Group #16819580 — subgroups

Subgroups — #16819580

Order 3712.

344 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₄⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊#6597	C₂	1	1	yes	maximal, characteristic
3	#14270925	C₂	1	4	yes	maximal, complemented
4	C₂₉×#380	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
6	C₂³×Dic₂₉	—	2	1	no	—
7	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
8	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
9	C₂×C₄⋊Dic₂₉	—	2	2	no	—
10	C₂×C₄⋊Dic₂₉	—	2	1	no	—
11	C₂×C₄⋊Dic₂₉	C₄	1	4	yes	complemented
12	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
13	C₂²×#6597	C₂²	1	2	yes	—
14	C₂₉×#95	—	2	1	no	—
15	C₂²⋊#6597	—	2	2	no	—
16	C₂⁴×C₂₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	—	2	4	no	—
18	C₂²×C₄×C₂₉	—	2	2	no	—
19	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₂₉	D₄	1	2	yes	—
21	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₂₉	—	2	4	no	—
24	C₂²×Dic₂₉	—	2	2	no	—
25	C₂²×Dic₂₉	—	4	4	no	—
26	C₄⋊C₄×C₂₉	—	2	4	no	—
27	C₂²⋊C₄×C₂₉	—	4	2	no	—
28	C₄⋊Dic₂₉	—	2	4	no	—
29	C₄⋊Dic₂₉	—	2	2	no	—
30	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
31	C₂×#6597	—	2	2	no	—
32	C₂×#6597	—	2	4	no	—
33	C₂³×C₂₉	—	2	2	no	—
34	C₂³×C₂₉	—	2	2	no	—
35	C₂³×C₂₉	C₂²⋊C₄	1	2	yes	—
36	C₂³×C₂₉	SD₁₆	1	2	yes	—
37	C₂³×C₂₉	Q₁₆	1	2	yes	—
38	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	—	2	4	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	—	4	2	no	—
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	#41	1	4	yes	—
49	C₂×Dic₂₉	—	2	4	no	—
50	C₂×Dic₂₉	—	4	8	no	—
51	C₂×Dic₂₉	—	4	4	no	—
52	#6597	—	4	2	no	—
53	#1824	—	29	1	no	maximal, Sylow
54	C₂²×C₂₉	—	2	2	no	—
55	C₂²×C₂₉	—	2	2	no	—
56	C₂²×C₂₉	—	2	4	no	—
57	C₂²×C₂₉	—	2	4	no	—
58	C₂²×C₂₉	#103	1	4	yes	—
59	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₂₉	#123	1	2	yes	—
61	C₂²×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
62	C₂²×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
63	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
64	C₄×C₂₉	—	2	2	no	—
65	C₄×C₂₉	—	8	2	no	—
66	C₄×C₂₉	#117	1	2	yes	—
67	C₄×C₂₉	#123	1	2	yes	—
68	Dic₂₉	—	4	4	no	—
69	C₂²×C₄⋊C₄	—	29	1	no	—
70	C₂×C₂²⋊C₈	—	29	1	no	—
71	#380	D₂₉	1	1	yes	characteristic
72	#340	—	29	4	no	—
73	C₂×C₂₉	—	2	4	no	—
74	C₂×C₂₉	#381	1	1	yes	characteristic
75	C₂×C₂₉	C₂×#103	1	1	yes	characteristic
76	C₂×C₂₉	#418	1	1	yes	characteristic
77	C₂×C₂₉	#481	1	2	yes	—
78	C₂×C₂₉	#484	1	2	yes	—
79	C₂³×C₄	—	58	1	no	—
80	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
81	C₂²×C₈	—	29	2	no	—
82	C₂×C₄⋊C₄	—	29	4	no	—
83	C₂×C₄⋊C₄	—	29	2	no	—
84	C₂×C₄⋊C₄	—	58	2	no	—
85	C₂×C₄⋊C₄	—	58	1	no	—
86	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
87	C₂×C₂²⋊C₄	—	2	1	no	—
88	C₂²⋊C₈	—	58	2	no	—
89	#95	—	2	1	no	—
90	C₂₉	#1824	1	1	yes	characteristic, complemented, Sylow
91	C₂⁴	C₂²⋊D₂₉	1	1	yes	characteristic
92	C₂²×C₄	—	2	4	no	—
93	C₂²×C₄	—	2	2	no	—
94	C₂²×C₄	—	58	4	no	—
95	C₂²×C₄	—	58	2	no	—
96	C₂²×C₄	—	116	4	no	—
97	C₂²×C₄	C₄×D₂₉	1	2	yes	—
98	C₂²×C₄	D₁₁₆	1	2	yes	—
99	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
100	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
101	C₂×C₈	—	58	2	no	—
102	C₂×C₈	—	58	4	no	—
103	C₄⋊C₄	—	2	4	no	—
104	C₄⋊C₄	—	29	4	no	—
105	C₄⋊C₄	—	58	4	no	—
106	C₄⋊C₄	—	58	2	no	—
107	C₂²⋊C₄	—	4	2	no	—
108	C₂³	—	2	2	no	—
109	C₂³	—	2	2	no	—
110	C₂³	#90781	1	2	yes	—
111	C₂³	#90783	1	2	yes	—
112	C₂³	#90785	1	2	yes	—
113	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	58	4	no	—
121	C₂×C₄	—	116	8	no	—
122	C₂×C₄	—	116	4	no	—
123	C₂×C₄	#90781	1	2	yes	—
124	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
125	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
126	C₂×C₄	#90807	1	4	yes	—
127	C₈	—	116	2	no	—
128	C₂²	—	2	4	no	—
129	C₂²	—	2	2	no	—
130	C₂²	—	2	2	no	—
131	C₂²	—	2	4	no	—
132	C₂²	#11745158	1	4	yes	—
133	C₂²	C₂×#90781	1	1	yes	characteristic
134	C₂²	C₂×#90783	1	1	yes	characteristic
135	C₂²	#11745297	1	2	yes	—
136	C₂²	C₂×#90785	1	1	yes	characteristic
137	C₂²	#11745311	1	2	yes	—
138	C₄	—	2	2	no	—
139	C₄	—	8	2	no	—
140	C₄	—	116	4	no	—
141	C₄	#11745239	1	2	yes	—
142	C₄	#11745248	1	2	yes	—
143	C₂	—	2	4	no	—
144	C₂	#14271024	1	1	yes	characteristic
145	C₂	C₂×#11745158	1	1	yes	characteristic
146	C₂	#14271167	1	1	yes	characteristic
147	C₂	#14271479	1	2	yes	—
148	C₂	#14271496	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₂₉

