Group #16835814 — subgroups

Subgroups — #16835814

Order 3712.

224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272173	C₂	1	1	yes	maximal, characteristic, complemented
3	#14272080	C₂	1	4	yes	maximal, complemented
4	C₂×#11745281	C₂	1	1	yes	maximal, characteristic
5	C₂×#90809	—	2	1	no	—
6	#11745345	—	2	1	no	—
7	C₂×Q₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
8	C₂×#90784	—	2	1	no	—
9	#11745281	—	2	1	no	—
10	#11745281	—	2	1	no	—
11	#11745281	C₄	1	2	yes	complemented
12	#11745281	C₂²	1	2	yes	—
13	C₂×D₂₃₂	C₄	1	1	yes	characteristic, complemented
14	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
15	#11745214	—	2	1	no	—
16	#11745210	—	2	1	no	—
17	#11745209	C₂²	1	2	yes	complemented
18	#11745206	C₂²	1	2	yes	complemented
19	D₂₉⋊C₁₆	—	2	1	no	—
20	C₂×Q₈×C₂₉	—	2	1	no	—
21	#90809	—	2	2	no	—
22	#90809	—	2	2	no	—
23	#90809	—	4	1	no	—
24	#90809	—	4	1	no	—
25	C₂×D₁₁₆	—	2	1	no	—
26	C₂×D₁₁₆	—	4	1	no	—
27	C₂×C₄×D₂₉	—	4	1	no	—
28	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
29	C₂²⋊#1181	—	4	1	no	—
30	C₄⋊#1181	—	2	2	no	—
31	C₄×#1181	—	4	1	no	—
32	Q₁₆×C₂₉	—	2	1	no	—
33	Q₁₆×C₂₉	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
35	#90784	—	2	2	no	—
36	#90784	—	2	2	no	—
37	C₂×#6597	D₄	1	1	yes	characteristic
38	D₂₃₂	—	2	1	no	—
39	D₂₃₂	C₂×C₄	1	2	yes	—
40	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
41	C₈×D₂₉	D₄	1	1	yes	characteristic
42	C₈×D₂₉	D₄	1	1	yes	characteristic
43	C₈×D₂₉	C₂³	1	1	yes	characteristic
44	#90770	—	2	2	no	—
45	C₂²×D₂₉	—	4	1	no	—
46	C₂²×D₂₉	D₈	1	1	yes	characteristic
47	C₂×#1181	—	4	2	no	—
48	Q₈×C₂₉	—	2	2	no	—
49	Q₈×C₂₉	—	4	1	no	—
50	C₂×C₄×C₂₉	—	4	1	no	—
51	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
53	D₁₁₆	—	2	2	no	—
54	D₁₁₆	—	4	2	no	—
55	D₁₁₆	—	4	2	no	—
56	D₁₁₆	—	4	1	no	—
57	C₄×D₂₉	—	4	2	no	—
58	C₄×D₂₉	—	4	2	no	—
59	C₄×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₄×D₂₉	D₈	1	1	yes	characteristic
61	C₄×D₂₉	SD₁₆	1	1	yes	characteristic
62	C₄×D₂₉	C₂×D₄	1	1	yes	characteristic
63	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
65	#6597	C₂²⋊C₄	1	1	yes	characteristic
66	#6597	C₂×D₄	1	1	yes	characteristic
67	#2145	—	29	1	no	maximal, Sylow
68	C₂²×C₂₉	#102	1	1	yes	characteristic
69	C₂×D₂₉	—	4	1	no	—
70	C₂×D₂₉	—	4	2	no	—
71	C₂×D₂₉	—	8	2	no	—
72	C₂×D₂₉	#102	1	1	yes	characteristic
73	C₂×D₂₉	C₂×D₈	1	1	yes	characteristic
74	#1181	—	8	2	no	—
75	C₄×C₂₉	—	4	2	no	—
