Group #16819709 — subgroups

Subgroups — #16819709

Order 3712.

272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14271641	C₂	1	1	yes	maximal, characteristic
2	#14271205	C₂	1	2	yes	maximal
3	#14271070	C₂	1	1	yes	maximal, characteristic
4	#14270924	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	#11745288	—	2	2	no	—
11	#11745288	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×#101	C₄	1	4	yes	complemented
15	#11745179	—	2	2	no	—
16	#11745166	—	2	2	no	—
17	#11745165	—	2	2	no	—
18	C₂×Q₈×C₂₉	—	2	2	no	—
19	C₂×Q₈×C₂₉	—	2	2	no	—
20	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
21	C₂×Q₈×C₂₉	Q₈	1	2	yes	—
22	C₂²×C₄×C₂₉	D₄	1	2	yes	—
23	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₂₉	—	2	1	no	—
25	C₂²×Dic₂₉	—	2	1	no	—
26	M₁₆×C₂₉	—	2	2	no	—
27	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
28	C₂×C₈×C₂₉	—	2	2	no	—
29	C₂²⋊Dic₂₉	—	2	2	no	—
30	C₄⋊Dic₂₉	—	2	2	no	—
31	C₄⋊Dic₂₉	—	2	2	no	—
32	C₄⋊Dic₂₉	—	2	2	no	—
33	C₄⋊Dic₂₉	D₄	1	2	yes	—
34	C₄⋊Dic₂₉	D₄	1	2	yes	—
35	C₄×Dic₂₉	—	2	4	no	—
36	C₄×Dic₂₉	—	2	2	no	—
37	C₄×Dic₂₉	—	2	2	no	—
38	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
39	Q₈×C₂₉	—	2	4	no	—
40	Q₈×C₂₉	—	2	4	no	—
41	C₂×C₄×C₂₉	—	2	2	no	—
42	C₂×C₄×C₂₉	—	2	2	no	—
43	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
44	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₂₉	#41	1	2	yes	—
48	C₂×Dic₂₉	—	2	2	no	—
49	C₂×Dic₂₉	—	2	2	no	—
50	C₂×Dic₂₉	—	2	2	no	—
51	C₂×Dic₂₉	—	4	1	no	—
52	C₂×Dic₂₉	—	4	1	no	—
53	C₂×Dic₂₉	—	4	2	no	—
54	C₂×Dic₂₉	—	4	1	no	—
55	C₈×C₂₉	—	2	4	no	—
56	#1857	—	29	1	no	maximal, Sylow
57	C₂²×C₂₉	—	2	1	no	—
58	C₂²×C₂₉	—	2	1	no	—
59	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₂₉	#120	1	1	yes	characteristic
61	C₂²×C₂₉	#123	1	1	yes	characteristic
62	C₄×C₂₉	—	2	4	no	—
63	C₄×C₂₉	C₄×D₄	1	2	yes	—
64	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
65	Dic₂₉	—	4	2	no	—
66	Dic₂₉	—	4	2	no	—
67	Dic₂₉	—	4	2	no	—
68	Dic₂₉	—	8	1	no	—
69	#519	—	29	1	no	—
70	#428	—	29	2	no	—
71	C₂×#101	D₂₉	1	1	yes	characteristic
72	#391	—	29	1	no	—
73	#339	—	29	2	no	—
74	C₂×C₂₉	—	2	1	no	—
75	C₂×C₂₉	—	2	1	no	—
76	C₂×C₂₉	#385	1	1	yes	characteristic
77	C₂×C₂₉	#454	1	1	yes	characteristic
78	C₂×C₂₉	#456	1	1	yes	characteristic
79	C₂²×Q₈	C₂×D₂₉	1	1	yes	characteristic
80	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
81	C₄×Q₈	—	58	2	no	—
82	C₄×Q₈	—	58	2	no	—
83	#117	—	29	2	no	—
84	#117	—	58	2	no	—
85	C₂×C₄⋊C₄	—	29	1	no	—
86	C₂×C₄²	—	29	1	no	—
87	#107	—	58	2	no	—
88	#106	—	58	2	no	—
89	#101	Dic₂₉	1	4	yes	complemented
90	#95	—	58	2	no	—
91	C₂₉	#1857	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	2	2	no	—
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	Dic₅₈	1	2	yes	—
95	C₂×Q₈	C₂×Dic₂₉	1	2	yes	—
96	C₂²×C₄	—	58	1	no	—
97	C₂²×C₄	—	58	1	no	—
98	C₂²×C₄	D₁₁₆	1	2	yes	—
99	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
100	M₁₆	—	2	2	no	—
101	M₁₆	C₂×Dic₂₉	1	4	yes	—
102	C₂×C₈	—	2	2	no	—
103	C₄⋊C₄	—	29	2	no	—
104	C₄⋊C₄	—	29	2	no	—
105	C₄⋊C₄	—	58	2	no	—
106	C₄⋊C₄	—	58	2	no	—
107	C₄⋊C₄	—	58	2	no	—
108	C₂²⋊C₄	—	58	2	no	—
109	C₄²	—	58	4	no	—
110	C₄²	—	58	2	no	—
111	C₄²	—	58	2	no	—
112	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
113	Q₈	—	2	4	no	—
114	Q₈	—	2	4	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	58	2	no	—
118	C₂×C₄	—	58	2	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	—	116	1	no	—
121	C₂×C₄	—	116	1	no	—
122	C₂×C₄	—	116	2	no	—
123	C₂×C₄	—	116	1	no	—
124	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
125	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
126	C₂×C₄	D₄×D₂₉	1	2	yes	—
127	C₂×C₄	#90807	1	2	yes	—
128	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
129	C₈	—	2	4	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	#11745244	1	1	yes	characteristic
133	C₂²	#11745248	1	1	yes	characteristic
134	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
135	C₄	—	2	4	no	—
136	C₄	—	116	2	no	—
137	C₄	—	116	2	no	—
138	C₄	—	116	2	no	—
139	C₄	—	232	1	no	—
140	C₄	#11745240	1	2	yes	—
141	C₄	D₄×Dic₂₉	1	2	yes	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#14271038	1	1	yes	characteristic
145	C₂	#14271338	1	1	yes	characteristic
146	C₂	#14271348	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271641

