Group #16820407 — subgroups

Subgroups — #16820407

Order 3712.

276 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 93 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×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745167	C₂	1	1	yes	maximal, characteristic
3	#14271171	C₂	1	2	yes	maximal
4	C₂×#11745172	C₂	1	2	yes	maximal
5	C₂₉×#405	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₈	C₂²	1	2	yes	—
7	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂₉×#117	C₂²	1	1	yes	characteristic
10	C₂×#90777	C₂²	1	2	yes	—
11	C₂×Dic₁₁₆	—	2	2	no	—
12	C₂×Dic₁₁₆	—	2	1	no	—
13	C₂×Dic₁₁₆	—	2	1	no	—
14	C₂×Dic₁₁₆	C₄	1	4	yes	complemented
15	C₂₉×#97	—	2	1	no	—
16	C₄×C₈×C₂₉	—	2	1	no	—
17	#11745172	—	2	4	no	—
18	#11745167	—	2	2	no	—
19	#11745158	—	2	4	no	—
20	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₂₉	—	2	2	no	—
22	C₂×Dic₅₈	—	2	2	no	—
23	C₂×Dic₅₈	—	2	2	no	—
24	C₂×Dic₅₈	—	2	2	no	—
25	C₂×Dic₅₈	—	2	2	no	—
26	C₂×Dic₅₈	—	2	2	no	—
27	C₂×Dic₅₈	C₂×C₄	1	4	yes	—
28	M₁₆×C₂₉	—	2	1	no	—
29	M₁₆×C₂₉	D₄	1	2	yes	—
30	C₂×C₈×C₂₉	—	2	1	no	—
31	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₂₉	D₄	1	2	yes	—
33	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
34	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
35	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
36	C₂²⋊C₄×C₂₉	—	2	1	no	—
37	C₄²×C₂₉	—	2	1	no	—
38	#90777	—	2	2	no	—
39	#90777	—	2	2	no	—
40	C₂×#6597	—	2	2	no	—
41	Dic₁₁₆	—	2	4	no	—
42	Dic₁₁₆	—	2	4	no	—
43	C₂³×C₂₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
51	C₂×Dic₂₉	—	2	4	no	—
52	C₂×Dic₂₉	—	4	2	no	—
53	C₂×Dic₂₉	—	4	2	no	—
54	Dic₅₈	—	2	4	no	—
55	Dic₅₈	—	2	4	no	—
56	Dic₅₈	—	4	2	no	—
57	Dic₅₈	—	4	2	no	—
58	C₈×C₂₉	—	2	2	no	—
59	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
60	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
61	#6597	—	4	2	no	—
62	#1979	—	29	1	no	maximal, Sylow
63	C₂²×C₂₉	—	2	2	no	—
64	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
65	C₂²×C₂₉	#121	1	1	yes	characteristic
66	C₂²×C₂₉	#124	1	1	yes	characteristic
67	C₄×C₂₉	—	4	2	no	—
68	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
70	C₄×C₂₉	#121	1	1	yes	characteristic
71	C₄×C₂₉	#127	1	1	yes	characteristic
72	Dic₂₉	—	4	4	no	—
73	C₂²×Q₁₆	—	29	1	no	—
74	C₂×#108	—	29	1	no	—
75	#419	—	29	2	no	—
76	C₂×#101	—	29	2	no	—
77	#405	D₂₉	1	1	yes	characteristic
78	C₂×C₂₉	—	2	1	no	—
79	C₂×C₂₉	—	2	1	no	—
80	C₂×C₂₉	#390	1	1	yes	characteristic
81	C₂×C₂₉	#473	1	2	yes	—
82	C₂²×Q₈	—	29	2	no	—
83	C₂×Q₁₆	—	29	4	no	—
84	C₂×Q₁₆	—	58	2	no	—
85	C₂×Q₁₆	—	58	1	no	—
86	C₂×Q₁₆	—	58	1	no	—
87	C₂×M₁₆	—	29	2	no	—
88	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
89	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
90	#117	C₂×D₂₉	1	1	yes	characteristic
91	#108	—	58	2	no	—
92	#103	—	58	4	no	—
93	#101	—	58	4	no	—
94	#97	—	2	1	no	—
95	C₄×C₈	—	2	1	no	—
96	C₂₉	#1979	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	29	4	no	—
98	C₂×Q₈	—	58	2	no	—
99	C₂×Q₈	—	58	2	no	—
100	C₂×Q₈	—	58	2	no	—
101	C₂×Q₈	—	58	2	no	—
102	C₂×Q₈	—	58	2	no	—
103	C₂²×C₄	—	58	2	no	—
104	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
105	Q₁₆	—	58	4	no	—
106	Q₁₆	—	58	4	no	—
107	M₁₆	—	2	1	no	—
108	M₁₆	—	58	2	no	—
109	M₁₆	—	58	2	no	—
110	M₁₆	D₁₁₆	1	2	yes	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	58	2	no	—
113	C₂×C₈	C₄×D₂₉	1	2	yes	—
114	C₂×C₈	D₁₁₆	1	2	yes	—
115	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
116	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
117	C₄⋊C₄	D₁₁₆	1	2	yes	—
118	C₂²⋊C₄	—	2	1	no	—
119	C₄²	—	2	1	no	—
120	C₂³	#90805	1	1	yes	characteristic
121	Q₈	—	58	4	no	—
122	Q₈	—	58	4	no	—
123	Q₈	—	116	2	no	—
124	Q₈	—	116	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	58	4	no	—
127	C₂×C₄	—	116	2	no	—
128	C₂×C₄	—	116	2	no	—
129	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
130	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
131	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
132	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
133	C₂×C₄	#90805	1	1	yes	characteristic
134	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
135	C₈	—	2	2	no	—
136	C₈	—	116	2	no	—
137	C₈	#90781	1	2	yes	—
138	C₈	#90781	1	2	yes	—
139	C₂²	—	2	2	no	—
140	C₂²	C₄×D₁₁₆	1	1	yes	characteristic
141	C₂²	#11745237	1	1	yes	characteristic
142	C₂²	#11745292	1	1	yes	characteristic
143	C₄	—	4	2	no	—
144	C₄	—	116	4	no	—
145	C₄	C₄×D₁₁₆	1	1	yes	characteristic
146	C₄	#11745236	1	1	yes	characteristic
147	C₄	C₂×#90781	1	1	yes	characteristic
148	C₄	#11745292	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	#14271065	1	1	yes	characteristic
152	C₂	#14271438	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₁₆

