Group #16820449 — subgroups

Subgroups — #16820449

Order 3712.

260 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11745232	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#6597	C₂	1	1	yes	maximal, characteristic
3	#14270925	C₂	1	2	yes	maximal
4	#14270925	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	—	2	1	no	—
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×#90779	—	2	1	no	—
12	C₂×#90779	—	2	1	no	—
13	C₂²×#6597	C₂²	1	2	yes	—
14	#11745232	—	2	2	no	—
15	#11745232	C₄	1	4	yes	complemented
16	C₂₉×#95	—	2	1	no	—
17	C₄⋊#6597	—	2	2	no	—
18	C₂²×C₄×C₂₉	—	2	2	no	—
19	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₂₉	—	2	1	no	—
23	C₂²×Dic₂₉	—	2	1	no	—
24	C₄⋊C₄×C₂₉	—	2	2	no	—
25	C₄⋊C₄×C₂₉	Q₈	1	4	yes	—
26	C₄²×C₂₉	—	4	2	no	—
27	C₄²×C₂₉	C₂×C₄	1	2	yes	—
28	C₄²×C₂₉	D₄	1	2	yes	—
29	C₄⋊Dic₂₉	—	2	1	no	—
30	C₄⋊Dic₂₉	—	2	1	no	—
31	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
32	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
33	#90779	—	2	4	no	—
34	#90779	—	2	4	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	4	no	—
42	C₂×C₄×C₂₉	—	4	2	no	—
43	C₂×C₄×C₂₉	—	4	2	no	—
44	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
45	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
46	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₂₉	#41	1	2	yes	—
50	C₂×Dic₂₉	—	2	2	no	—
51	C₂×Dic₂₉	—	2	2	no	—
52	C₂×Dic₂₉	—	4	2	no	—
53	C₂×Dic₂₉	—	4	1	no	—
54	C₂×Dic₂₉	—	4	1	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	4	no	—
65	C₄×C₂₉	C₄×Q₈	1	2	yes	—
66	C₄×C₂₉	#124	1	1	yes	characteristic
67	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
68	Dic₂₉	—	4	2	no	—
69	Dic₂₉	—	4	2	no	—
70	C₂×#125	—	29	1	no	—
71	C₂×C₄⋊C₈	—	29	1	no	—
72	C₄×C₄⋊C₄	D₂₉	1	1	yes	characteristic
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	—	29	4	no	—
82	#125	—	58	2	no	—
83	C₂×C₄⋊C₄	—	29	1	no	—
84	C₂×C₄⋊C₄	—	29	1	no	—
85	C₂×C₄⋊C₄	—	58	1	no	—
86	C₂×C₄⋊C₄	—	58	1	no	—
87	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
88	C₂×C₄²	—	2	1	no	—
89	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
90	C₄⋊C₈	—	58	2	no	—
91	#95	—	2	1	no	—
92	C₂₉	#1989	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	2	2	no	—
94	C₂²×C₄	—	58	1	no	—
95	C₂²×C₄	—	58	1	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	2	no	—
100	C₂×C₈	—	58	4	no	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	29	2	no	—
103	C₄⋊C₄	—	29	2	no	—
104	C₄⋊C₄	—	58	4	no	—
105	C₄⋊C₄	—	58	4	no	—
106	C₄⋊C₄	—	58	1	no	—
107	C₄⋊C₄	—	58	1	no	—
108	C₄⋊C₄	Dic₅₈	1	4	yes	—
109	C₄²	—	4	2	no	—
110	C₄²	C₄×D₂₉	1	2	yes	—
111	C₄²	D₁₁₆	1	2	yes	—
112	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	—	58	2	no	—
121	C₂×C₄	—	116	1	no	—
122	C₂×C₄	—	116	1	no	—
123	C₂×C₄	—	116	2	no	—
124	C₂×C₄	#90781	1	2	yes	—
125	C₂×C₄	#90781	1	2	yes	—
126	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
127	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
128	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
129	C₂×C₄	#90805	1	2	yes	—
130	C₈	—	116	2	no	—
131	C₂²	#11745286	1	2	yes	—
132	C₂²	C₂×#90781	1	1	yes	characteristic
133	C₂²	#11745294	1	1	yes	characteristic
134	C₂²	#11745304	1	1	yes	characteristic
135	C₂²	#11745312	1	2	yes	—
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	4	4	no	—
139	C₄	—	116	2	no	—
140	C₄	—	116	2	no	—
141	C₄	C₄×Dic₅₈	1	2	yes	—
142	C₄	#11745231	1	1	yes	characteristic
143	C₄	#11745237	1	1	yes	characteristic
144	C₂	#14271069	1	1	yes	characteristic
145	C₂	#14271157	1	1	yes	characteristic
146	C₂	#14271162	1	1	yes	characteristic
147	C₂	#14271463	1	2	yes	—
148	C₂	#14271470	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal, characteristic

C₂×C₄⋊#6597

C₂

yes

maximal, characteristic

#14270925

C₂

yes

maximal

#14270925

C₂

yes

maximal

C₄×C₄⋊C₄×C₂₉

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂×#90779

—

C₂×#90779

—

C₂²×#6597

C₂²

yes

—

#11745232

—

#11745232

C₄

yes

complemented

C₂₉×#95

—

C₄⋊#6597

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

Q₈

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

—

—

—

—

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

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

—

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×Q₈

yes

—

C₄×C₂₉

#124

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂×#125

—

C₂×C₄⋊C₈

—

C₄×C₄⋊C₄

D₂₉

yes

characteristic

#340

—

#340

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#479

yes

—

C₂²×C₈

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

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

—

108

C₄⋊C₄

Dic₅₈

yes

—

109

C₄²

—

110

C₄²

C₄×D₂₉

yes

—

111

C₄²

D₁₁₆

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

—

116

—

122

C₂×C₄

—

116

—

123

C₂×C₄

—

116

—

124

C₂×C₄

#90781

yes

—

125

C₂×C₄

#90781

yes

—

126

C₂×C₄

C₂×Dic₅₈

yes

—

127

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

128

C₂×C₄

C₂×D₁₁₆

yes

characteristic

129

C₂×C₄

#90805

yes

—

130

C₈

—

116

—

131

C₂²

#11745286

yes

—

132

C₂²

C₂×#90781

yes

characteristic

133

C₂²

#11745294

yes

characteristic

134

C₂²

#11745304

yes

characteristic

135

C₂²

#11745312

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

116

—

140

C₄

—

116

—

141

C₄

C₄×Dic₅₈

yes

—

142

C₄

#11745231

yes

characteristic

143

C₄

#11745237

yes

characteristic

144

C₂

#14271069

yes

characteristic

145

C₂

#14271157

yes

characteristic

146

C₂

#14271162

yes

characteristic

147

C₂

#14271463

yes

—

148

C₂

#14271470

yes

—

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

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₄×C₄⋊C₄×C₂₉

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₄×C₄⋊C₄

D₂₉

hypocenter

C₂₉

#1989

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
15. #11745232	C₄	semidirect
92. C₂₉	#1989	semidirect

H ≅ G/N

type

15. #11745232

C₄

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×#11745232	2
C₂×C₄⋊#6597	2
#14270925	2
C₄×C₄⋊C₄×C₂₉	2
#1989	29

subgroup

index

C₂×#11745232

C₂×C₄⋊#6597

#14270925

C₄×C₄⋊C₄×C₂₉

#1989

Subgroups — #16820449

Conjugacy classes of subgroups

Complements

Maximal subgroups