Group #16835277 — subgroups

Subgroups — #16835277

Order 3712.

292 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 122 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×#11745220	C₂	1	2	yes	maximal
2	C₂×#11745218	C₂	1	2	yes	maximal
3	#14272029	C₂	1	2	yes	maximal
4	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6599	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	#11745220	C₄	1	8	yes	complemented
14	#11745218	—	2	4	no	—
15	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
22	C₂×#6599	—	2	4	no	—
23	C₂×#6599	—	2	4	no	—
24	C₂×#6599	C₂×C₄	1	8	yes	—
25	C₄²×C₂₉	—	2	2	no	—
26	C₄×Dic₂₉	—	2	2	no	—
27	C₄×Dic₂₉	—	2	2	no	—
28	C₄×Dic₂₉	—	2	2	no	—
29	C₄×Dic₂₉	—	2	2	no	—
30	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
31	C₄×Dic₂₉	D₄	1	2	yes	—
32	C₄×Dic₂₉	Q₈	1	2	yes	—
33	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	—	2	1	no	—
35	C₂×C₄×C₂₉	—	2	1	no	—
36	C₂×C₄×C₂₉	—	2	1	no	—
37	C₂×C₄×C₂₉	—	2	1	no	—
38	C₂×C₄×C₂₉	—	2	1	no	—
39	C₂×C₄×C₂₉	—	2	1	no	—
40	C₂×C₄×C₂₉	C₄²	1	2	yes	—
41	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
42	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
43	C₂×Dic₂₉	—	2	1	no	—
44	C₂×Dic₂₉	—	2	1	no	—
45	C₂×Dic₂₉	—	2	1	no	—
46	C₂×Dic₂₉	—	2	1	no	—
47	C₂×Dic₂₉	C₄²	1	2	yes	—
48	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
49	C₂×Dic₂₉	M₁₆	1	2	yes	—
50	C₂×Dic₂₉	M₁₆	1	2	yes	—
51	C₂×Dic₂₉	M₁₆	1	2	yes	—
52	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
53	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×Dic₂₉	#41	1	2	yes	—
56	#6599	—	2	8	no	—
57	#1767	—	29	1	no	maximal, Sylow
58	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
59	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₂₉	#117	1	1	yes	characteristic
61	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
62	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
63	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
64	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
65	C₄×C₂₉	—	2	2	no	—
66	C₄×C₂₉	—	2	2	no	—
67	C₄×C₂₉	—	2	2	no	—
68	Dic₂₉	—	2	2	no	—
69	Dic₂₉	—	2	2	no	—
70	Dic₂₉	#97	1	4	yes	complemented
71	Dic₂₉	C₄×D₄	1	2	yes	—
72	Dic₂₉	C₄×Q₈	1	2	yes	—
73	C₂×C₄⋊C₈	—	29	2	no	—
74	C₂×#97	—	29	2	no	—
75	C₄³	—	29	1	no	—
76	#336	—	29	2	no	—
77	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
79	C₂×C₂₉	C₄×M₁₆	1	1	yes	characteristic
80	C₂×C₂₉	#423	1	1	yes	characteristic
81	C₂×C₂₉	#423	1	1	yes	characteristic
82	C₂×C₂₉	#432	1	1	yes	characteristic
83	C₂×C₂₉	#432	1	1	yes	characteristic
84	C₂²×C₈	—	29	4	no	—
85	C₂×C₄²	—	29	1	no	—
86	C₂×C₄²	—	29	1	no	—
87	C₂×C₄²	—	29	1	no	—
88	C₂×C₄²	—	29	1	no	—
89	C₂×C₄²	—	29	1	no	—
90	C₂×C₄²	—	29	1	no	—
91	C₂×C₄²	#1181	1	1	yes	characteristic
92	C₄⋊C₈	—	29	8	no	—
93	#97	—	58	4	no	—
94	C₂₉	#1767	1	1	yes	characteristic, complemented, Sylow
95	C₂²×C₄	—	29	1	no	—
96	C₂²×C₄	—	29	1	no	—
97	C₂²×C₄	—	29	1	no	—
98	C₂²×C₄	—	29	1	no	—
99	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
100	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
101	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
102	C₂×C₈	—	29	8	no	—
103	C₂×C₈	—	58	4	no	—
104	C₂×C₈	—	58	4	no	—
105	C₄²	—	2	2	no	—
106	C₄²	—	29	4	no	—
107	C₄²	—	29	2	no	—
108	C₄²	—	29	2	no	—
109	C₄²	—	58	2	no	—
110	C₄²	—	58	2	no	—
111	C₄²	—	58	2	no	—
112	C₄²	—	58	2	no	—
113	C₂³	C₂²×#1181	1	1	yes	characteristic
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	29	2	no	—
121	C₂×C₄	—	29	2	no	—
122	C₂×C₄	—	29	2	no	—
123	C₂×C₄	—	29	2	no	—
124	C₂×C₄	—	29	1	no	—
125	C₂×C₄	—	29	1	no	—
126	C₂×C₄	—	29	2	no	—
127	C₂×C₄	—	29	2	no	—
128	C₂×C₄	—	29	2	no	—
129	C₂×C₄	—	58	1	no	—
130	C₂×C₄	—	58	1	no	—
131	C₂×C₄	—	58	1	no	—
132	C₂×C₄	—	58	1	no	—
133	C₂×C₄	C₄×#1181	1	2	yes	—
134	C₂×C₄	C₄⋊#1181	1	2	yes	—
135	C₂×C₄	#90800	1	2	yes	—
136	C₈	—	58	8	no	—
137	C₂²	D₂₉⋊M₁₆	1	1	yes	characteristic
138	C₂²	D₂₉⋊M₁₆	1	1	yes	characteristic
139	C₂²	D₂₉⋊M₁₆	1	1	yes	characteristic
140	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
141	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
142	C₂²	#11745345	1	1	yes	characteristic
143	C₂²	C₂×#90800	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	29	2	no	—
148	C₄	—	29	2	no	—
149	C₄	—	29	4	no	—
150	C₄	—	58	2	no	—
151	C₄	—	58	2	no	—
152	C₂	C₄×C₄⋊#1181	1	1	yes	characteristic
153	C₂	#14272122	1	1	yes	characteristic
154	C₂	C₄×#90800	1	1	yes	characteristic
155	C₂	#14272166	1	1	yes	characteristic
156	C₂	#14272168	1	1	yes	characteristic
157	C₂	#14272183	1	1	yes	characteristic
158	C₂	#14272186	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745220

