Group #16820450 — subgroups

Subgroups — #16820450

Order 3712.

260 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 113 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×C₄⋊#6597	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	#14270925	C₂	1	2	yes	maximal
4	#14270925	C₂	1	2	yes	maximal
5	C₂×C₂₉×#125	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#125	—	2	2	no	—
7	C₂₉×#125	C₄	1	4	yes	complemented
8	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
10	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
14	C₂×C₄×Dic₂₉	—	2	1	no	—
15	C₂²×#6597	C₂²	1	2	yes	—
16	#11745179	—	2	1	no	—
17	C₄⋊#6597	—	2	2	no	—
18	C₂²×C₄×C₂₉	—	2	1	no	—
19	C₂²×C₄×C₂₉	—	2	1	no	—
20	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₂₉	—	2	2	no	—
24	C₄⋊C₄×C₂₉	—	2	4	no	—
25	C₄⋊C₄×C₂₉	—	2	4	no	—
26	C₄⋊C₄×C₂₉	—	2	1	no	—
27	C₄⋊C₄×C₂₉	—	2	1	no	—
28	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
29	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
30	C₄²×C₂₉	C₂×C₄	1	2	yes	—
31	C₄²×C₂₉	D₄	1	2	yes	—
32	C₄⋊Dic₂₉	—	2	2	no	—
33	C₄⋊Dic₂₉	Q₈	1	4	yes	—
34	C₄×Dic₂₉	—	4	2	no	—
35	C₂×#6597	—	2	2	no	—
36	C₂×#6597	—	2	4	no	—
37	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	1	no	—
40	C₂×C₄×C₂₉	—	2	1	no	—
41	C₂×C₄×C₂₉	—	2	2	no	—
42	C₂×C₄×C₂₉	—	2	2	no	—
43	C₂×C₄×C₂₉	—	4	2	no	—
44	C₂×C₄×C₂₉	—	4	1	no	—
45	C₂×C₄×C₂₉	—	4	1	no	—
46	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
51	C₂×C₄×C₂₉	#41	1	2	yes	—
52	C₂×Dic₂₉	—	2	4	no	—
53	C₂×Dic₂₉	—	4	2	no	—
54	C₂×Dic₂₉	—	4	2	no	—
55	#6597	—	4	2	no	—
56	#1989	—	29	1	no	maximal, Sylow
57	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₂₉	C₂²⋊Q₈	1	2	yes	—
59	C₂²×C₂₉	#135	1	2	yes	—
60	C₂²×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂²×C₂₉	#137	1	1	yes	characteristic
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	—	2	2	no	—
64	C₄×C₂₉	—	4	2	no	—
65	C₄×C₂₉	—	4	2	no	—
66	C₄×C₂₉	C₄×Q₈	1	2	yes	—
67	C₄×C₂₉	#124	1	1	yes	characteristic
68	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
69	Dic₂₉	—	4	4	no	—
70	C₂×#125	D₂₉	1	1	yes	characteristic
71	C₂×C₄⋊C₈	—	29	1	no	—
72	C₄×C₄⋊C₄	—	29	1	no	—
73	#340	—	29	2	no	—
74	#340	—	29	2	no	—
75	C₂×C₂₉	#391	1	1	yes	characteristic
76	C₂×C₂₉	#416	1	1	yes	characteristic
77	C₂×C₂₉	#417	1	1	yes	characteristic
78	C₂×C₂₉	#478	1	2	yes	—
79	C₂×C₂₉	#479	1	2	yes	—
80	C₂²×C₈	—	29	2	no	—
81	#125	—	2	2	no	—
82	#125	Dic₂₉	1	4	yes	complemented
83	C₂×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄⋊C₄	—	29	2	no	—
86	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
88	C₂×C₄²	—	58	1	no	—
89	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
90	C₄⋊C₈	—	58	2	no	—
91	#95	—	58	1	no	—
92	C₂₉	#1989	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	58	2	no	—
96	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
99	C₂×C₈	—	58	4	no	—
100	C₂×C₈	—	58	2	no	—
101	C₄⋊C₄	—	2	4	no	—
102	C₄⋊C₄	—	2	4	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	29	4	no	—
106	C₄⋊C₄	—	58	2	no	—
107	C₄⋊C₄	C₂×Dic₂₉	1	2	yes	—
108	C₄⋊C₄	C₂×Dic₂₉	1	2	yes	—
109	C₄²	—	116	2	no	—
110	C₄²	C₂×Dic₂₉	1	2	yes	—
111	C₄²	C₂²⋊D₂₉	1	2	yes	—
112	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	58	4	no	—
122	C₂×C₄	—	116	2	no	—
123	C₂×C₄	—	116	2	no	—
124	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
125	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
126	C₂×C₄	Q₈×D₂₉	1	2	yes	—
127	C₂×C₄	#90809	1	2	yes	—
128	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
129	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
130	C₈	—	116	2	no	—
131	C₂²	#11745308	1	2	yes	—
132	C₂²	#11745311	1	1	yes	characteristic
133	C₂²	#11745312	1	2	yes	—
134	C₂²	#11745313	1	1	yes	characteristic
135	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	4	2	no	—
139	C₄	—	4	2	no	—
140	C₄	—	116	4	no	—
141	C₄	#11745306	1	1	yes	characteristic
142	C₄	Q₈×Dic₂₉	1	2	yes	—
143	C₄	#11745309	1	1	yes	characteristic
144	C₂	#14271070	1	1	yes	characteristic
145	C₂	#14271159	1	1	yes	characteristic
146	C₂	#14271164	1	1	yes	characteristic
147	C₂	#14271460	1	2	yes	—
148	C₂	#14271467	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6597