76	C₄×C₂₉	#102	1	1	yes	characteristic
77	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	Dic₂₉	#102	1	1	yes	characteristic
79	Dic₂₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₂×#135	—	29	1	no	—
81	C₂×M₃₂	—	29	1	no	—
82	#427	—	29	1	no	—
83	#360	—	29	4	no	—
84	C₂×C₂₉	—	2	1	no	—
85	C₂×C₂₉	C₂×#102	1	1	yes	characteristic
86	D₂₉	—	2	1	no	—
87	D₂₉	—	2	1	no	—
88	D₂₉	—	8	2	no	—
89	C₂×#41	—	58	1	no	—
90	#135	—	29	2	no	—
91	#135	—	29	2	no	—
92	#135	—	58	1	no	—
93	#135	—	58	1	no	—
94	C₂×Q₁₆	#1181	1	1	yes	characteristic, complemented
95	C₂×SD₁₆	—	58	1	no	—
96	C₂×D₈	—	29	1	no	—
97	C₂²×C₈	—	29	1	no	—
98	#117	—	58	1	no	—
99	M₃₂	—	29	2	no	—
100	M₃₂	—	58	1	no	—
101	C₂×C₁₆	—	58	1	no	—
102	#107	—	58	1	no	—
103	#106	—	29	2	no	—
104	C₂₉	#2145	1	1	yes	characteristic, complemented, Sylow
105	#41	—	58	2	no	—
106	#41	—	58	2	no	—
107	#41	—	116	1	no	—
108	#41	—	116	1	no	—
109	C₂×Q₈	—	2	1	no	—
110	C₂×D₄	—	58	1	no	—
111	C₂×D₄	—	116	1	no	—
112	C₂²×C₄	—	29	1	no	—
113	C₂²×C₄	—	116	1	no	—
114	Q₁₆	—	2	1	no	—
115	Q₁₆	C₂×#1181	1	2	yes	—
116	SD₁₆	—	58	2	no	—
117	SD₁₆	—	58	2	no	—
118	D₈	—	29	2	no	—
119	D₈	—	58	1	no	—
120	C₂×C₈	—	29	1	no	—
121	C₂×C₈	—	29	1	no	—
122	C₂×C₈	—	29	1	no	—
123	C₂×C₈	—	29	1	no	—
124	C₂×C₈	—	29	1	no	—
125	C₂×C₈	C₂×#1181	1	1	yes	characteristic
126	C₄⋊C₄	—	58	2	no	—
127	C₂²⋊C₄	—	116	1	no	—
128	C₄²	—	116	1	no	—
129	C₁₆	—	58	2	no	—
130	C₂³	—	29	1	no	—
131	C₂³	—	116	1	no	—
132	Q₈	—	2	2	no	—
133	Q₈	—	4	1	no	—
134	D₄	—	58	2	no	—
135	D₄	—	116	2	no	—
136	D₄	—	116	2	no	—
137	D₄	—	116	1	no	—
138	C₂×C₄	—	4	1	no	—
139	C₂×C₄	—	29	1	no	—
140	C₂×C₄	—	29	1	no	—
141	C₂×C₄	—	29	1	no	—
142	C₂×C₄	—	29	1	no	—
143	C₂×C₄	—	29	1	no	—
144	C₂×C₄	—	116	2	no	—
145	C₂×C₄	—	116	2	no	—
146	C₂×C₄	—	116	2	no	—
147	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
148	C₈	—	29	1	no	—
149	C₈	—	29	1	no	—
150	C₈	C₂²⋊#1181	1	1	yes	characteristic
151	C₈	C₂²×#1181	1	1	yes	characteristic
152	C₂²	—	29	1	no	—
153	C₂²	—	29	1	no	—
154	C₂²	—	116	1	no	—
155	C₂²	—	116	2	no	—
156	C₂²	—	232	2	no	—
157	C₂²	#11745223	1	1	yes	characteristic
158	C₄	—	4	2	no	—
159	C₄	—	29	1	no	—
160	C₄	—	29	1	no	—
161	C₄	—	232	2	no	—
162	C₄	#11745223	1	1	yes	characteristic
163	C₄	C₂×C₂²⋊#1181	1	1	yes	characteristic
164	C₂	—	2	1	no	—
165	C₂	—	58	1	no	—
166	C₂	—	58	1	no	—
167	C₂	—	232	2	no	—
168	C₂	C₂×#11745223	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₂₉⋊M₃₂