C₂

yes

maximal

C₂×#11745218

C₂

yes

maximal

#14272029

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

C₂²×#6599

C₂²

yes

—

C₂×C₄²×C₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

#11745220

C₄

yes

complemented

#11745218

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

—

C₂×C₄

yes

—

C₄²×C₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

#41

yes

—

#6599

—

#1767

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#97

yes

complemented

Dic₂₉

C₄×D₄

yes

—

Dic₂₉

C₄×Q₈

yes

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₄³

—

#336

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

C₂×#97

yes

characteristic

C₂×C₂₉

C₄×M₁₆

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#1181

yes

characteristic

C₄⋊C₈

—

#97

—

C₂₉

#1767

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

characteristic

100

C₂²×C₄

C₂×#1181

yes

characteristic

101

C₂²×C₄

C₂×#1181

yes

characteristic

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₂³

C₂²×#1181

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

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

C₄×#1181

yes

—

134

C₂×C₄

C₄⋊#1181

yes

—

135

C₂×C₄

#90800

yes

—

136

C₈

—

137

C₂²

D₂₉⋊M₁₆

yes

characteristic

138

C₂²

D₂₉⋊M₁₆

yes

characteristic

139

C₂²

D₂₉⋊M₁₆

yes

characteristic

140

C₂²

C₂×C₄×#1181

yes

characteristic

141

C₂²

C₂×C₄⋊#1181

yes

characteristic

142

C₂²

#11745345

yes

characteristic

143

C₂²

C₂×#90800

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₂

C₄×C₄⋊#1181

yes

characteristic

153

C₂

#14272122

yes

characteristic

154

C₂

C₄×#90800

yes

characteristic

155

C₂

#14272166

yes

characteristic

156

C₂

#14272168

yes

characteristic

157

C₂

#14272183

yes

characteristic

158

C₂

#14272186

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator	C₂²×C₂₉	C₂×C₄²
Fitting	C₂×C₄²×C₂₉	C₄
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	C₂×C₄²	#1181
hypocenter	C₂₉	#1767
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂²×#1181

commutator

C₂²×C₂₉

C₂×C₄²

Fitting

C₂×C₄²×C₂₉

C₄

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×Dic₂₉

C₂³

C₂×C₄²

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₂×C₄²

N	H ≅ G/N	type
13. #11745220	C₄	semidirect
70. Dic₂₉	#97	semidirect
94. C₂₉	#1767	semidirect

H ≅ G/N

type

13. #11745220

C₄

semidirect

70. Dic₂₉

#97

semidirect

94. C₂₉

#1767

semidirect

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

subgroup	index
C₂×#11745220	2
C₂×#11745218	2
#14272029	2
C₄²×Dic₂₉	2
#1767	29

subgroup

index

C₄²×Dic₂₉

Subgroups — #16835277

Conjugacy classes of subgroups

Complements

Maximal subgroups