Group #16834988 — subgroups

Subgroups — D₂₉⋊#332 #16834988

Order 3712.

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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	D₂₉⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	D₂₉⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14272022	C₂	1	4	yes	maximal, complemented
4	C₄⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×D₂₉	—	2	1	no	—
6	C₂×D₂₉⋊C₈	—	2	1	no	—
7	C₂×D₂₉⋊C₈	—	2	1	no	—
8	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
9	#11745306	—	2	1	no	—
10	C₄⋊C₄×D₂₉	—	2	1	no	—
11	C₄⋊C₄×D₂₉	C₄	1	2	yes	—
12	#11745250	—	2	1	no	—
13	#11745250	C₂²	1	2	yes	—
14	C₄²×D₂₉	C₂²	1	1	yes	characteristic
15	#11745231	C₄	1	1	yes	characteristic
16	#11745220	C₂²	1	2	yes	—
17	#11745220	C₂²	1	2	yes	—
18	C₄⋊#6599	—	2	1	no	—
19	C₄⋊#6599	—	2	1	no	—
20	C₂×Q₈×C₂₉	—	2	1	no	—
21	Q₈×D₂₉	—	4	2	no	—
22	Q₈×D₂₉	—	4	2	no	—
23	C₂×C₄×D₂₉	—	2	2	no	—
24	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
26	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
27	C₂×Dic₅₈	—	2	1	no	—
28	C₂×Dic₅₈	—	2	2	no	—
29	C₂×#6599	—	2	2	no	—
30	C₂×#6599	—	2	2	no	—
31	D₂₉⋊C₈	—	4	2	no	—
32	D₂₉⋊C₈	—	4	2	no	—
33	C₄⋊C₄×C₂₉	—	2	1	no	—
34	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
35	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
36	C₄⋊Dic₂₉	—	2	1	no	—
37	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
38	#90779	—	2	2	no	—
39	#90779	—	2	2	no	—
40	C₄×Dic₂₉	D₄	1	1	yes	characteristic
41	C₄×Dic₂₉	D₄	1	1	yes	characteristic
42	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
43	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
44	Q₈×C₂₉	—	4	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	C₂²×C₄	1	1	yes	characteristic
49	C₂×Dic₂₉	—	2	2	no	—
50	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
53	C₄×D₂₉	—	2	2	no	—
54	C₄×D₂₉	—	4	4	no	—
55	C₄×D₂₉	D₈	1	2	yes	—
56	C₄×D₂₉	SD₁₆	1	2	yes	—
57	C₄×D₂₉	SD₁₆	1	2	yes	—
58	C₄×D₂₉	Q₁₆	1	2	yes	—
59	Dic₅₈	—	4	2	no	—
60	Dic₅₈	—	4	2	no	—
61	Dic₅₈	—	4	2	no	—
62	#6599	—	4	2	no	—
63	#6599	—	4	2	no	—
64	C₂×#332	—	29	1	no	maximal, Sylow
65	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×D₂₉	#101	1	2	yes	—
67	C₂×D₂₉	#102	1	2	yes	—
68	C₂×D₂₉	#103	1	2	yes	—
69	C₄×C₂₉	—	2	1	no	—
70	C₄×C₂₉	—	4	2	no	—
71	C₄×C₂₉	#102	1	2	yes	—
72	C₄×C₂₉	#103	1	2	yes	—
73	Dic₂₉	—	2	1	no	—
74	Dic₂₉	—	4	2	no	—
75	Dic₂₉	C₂×D₈	1	1	yes	characteristic
76	Dic₂₉	C₂×SD₁₆	1	1	yes	characteristic
77	Dic₂₉	C₂×SD₁₆	1	1	yes	characteristic
78	Dic₂₉	C₂×Q₁₆	1	1	yes	characteristic
79	C₂×C₄⋊Q₈	—	29	1	no	—
80	C₂×C₄⋊C₈	—	29	1	no	—
81	C₂×C₄⋊C₈	—	29	1	no	—
82	#332	—	29	4	no	—
83	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
84	C₂×C₂₉	C₂×#102	1	1	yes	characteristic
85	C₂×C₂₉	C₂×#103	1	1	yes	characteristic
86	D₂₉	#332	1	4	yes	complemented
87	C₂²×Q₈	—	58	1	no	—
88	C₂²×C₈	—	58	1	no	—
89	C₂²×C₈	—	58	1	no	—
90	C₄⋊Q₈	—	29	2	no	—
91	C₄⋊Q₈	—	29	1	no	—
92	C₄⋊Q₈	—	58	1	no	—
93	C₄⋊Q₈	—	58	1	no	—
94	C₄⋊Q₈	#1181	1	1	yes	characteristic
95	C₂×C₄⋊C₄	—	29	2	no	—
96	C₂×C₄⋊C₄	—	58	1	no	—
97	C₂×C₄²	—	29	1	no	—
98	C₄⋊C₈	—	29	2	no	—
99	C₄⋊C₈	—	29	2	no	—
100	C₄⋊C₈	—	58	1	no	—
101	C₄⋊C₈	—	58	1	no	—
102	C₂₉	C₂×#332	1	1	yes	characteristic, complemented, Sylow
103	C₂×Q₈	—	2	1	no	—
104	C₂×Q₈	—	58	2	no	—
105	C₂×Q₈	—	58	1	no	—
106	C₂×Q₈	—	116	2	no	—
107	C₂×Q₈	—	116	2	no	—
108	C₂²×C₄	—	29	1	no	—
109	C₂²×C₄	—	29	1	no	—
110	C₂²×C₄	—	29	1	no	—
111	C₂²×C₄	—	58	2	no	—
112	C₂×C₈	—	58	2	no	—
113	C₂×C₈	—	58	2	no	—
114	C₂×C₈	—	116	2	no	—
115	C₂×C₈	—	116	2	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	29	2	no	—
118	C₄⋊C₄	—	58	2	no	—
119	C₄⋊C₄	—	58	2	no	—
120	C₄⋊C₄	—	58	1	no	—
121	C₄⋊C₄	C₂×#1181	1	2	yes	—
122	C₄²	—	29	1	no	—
123	C₄²	—	29	1	no	—
124	C₄²	—	29	1	no	—
125	C₄²	C₂×#1181	1	1	yes	characteristic
126	C₂³	—	29	1	no	—
127	Q₈	—	4	2	no	—
128	Q₈	—	116	2	no	—
129	Q₈	—	116	2	no	—
130	Q₈	—	116	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	29	1	no	—
133	C₂×C₄	—	29	1	no	—
134	C₂×C₄	—	29	2	no	—
135	C₂×C₄	—	29	2	no	—
136	C₂×C₄	—	29	2	no	—
137	C₂×C₄	—	29	2	no	—
138	C₂×C₄	—	29	1	no	—
139	C₂×C₄	—	58	2	no	—
140	C₂×C₄	—	58	2	no	—
141	C₂×C₄	—	116	4	no	—
142	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
143	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
144	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
145	C₈	—	116	2	no	—
146	C₈	—	116	2	no	—
147	C₂²	—	29	2	no	—
148	C₂²	—	29	2	no	—
149	C₂²	—	29	2	no	—
150	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	4	2	no	—
153	C₄	—	29	1	no	—
154	C₄	—	29	1	no	—
155	C₄	—	29	1	no	—
156	C₄	—	29	1	no	—
157	C₄	—	58	1	no	—
158	C₄	—	116	2	no	—
159	C₄	#11745223	1	2	yes	—
160	C₄	#11745225	1	2	yes	—
161	C₂	—	29	4	no	—
162	C₂	D₂₉⋊#101	1	1	yes	characteristic
163	C₂	C₂×#11745223	1	1	yes	characteristic
164	C₂	C₂×#11745225	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₂₉⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

