Group #16819486 — subgroups

Subgroups — #16819486

Order 3712.

272 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 95 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×Q₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	#14271186	C₂	1	2	yes	maximal
3	C₂×#11745184	C₂	1	1	yes	maximal, characteristic
4	#14270931	C₂	1	2	yes	maximal
5	C₂×C₂₉×#101	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	Q₈×Dic₂₉	—	2	2	no	—
9	Q₈×Dic₂₉	—	2	2	no	—
10	C₂×C₄⋊Dic₂₉	C₄	1	2	yes	—
11	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
13	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#90777	C₂²	1	2	yes	—
15	C₂₉×#101	—	2	2	no	—
16	#11745184	—	2	2	no	—
17	#11745162	—	2	2	no	—
18	#11745162	—	2	2	no	—
19	C₂×Q₈×C₂₉	—	2	2	no	—
20	C₂×Q₈×C₂₉	—	2	2	no	—
21	C₂×Q₈×C₂₉	D₄	1	2	yes	—
22	C₂×Q₈×C₂₉	Q₈	1	2	yes	—
23	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
27	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
28	M₁₆×C₂₉	—	2	2	no	—
29	M₁₆×C₂₉	—	2	2	no	—
30	C₂×C₈×C₂₉	—	2	2	no	—
31	C₄⋊Dic₂₉	—	2	2	no	—
32	C₄⋊Dic₂₉	—	2	4	no	—
33	C₄×Dic₂₉	—	2	2	no	—
34	C₄×Dic₂₉	—	2	2	no	—
35	C₄×Dic₂₉	D₄	1	2	yes	—
36	C₄×Dic₂₉	D₄	1	2	yes	—
37	#90777	—	2	2	no	—
38	#90777	—	2	2	no	—
39	C₂×#6597	—	2	2	no	—
40	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	Q₈×C₂₉	—	2	4	no	—
42	Q₈×C₂₉	—	2	4	no	—
43	C₂×C₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
46	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₄×C₂₉	#41	1	2	yes	—
50	C₂×Dic₂₉	—	2	2	no	—
51	C₂×Dic₂₉	—	2	2	no	—
52	C₂×Dic₂₉	—	4	1	no	—
53	C₂×Dic₂₉	—	4	2	no	—
54	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
56	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₈×C₂₉	—	4	2	no	—
58	#6597	—	4	2	no	—
59	#1801	—	29	1	no	maximal, Sylow
60	C₂²×C₂₉	—	2	1	no	—
61	C₂²×C₂₉	—	2	1	no	—
62	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₂₉	#117	1	1	yes	characteristic
65	C₄×C₂₉	—	2	4	no	—
66	C₄×C₂₉	#121	1	2	yes	—
67	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
68	Dic₂₉	—	2	1	no	—
69	Dic₂₉	—	2	2	no	—
70	Dic₂₉	—	4	2	no	—
71	Dic₂₉	#101	1	2	yes	complemented
72	C₂×C₄×Q₈	—	29	1	no	—
73	#423	—	29	2	no	—
74	C₂×#101	—	29	1	no	—
75	C₂×#101	D₂₉	1	1	yes	characteristic
76	#343	—	29	2	no	—
77	C₂×C₂₉	—	2	1	no	—
78	C₂×C₂₉	—	2	1	no	—
79	C₂×C₂₉	#380	1	1	yes	characteristic
80	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
81	C₂×C₂₉	#413	1	1	yes	characteristic
82	C₂²×Q₈	C₂×D₂₉	1	1	yes	characteristic
83	C₂×M₁₆	—	29	2	no	—
84	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
85	C₄×Q₈	—	58	2	no	—
86	C₄×Q₈	—	58	2	no	—
87	C₂×C₄⋊C₄	—	29	2	no	—
88	C₂×C₄⋊C₄	—	29	1	no	—
89	C₂×C₄²	—	29	1	no	—
90	C₂×C₄²	—	29	2	no	—
91	C₄⋊C₈	—	58	2	no	—
92	C₄⋊C₈	—	58	2	no	—
93	#101	—	2	2	no	—
94	#101	—	58	2	no	—
95	C₂₉	#1801	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	2	no	—
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	Dic₅₈	1	2	yes	—
99	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
100	C₂²×C₄	—	29	1	no	—
101	C₂²×C₄	—	29	1	no	—
102	C₂²×C₄	—	29	2	no	—
103	C₂²×C₄	C₄×D₂₉	1	2	yes	—
104	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
105	M₁₆	—	2	2	no	—
106	M₁₆	—	2	2	no	—
107	M₁₆	—	58	2	no	—
108	M₁₆	—	58	2	no	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	58	2	no	—
111	C₄⋊C₄	—	58	4	no	—
112	C₄⋊C₄	—	58	2	no	—
113	C₄²	—	29	2	no	—
114	C₄²	—	29	2	no	—
115	C₄²	—	58	2	no	—
116	C₄²	—	58	2	no	—
117	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
118	Q₈	—	2	4	no	—
119	Q₈	—	2	4	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	29	1	no	—
123	C₂×C₄	—	29	1	no	—
124	C₂×C₄	—	29	2	no	—
125	C₂×C₄	—	58	2	no	—
126	C₂×C₄	—	58	2	no	—
127	C₂×C₄	—	116	1	no	—
128	C₂×C₄	—	116	2	no	—
129	C₂×C₄	#90779	1	4	yes	—
130	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
131	C₂×C₄	D₄×D₂₉	1	2	yes	—
132	C₂×C₄	#90807	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
134	C₈	—	4	2	no	—
135	C₈	—	116	2	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	#11745239	1	1	yes	characteristic
139	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
140	C₂²	C₂×#90779	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	29	2	no	—
143	C₄	—	58	1	no	—
144	C₄	—	58	2	no	—
145	C₄	—	116	2	no	—
146	C₄	#11745240	1	2	yes	—
147	C₄	#11745301	1	2	yes	—
148	C₂	—	2	1	no	—
149	C₂	—	2	1	no	—
150	C₂	#14271021	1	1	yes	characteristic
151	C₂	#101×D₂₉	1	1	yes	characteristic
152	C₂	#14271146	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₂₉

