Group #16820592 — subgroups

Subgroups — #16820592

Order 3712.

370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₂²×#90785	C₂	1	2	yes	maximal
2	C₂×#11745183	C₂	1	2	yes	maximal
3	#14271069	C₂	1	1	yes	maximal, characteristic
4	#14270918	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₂₉	C₂²	1	2	yes	—
7	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
8	C₂₉×C₄⋊Q₈	—	2	4	no	—
9	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×#90785	—	2	4	no	—
12	C₂×#90785	—	2	4	no	—
13	C₂×#90785	—	2	4	no	—
14	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
15	C₂²×#6597	C₂²	1	2	yes	—
16	#11745183	—	2	4	no	—
17	#11745179	—	2	2	no	—
18	C₂×Q₈×C₂₉	—	2	2	no	—
19	C₂×Q₈×C₂₉	—	2	2	no	—
20	C₂×Q₈×C₂₉	—	2	2	no	—
21	C₂×Q₈×C₂₉	—	2	2	no	—
22	C₂×Q₈×C₂₉	—	2	2	no	—
23	C₂×Q₈×C₂₉	D₄	1	4	yes	—
24	C₂²×C₄×C₂₉	—	2	2	no	—
25	C₂²×C₄×C₂₉	D₄	1	2	yes	—
26	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₂₉	—	2	1	no	—
28	C₂²×Dic₂₉	—	2	1	no	—
29	C₂×Dic₅₈	—	2	2	no	—
30	C₂×Dic₅₈	—	2	2	no	—
31	C₂×Dic₅₈	—	2	1	no	—
32	C₂×Dic₅₈	D₄	1	2	yes	—
33	C₄⋊C₄×C₂₉	—	2	8	no	—
34	C₄²×C₂₉	—	2	2	no	—
35	#90785	—	2	16	no	—
36	C₄⋊Dic₂₉	—	2	2	no	—
37	C₂×#6597	—	2	2	no	—
38	C₂×#6597	—	2	2	no	—
39	C₂×#6597	D₄	1	4	yes	—
40	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₂₉	—	2	4	no	—
42	Q₈×C₂₉	—	2	4	no	—
43	Q₈×C₂₉	—	4	2	no	—
44	Q₈×C₂₉	—	4	2	no	—
45	C₂×C₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	—	2	2	no	—
47	C₂×C₄×C₂₉	—	2	4	no	—
48	C₂×C₄×C₂₉	—	4	2	no	—
49	C₂×C₄×C₂₉	—	4	2	no	—
50	C₂×C₄×C₂₉	Q₁₆	1	4	yes	complemented
51	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
55	C₂×Dic₂₉	—	2	2	no	—
56	C₂×Dic₂₉	—	4	1	no	—
57	C₂×Dic₂₉	—	4	1	no	—
58	C₂×Dic₂₉	—	4	1	no	—
59	C₂×Dic₂₉	—	4	2	no	—
60	Dic₅₈	—	2	4	no	—
61	Dic₅₈	—	4	2	no	—
62	#6597	—	2	4	no	—
63	#2016	—	29	1	no	maximal, Sylow
64	C₂²×C₂₉	#120	1	1	yes	characteristic
65	C₂²×C₂₉	#121	1	1	yes	characteristic
66	C₂²×C₂₉	#127	1	1	yes	characteristic
67	C₂²×C₂₉	C₂×Q₁₆	1	2	yes	—
68	C₂²×C₂₉	#137	1	2	yes	—
69	C₄×C₂₉	—	2	4	no	—
70	C₄×C₂₉	—	4	4	no	—
71	C₄×C₂₉	#120	1	2	yes	—
72	C₄×C₂₉	#121	1	2	yes	—
73	Dic₂₉	—	4	2	no	—
74	Dic₂₉	—	8	1	no	—
75	C₂²×Q₁₆	—	29	2	no	—
76	C₂×C₄⋊Q₈	D₂₉	1	1	yes	characteristic
77	C₂×#103	—	29	2	no	—
78	#391	—	29	1	no	—
79	#336	—	29	1	no	—
80	C₂×C₂₉	#392	1	1	yes	characteristic
81	C₂×C₂₉	#451	1	2	yes	—
82	C₂×C₂₉	#462	1	2	yes	—
83	C₂×C₂₉	#494	1	1	yes	characteristic
84	C₂×C₂₉	#497	1	1	yes	characteristic
85	C₂²×Q₈	—	29	1	no	—
86	C₂²×Q₈	C₂×D₂₉	1	2	yes	—
87	C₂×Q₁₆	—	58	4	no	—
88	C₂×Q₁₆	—	58	4	no	—
89	C₂×Q₁₆	—	58	4	no	—
90	C₂²×C₈	—	29	2	no	—
91	C₄⋊Q₈	—	2	4	no	—
92	C₂×C₄⋊C₄	—	2	2	no	—
93	C₂×C₄⋊C₄	—	29	1	no	—
94	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
95	#103	—	58	4	no	—
96	#95	—	58	2	no	—
97	C₂₉	#2016	1	1	yes	characteristic, complemented, Sylow
98	C₂×Q₈	—	2	2	no	—
99	C₂×Q₈	—	2	2	no	—
100	C₂×Q₈	—	2	2	no	—
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	2	2	no	—
103	C₂×Q₈	—	29	2	no	—
104	C₂×Q₈	—	58	1	no	—
105	C₂×Q₈	—	58	2	no	—
106	C₂×Q₈	—	58	2	no	—
107	C₂×Q₈	C₂²⋊D₂₉	1	4	yes	—
108	C₂²×C₄	—	2	2	no	—
109	C₂²×C₄	—	58	1	no	—
110	C₂²×C₄	—	58	1	no	—
111	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
112	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
113	Q₁₆	—	58	16	no	—
114	C₂×C₈	—	29	4	no	—
115	C₂×C₈	—	58	2	no	—
116	C₂×C₈	—	58	2	no	—
117	C₄⋊C₄	—	2	8	no	—
118	C₄⋊C₄	—	58	2	no	—
119	C₄²	—	2	2	no	—
120	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
121	Q₈	—	2	4	no	—
122	Q₈	—	2	4	no	—
123	Q₈	—	4	2	no	—
124	Q₈	—	4	2	no	—
125	Q₈	—	58	4	no	—
126	Q₈	—	116	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	58	2	no	—
133	C₂×C₄	—	116	1	no	—
134	C₂×C₄	—	116	1	no	—
135	C₂×C₄	—	116	1	no	—
136	C₂×C₄	—	116	2	no	—
137	C₂×C₄	#90785	1	4	yes	complemented
138	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
139	C₂×C₄	D₄×D₂₉	1	2	yes	—
140	C₂×C₄	#90807	1	1	yes	characteristic
141	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
142	C₈	—	58	4	no	—
143	C₂²	#11745300	1	1	yes	characteristic
144	C₂²	#11745302	1	1	yes	characteristic
145	C₂²	#11745304	1	2	yes	—
146	C₂²	C₂×#90785	1	2	yes	—
147	C₂²	#11745315	1	1	yes	characteristic
148	C₄	—	2	4	no	—
149	C₄	—	4	4	no	—
150	C₄	—	116	2	no	—
151	C₄	—	232	1	no	—
152	C₄	#11745299	1	2	yes	—
153	C₄	#11745301	1	2	yes	—
154	C₂	#14271071	1	1	yes	characteristic
155	C₂	#14271319	1	2	yes	—
156	C₂	#14271370	1	2	yes	—
157	C₂	#14271542	1	1	yes	characteristic
158	C₂	#14271555	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#90785

