144

C₈

—

145

C₂²

C₄²×D₂₉

yes

characteristic

146

C₂²

#11745239

yes

characteristic

147

C₂²

#11745254

yes

characteristic

148

C₂²

#11745263

yes

—

149

C₂²

#11745269

yes

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

116

—

154

C₄

#11745239

yes

characteristic

155

C₄

#11745239

yes

characteristic

156

C₄

#11745254

yes

characteristic

157

C₄

#11745254

yes

characteristic

158

C₂

#14271008

yes

characteristic

159

C₂

#14271117

yes

characteristic

160

C₂

#14271120

yes

characteristic

161

C₂

#14271221

yes

—

162

C₂

#14271223

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	#1746
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
17. #11745163	C₄	semidirect
18. C₈×Dic₂₉	C₄	semidirect
100. C₂₉	#1746	semidirect

H ≅ G/N

type

17. #11745163

C₄

semidirect

18. C₈×Dic₂₉

C₄

semidirect

100. C₂₉

#1746

semidirect

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

subgroup	index
C₂×#11745163	2
C₂×C₈×Dic₂₉	2
#14271009	2
#14270918	2
#14270917	2
C₂₉×#336	2
#1746	29

subgroup

index

C₂×C₈×Dic₂₉

C₂₉×#336

Subgroups — #16819242

Conjugacy classes of subgroups

Complements

Maximal subgroups