C₂

yes

maximal, characteristic

#14271186

C₂

yes

maximal

C₂×#11745184

C₂

yes

maximal, characteristic

#14270931

C₂

yes

maximal

C₂×C₂₉×#101

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

Q₈×Dic₂₉

—

Q₈×Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₄

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂₉×#101

—

#11745184

—

#11745162

—

#11745162

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂×Q₈×C₂₉

Q₈

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

D₄

yes

—

#90777

—

#90777

—

C₂×#6597

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₈×C₂₉

—

#6597

—

#1801

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

#121

yes

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#101

yes

complemented

C₂×C₄×Q₈

—

#423

—

C₂×#101

—

C₂×#101

D₂₉

yes

characteristic

#343

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

C₂×D₂₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

#101

—

#101

—

C₂₉

#1801

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₅₈

yes

—

C₂×Q₈

C₂²⋊D₂₉

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₂₉

yes

—

104

C₂²×C₄

C₂²×D₂₉

yes

characteristic

105

M₁₆

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₂³

C₂×C₄×D₂₉

yes

characteristic

118

Q₈

—

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

116

—

128

C₂×C₄

—

116

—

129

C₂×C₄

#90779

yes

—

130

C₂×C₄

C₂×Dic₅₈

yes

characteristic

131

C₂×C₄

D₄×D₂₉

yes

—

132

C₂×C₄

#90807

yes

—

133

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

134

C₈

—

135

C₈

—

116

—

136

C₂²

—

137

C₂²

—

138

C₂²

#11745239

yes

characteristic

139

C₂²

C₂²⋊C₄×D₂₉

yes

characteristic

140

C₂²

C₂×#90779

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

116

—

146

C₄

#11745240

yes

—

147

C₄

#11745301

yes

—

148

C₂

—

149

C₂

—

150

C₂

#14271021

yes

characteristic

151

C₂

#101×D₂₉

yes

characteristic

152

C₂

#14271146

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₉
commutator, prime radical	C₂³×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#101	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#101	D₂₉
hypocenter	C₂₉	#1801
LCS	G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₉

commutator, prime radical

C₂³×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#101

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
71. Dic₂₉	#101	semidirect
95. C₂₉	#1801	semidirect

H ≅ G/N

type

71. Dic₂₉

#101

semidirect

95. C₂₉

#1801

semidirect

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

subgroup	index
C₂×Q₈×Dic₂₉	2
#14271186	2
C₂×#11745184	2
#14270931	2
C₂×C₂₉×#101	2
#1801	29

subgroup

index

C₂×Q₈×Dic₂₉

C₂×C₂₉×#101

Subgroups — #16819486

Conjugacy classes of subgroups

Complements

Maximal subgroups