D₂₉⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

#14272022

C₂

yes

maximal, complemented

C₄⋊Q₈×D₂₉

C₂

yes

maximal, characteristic

C₂×Q₈×D₂₉

—

C₂×D₂₉⋊C₈

—

C₂×D₂₉⋊C₈

—

C₂₉×C₄⋊Q₈

C₄

yes

characteristic

#11745306

—

C₄⋊C₄×D₂₉

—

C₄⋊C₄×D₂₉

C₄

yes

—

#11745250

—

#11745250

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745231

C₄

yes

characteristic

#11745220

C₂²

yes

—

#11745220

C₂²

yes

—

C₄⋊#6599

—

C₄⋊#6599

—

C₂×Q₈×C₂₉

—

Q₈×D₂₉

—

Q₈×D₂₉

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×#6599

—

C₂×#6599

—

D₂₉⋊C₈

—

D₂₉⋊C₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

#90779

—

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂²⋊C₄

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

D₈

yes

—

C₄×D₂₉

SD₁₆

yes

—

C₄×D₂₉

SD₁₆

yes

—

C₄×D₂₉

Q₁₆

yes

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

#101

yes

—

C₂×D₂₉

#102

yes

—

C₂×D₂₉

#103

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#102

yes

—

C₄×C₂₉

#103

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

C₂×D₈

yes

characteristic

Dic₂₉

C₂×SD₁₆

yes

characteristic

Dic₂₉

C₂×SD₁₆

yes

characteristic

Dic₂₉

C₂×Q₁₆

yes

characteristic

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#332

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

yes

C₂²×Q₈

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

#1181

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₂₉

C₂×#332

yes

characteristic, complemented, Sylow

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

116

—

107

C₂×Q₈

—

116

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

116

—

115

C₂×C₈

—

116

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

C₂×#1181

yes

—

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₄²

C₂×#1181

yes

characteristic

126

C₂³

—

127

Q₈

—

128

Q₈

—

116

—

129

Q₈

—

116

—

130

Q₈

—

116

—

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

—

140

C₂×C₄

—

141

C₂×C₄

—

116

—

142

C₂×C₄

C₂²⋊#1181

yes

characteristic

143

C₂×C₄

C₂²⋊#1181

yes

characteristic

144

C₂×C₄

C₂²×#1181

yes

characteristic

145

C₈

—

116

—

146

C₈

—

116

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

C₂×C₂²⋊#1181

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

116

—

159

C₄

#11745223

yes

—

160

C₄

#11745225

yes

—

161

C₂

—

162

C₂

D₂₉⋊#101

yes

characteristic

163

C₂

C₂×#11745223

yes

characteristic

164

C₂

C₂×#11745225

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×C₄⋊Q₈	C₄
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	C₂×#332
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×C₄⋊Q₈

C₄

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄×Dic₂₉

C₂³

C₄⋊Q₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
3. #14272022	C₂	semidirect
86. D₂₉	#332	semidirect
102. C₂₉	C₂×#332	semidirect

H ≅ G/N

type

3. #14272022

C₂

semidirect

86. D₂₉

#332

semidirect

102. C₂₉

C₂×#332

semidirect

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

subgroup	index
D₂₉⋊(C₄⋊C₈)	2
#14272022	2
C₄⋊Q₈×D₂₉	2
C₂×#332	29

subgroup

index

D₂₉⋊(C₄⋊C₈)

#14272022

C₄⋊Q₈×D₂₉

C₂×#332

Subgroups — D₂₉⋊#332 #16834988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D29⋊#332 #16834988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉⋊#332 #16834988