C₂

yes

maximal, characteristic

C₂×C₂²⋊#6597

C₂

yes

maximal, characteristic

#14270925

C₂

yes

maximal, complemented

C₂₉×#380

C₂

yes

maximal, characteristic

C₂³×C₄×C₂₉

C₂²

yes

characteristic

C₂³×Dic₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₂₉

—

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₄

yes

complemented

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

C₂₉×#95

—

C₂²⋊#6597

—

C₂⁴×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂²⋊C₄

yes

—

C₂³×C₂₉

SD₁₆

yes

—

C₂³×C₂₉

Q₁₆

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

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#1824

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#103

yes

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

#123

yes

—

C₂²×C₂₉

C₂×SD₁₆

yes

characteristic

C₂²×C₂₉

C₂×Q₁₆

yes

characteristic

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

C₄×C₂₉

#123

yes

—

Dic₂₉

—

C₂²×C₄⋊C₄

—

C₂×C₂²⋊C₈

—

#380

D₂₉

yes

characteristic

#340

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#484

yes

—

C₂³×C₄

—

C₂³×C₄

C₂×D₂₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₂²⋊C₄

—

C₂²⋊C₈

—

#95

—

C₂₉

#1824

yes

characteristic, complemented, Sylow

C₂⁴

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

116

—

C₂²×C₄

C₄×D₂₉

yes

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

100

C₂²×C₄

C₂²×D₂₉

yes

characteristic

101

C₂×C₈

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₂³

—

109

C₂³

—

110

C₂³

#90781

yes

—

111

C₂³

#90783

yes

—

112

C₂³

#90785

yes

—

113

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

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

#90781

yes

—

124

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

125

C₂×C₄

C₂×D₁₁₆

yes

characteristic

126

C₂×C₄

#90807

yes

—

127

C₈

—

116

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

#11745158

yes

—

133

C₂²

C₂×#90781

yes

characteristic

134

C₂²

C₂×#90783

yes

characteristic

135

C₂²

#11745297

yes

—

136

C₂²

C₂×#90785

yes

characteristic

137

C₂²

#11745311

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

116

—

141

C₄

#11745239

yes

—

142

C₄

#11745248

yes

—

143

C₂

—

144

C₂

#14271024

yes

characteristic

145

C₂

C₂×#11745158

yes

characteristic

146

C₂

#14271167

yes

characteristic

147

C₂

#14271479

yes

—

148

C₂

#14271496

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#380	C₂
socle	C₂³×C₂₉	C₂×D₄
prime radical	C₂⁴×C₂₉	D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#380	D₂₉
hypocenter	C₂₉	#1824
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#380

C₂

socle

C₂³×C₂₉

C₂×D₄

prime radical

C₂⁴×C₂₉

D₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

N	H ≅ G/N	type
3. #14270925	C₂	semidirect
11. C₂×C₄⋊Dic₂₉	C₄	semidirect
90. C₂₉	#1824	semidirect

H ≅ G/N

type

3. #14270925

C₂

semidirect

11. C₂×C₄⋊Dic₂₉

C₄

semidirect

90. C₂₉

#1824

semidirect

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

subgroup	index
C₂²×C₄⋊Dic₂₉	2
C₂×C₂²⋊#6597	2
#14270925	2
C₂₉×#380	2
#1824	29

subgroup

index

C₂²×C₄⋊Dic₂₉

C₂×C₂²⋊#6597

#14270925

C₂₉×#380

#1824

Subgroups — #16819580

Conjugacy classes of subgroups

Complements

Maximal subgroups