C₂

yes

maximal, characteristic

C₂×#11745167

C₂

yes

maximal, characteristic

#14271171

C₂

yes

maximal

C₂×#11745172

C₂

yes

maximal

C₂₉×#405

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₂²

yes

—

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#117

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂×Dic₁₁₆

—

C₂×Dic₁₁₆

—

C₂×Dic₁₁₆

—

C₂×Dic₁₁₆

C₄

yes

complemented

C₂₉×#97

—

C₄×C₈×C₂₉

—

#11745172

—

#11745167

—

#11745158

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

C₂×C₄

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄⋊C₄×C₂₉

D₄

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

#90777

—

#90777

—

C₂×#6597

—

Dic₁₁₆

—

Dic₁₁₆

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

C₂²⋊C₄

yes

—

C₈×C₂₉

C₂²⋊C₄

yes

—

#6597

—

#1979

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₄×D₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

C₂²×Q₁₆

—

—

—

—

D₂₉

yes

characteristic

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#390

yes

characteristic

C₂×C₂₉

#473

yes

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

characteristic

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

C₂×D₂₉

yes

—

—

—

—

C₄×C₈

—

C₂₉

#1979

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²×D₂₉

yes

characteristic

105

Q₁₆

—

106

Q₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

D₁₁₆

yes

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₄×D₂₉

yes

—

114

C₂×C₈

D₁₁₆

yes

—

115

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

116

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

117

C₄⋊C₄

D₁₁₆

yes

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₂³

#90805

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

116

—

124

Q₈

—

116

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

116

—

128

C₂×C₄

—

116

—

129

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

130

C₂×C₄

C₂×D₁₁₆

yes

characteristic

131

C₂×C₄

C₂×D₁₁₆

yes

characteristic

132

C₂×C₄

C₂×D₁₁₆

yes

characteristic

133

C₂×C₄

#90805

yes

characteristic

134

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

135

C₈

—

136

C₈

—

116

—

137

C₈

#90781

yes

—

138

C₈

#90781

yes

—

139

C₂²

—

140

C₂²

C₄×D₁₁₆

yes

characteristic

141

C₂²

#11745237

yes

characteristic

142

C₂²

#11745292

yes

characteristic

143

C₄

—

144

C₄

—

116

—

145

C₄

C₄×D₁₁₆

yes

characteristic

146

C₄

#11745236

yes

characteristic

147

C₄

C₂×#90781

yes

characteristic

148

C₄

#11745292

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

#14271065

yes

characteristic

152

C₂

#14271438

yes

—

	subgroup	G/H
center	C₂²	#11745292
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#405	C₂
socle	C₂²×C₂₉	#121
prime radical	C₂³×C₂₉	#41
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#405	D₂₉
hypocenter	C₂₉	#1979
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

subgroup

G/H

center

C₂²

#11745292

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#405

C₂

C₂²×C₂₉

C₂³×C₂₉

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

N	H ≅ G/N	type
14. C₂×Dic₁₁₆	C₄	semidirect
96. C₂₉	#1979	semidirect

H ≅ G/N

type

14. C₂×Dic₁₁₆

C₄

semidirect

96. C₂₉

#1979

semidirect

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

subgroup	index
C₂²×Dic₁₁₆	2
C₂×#11745167	2
#14271171	2
C₂×#11745172	2
C₂₉×#405	2
#1979	29

subgroup

index

C₂²×Dic₁₁₆

C₂₉×#405

Subgroups — #16820407

Conjugacy classes of subgroups

Complements

Maximal subgroups