C₂

yes

maximal

C₂×#11745183

C₂

yes

maximal

#14271069

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

C₂×C₂₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

—

C₂²×Dic₅₈

C₂²

yes

characteristic

C₂₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄²×C₂₉

C₂²

yes

—

—

—

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

—

#11745183

—

#11745179

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

—

#90785

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

D₄

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

Q₁₆

yes

complemented

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

—

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

C₂×Q₁₆

yes

—

C₂²×C₂₉

#137

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#120

yes

—

C₄×C₂₉

#121

yes

—

Dic₂₉

—

Dic₂₉

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

D₂₉

yes

—

—

—

C₂×C₂₉

#392

yes

characteristic

C₂×C₂₉

#451

yes

—

C₂×C₂₉

#462

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

—

C₂²×Q₈

C₂×D₂₉

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#103

—

#95

—

C₂₉

#2016

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

C₂²⋊D₂₉

yes

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊D₂₉

yes

—

112

C₂²×C₄

C₂²×D₂₉

yes

characteristic

113

Q₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄²

—

120

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

Q₈

—

116

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

116

—

134

C₂×C₄

—

116

—

135

C₂×C₄

—

116

—

136

C₂×C₄

—

116

—

137

C₂×C₄

#90785

yes

complemented

138

C₂×C₄

D₄×D₂₉

yes

characteristic

139

C₂×C₄

D₄×D₂₉

yes

—

140

C₂×C₄

#90807

yes

characteristic

141

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

142

C₈

—

143

C₂²

#11745300

yes

characteristic

144

C₂²

#11745302

yes

characteristic

145

C₂²

#11745304

yes

—

146

C₂²

C₂×#90785

yes

—

147

C₂²

#11745315

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

116

—

151

C₄

—

232

—

152

C₄

#11745299

yes

—

153

C₄

#11745301

yes

—

154

C₂

#14271071

yes

characteristic

155

C₂

#14271319

yes

—

156

C₂

#14271370

yes

—

157

C₂

#14271542

yes

characteristic

158

C₂

#14271555

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#2016
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₂₉

hypocenter

C₂₉

#2016

LCS

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
50. C₂×C₄×C₂₉	Q₁₆	semidirect
97. C₂₉	#2016	semidirect
137. C₂×C₄	#90785	semidirect

H ≅ G/N

type

50. C₂×C₄×C₂₉

Q₁₆

semidirect

97. C₂₉

#2016

semidirect

137. C₂×C₄

#90785

semidirect

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

subgroup	index
C₂²×#90785	2
C₂×#11745183	2
#14271069	2
#14270918	2
C₂×C₂₉×C₄⋊Q₈	2
#2016	29

subgroup

index

C₂²×#90785

C₂×C₂₉×C₄⋊Q₈

Subgroups — #16820592

Conjugacy classes of subgroups

Complements

Maximal subgroups