C₂

yes

maximal, characteristic, complemented

#14272173

C₂

yes

maximal, characteristic, complemented

#14272080

C₂

yes

maximal, complemented

C₂×#11745281

C₂

yes

maximal, characteristic

C₂×#90809

—

#11745345

—

C₂×Q₁₆×C₂₉

C₄

yes

characteristic, complemented

—

—

—

C₄

yes

complemented

#11745281

C₂²

yes

—

C₂×D₂₃₂

C₄

yes

characteristic, complemented

C₂×C₈×D₂₉

C₂²

yes

—

—

C₂²

yes

complemented

#11745206

C₂²

yes

complemented

D₂₉⋊C₁₆

—

C₂×Q₈×C₂₉

—

—

—

—

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂²⋊#1181

—

C₄⋊#1181

—

C₄×#1181

—

Q₁₆×C₂₉

—

Q₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

—

D₄

yes

characteristic

D₂₃₂

—

D₂₃₂

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

characteristic

C₈×D₂₉

D₄

yes

characteristic

C₈×D₂₉

D₄

yes

characteristic

C₈×D₂₉

C₂³

yes

characteristic

#90770

—

C₂²×D₂₉

—

C₂²×D₂₉

D₈

yes

characteristic

C₂×#1181

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

SD₁₆

yes

characteristic

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

C₂²⋊C₄

yes

characteristic

C₄×D₂₉

D₈

yes

characteristic

C₄×D₂₉

SD₁₆

yes

characteristic

C₄×D₂₉

C₂×D₄

yes

characteristic

C₈×C₂₉

C₂²⋊C₄

yes

characteristic

C₈×C₂₉

C₂²×C₄

yes

characteristic

#6597

C₂²⋊C₄

yes

characteristic

#6597

C₂×D₄

yes

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

#102

yes

characteristic

C₂×D₂₉

C₂×D₈

yes

characteristic

#1181

—

C₄×C₂₉

—

C₄×C₂₉

#102

yes

characteristic

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

Dic₂₉

#102

yes

characteristic

Dic₂₉

C₂×SD₁₆

yes

characteristic

C₂×#135

—

C₂×M₃₂

—

#427

—

#360

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#102

yes

characteristic

D₂₉

—

D₂₉

—

D₂₉

—

C₂×#41

—

—

—

—

—

C₂×Q₁₆

#1181

yes

characteristic, complemented

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

—

#117

—

M₃₂

—

100

M₃₂

—

101

C₂×C₁₆

—

102

#107

—

103

#106

—

104

C₂₉

#2145

yes

characteristic, complemented, Sylow

105

#41

—

106

#41

—

107

#41

—

116

—

108

#41

—

116

—

109

C₂×Q₈

—

110

C₂×D₄

—

111

C₂×D₄

—

116

—

112

C₂²×C₄

—

113

C₂²×C₄

—

116

—

114

Q₁₆

—

115

Q₁₆

C₂×#1181

yes

—

116

SD₁₆

—

117

SD₁₆

—

118

D₈

—

119

D₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂×#1181

yes

characteristic

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

116

—

128

C₄²

—

116

—

129

C₁₆

—

130

C₂³

—

131

C₂³

—

116

—

132

Q₈

—

133

Q₈

—

134

D₄

—

135

D₄

—

116

—

136

D₄

—

116

—

137

D₄

—

116

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

116

—

145

C₂×C₄

—

116

—

146

C₂×C₄

—

116

—

147

C₂×C₄

C₂²⋊#1181

yes

characteristic

148

C₈

—

149

C₈

—

150

C₈

C₂²⋊#1181

yes

characteristic

151

C₈

C₂²×#1181

yes

characteristic

152

C₂²

—

153

C₂²

—

154

C₂²

—

116

—

155

C₂²

—

116

—

156

C₂²

—

232

—

157

C₂²

#11745223

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

232

—

162

C₄

#11745223

yes

characteristic

163

C₄

C₂×C₂²⋊#1181

yes

characteristic

164

C₂

—

165

C₂

—

166

C₂

—

167

C₂

—

232

—

168

C₂

C₂×#11745223

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#11745223
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₈	C₂²×#1181
Fitting	C₂×Q₁₆×C₂₉	C₄
socle	C₂×C₂₉	C₂×#102
prime radical	C₂×#11745281	C₂
cosocle	C₈×D₂₉	C₂³
hypercenter	C₂×Q₁₆	#1181
hypocenter	C₂₉	#2145
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂

C₂×#11745223

commutator

C₈×C₂₉

C₂²×C₄

Frattini

C₈

C₂²×#1181

Fitting

C₂×Q₁₆×C₂₉

C₄

C₂×C₂₉

C₂

C₈×D₂₉

C₂³

C₂×Q₁₆

C₂₉

G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

N	H ≅ G/N	type
1. D₂₉⋊M₃₂	C₂	semidirect
2. #14272173	C₂	semidirect
3. #14272080	C₂	semidirect
7. C₂×Q₁₆×C₂₉	C₄	semidirect
11. #11745281	C₄	semidirect
13. C₂×D₂₃₂	C₄	semidirect
17. #11745209	C₂²	semidirect
18. #11745206	C₂²	semidirect
94. C₂×Q₁₆	#1181	semidirect
104. C₂₉	#2145	semidirect

H ≅ G/N

type

1. D₂₉⋊M₃₂

C₂

semidirect

2. #14272173

C₂

semidirect

3. #14272080

C₂

semidirect

7. C₂×Q₁₆×C₂₉

C₄

semidirect

11. #11745281

C₄

semidirect

13. C₂×D₂₃₂

C₄

semidirect

17. #11745209

C₂²

semidirect

18. #11745206

C₂²

semidirect

94. C₂×Q₁₆

#1181

semidirect

104. C₂₉

#2145

semidirect

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

subgroup	index
D₂₉⋊M₃₂	2
#14272173	2
#14272080	2
C₂×#11745281	2
#2145	29

subgroup

index

D₂₉⋊M₃₂

Subgroups — #16835814

Conjugacy classes of subgroups

Complements

Maximal subgroups