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₂₉

C₂

yes

maximal, characteristic

#14270925

C₂

yes

maximal

#14270925

C₂

yes

maximal

C₂×C₂₉×#125

C₂

yes

maximal, characteristic

C₂₉×#125

—

C₂₉×#125

C₄

yes

complemented

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

—

C₂²×#6597

C₂²

yes

—

#11745179

—

C₄⋊#6597

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

Q₈

yes

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#1989

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

C₂²⋊Q₈

yes

—

C₂²×C₂₉

#135

yes

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

#124

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

C₂×#125

D₂₉

yes

characteristic

C₂×C₄⋊C₈

—

C₄×C₄⋊C₄

—

#340

—

#340

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#479

yes

—

C₂²×C₈

—

#125

—

#125

Dic₂₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

#95

—

C₂₉

#1989

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

C₂×Dic₂₉

yes

—

108

C₄⋊C₄

C₂×Dic₂₉

yes

—

109

C₄²

—

116

—

110

C₄²

C₂×Dic₂₉

yes

—

111

C₄²

C₂²⋊D₂₉

yes

—

112

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

113

C₂×C₄

—

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

—

116

—

123

C₂×C₄

—

116

—

124

C₂×C₄

C₂²⋊Dic₂₉

yes

—

125

C₂×C₄

C₂²⋊Dic₂₉

yes

—

126

C₂×C₄

Q₈×D₂₉

yes

—

127

C₂×C₄

#90809

yes

—

128

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

129

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

130

C₈

—

116

—

131

C₂²

#11745308

yes

—

132

C₂²

#11745311

yes

characteristic

133

C₂²

#11745312

yes

—

134

C₂²

#11745313

yes

characteristic

135

C₂²

C₂×C₂²⋊Dic₂₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

116

—

141

C₄

#11745306

yes

characteristic

142

C₄

Q₈×Dic₂₉

yes

—

143

C₄

#11745309

yes

characteristic

144

C₂

#14271070

yes

characteristic

145

C₂

#14271159

yes

characteristic

146

C₂

#14271164

yes

characteristic

147

C₂

#14271460

yes

—

148

C₂

#14271467

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#125	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#125	D₂₉
hypocenter	C₂₉	#1989
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#125

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
7. C₂₉×#125	C₄	semidirect
82. #125	Dic₂₉	semidirect
92. C₂₉	#1989	semidirect

H ≅ G/N

type

7. C₂₉×#125

C₄

semidirect

82. #125

Dic₂₉

semidirect

92. C₂₉

#1989

semidirect

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

subgroup	index
C₂×C₄⋊#6597	2
C₄×C₄⋊Dic₂₉	2
#14270925	2
C₂×C₂₉×#125	2
#1989	29

subgroup

index

C₂×C₄⋊#6597

C₄×C₄⋊Dic₂₉

#14270925

C₂×C₂₉×#125

#1989

Subgroups — #16820450

Conjugacy classes of subgroups

Complements

Maximal subgroups