C₂

yes

maximal, characteristic

#14271205

C₂

yes

maximal

#14271070

C₂

yes

maximal, characteristic

#14270924

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

—

#11745288

—

#11745288

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂₉×#101

C₄

yes

—

—

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

C₂×Q₈×C₂₉

Q₈

yes

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

#1857

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

#519

—

#428

—

C₂×#101

D₂₉

yes

characteristic

#391

—

#339

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

C₂×D₂₉

yes

characteristic

C₂×M₁₆

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#107

—

#106

—

#101

Dic₂₉

yes

complemented

#95

—

C₂₉

#1857

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₅₈

yes

—

C₂×Q₈

C₂×Dic₂₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

100

M₁₆

—

101

M₁₆

C₂×Dic₂₉

yes

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₂³

C₂×D₁₁₆

yes

characteristic

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

116

—

121

C₂×C₄

—

116

—

122

C₂×C₄

—

116

—

123

C₂×C₄

—

116

—

124

C₂×C₄

C₄⋊Dic₂₉

yes

—

125

C₂×C₄

C₂×Dic₅₈

yes

characteristic

126

C₂×C₄

D₄×D₂₉

yes

—

127

C₂×C₄

#90807

yes

—

128

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

129

C₈

—

130

C₂²

—

131

C₂²

—

132

C₂²

#11745244

yes

characteristic

133

C₂²

#11745248

yes

characteristic

134

C₂²

C₂×C₄⋊Dic₂₉

yes

characteristic

135

C₄

—

136

C₄

—

116

—

137

C₄

—

116

—

138

C₄

—

116

—

139

C₄

—

232

—

140

C₄

#11745240

yes

—

141

C₄

D₄×Dic₂₉

yes

—

142

C₂

—

143

C₂

—

144

C₂

#14271038

yes

characteristic

145

C₂

#14271338

yes

characteristic

146

C₂

#14271348

yes

characteristic

	subgroup	G/H
center	C₂²	#11745244
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#101	C₂
socle	C₂²×C₂₉	#120
prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#101	D₂₉
hypocenter	C₂₉	#1857
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

#11745244

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#101

C₂

socle

C₂²×C₂₉

#120

prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
14. C₂₉×#101	C₄	semidirect
89. #101	Dic₂₉	semidirect
91. C₂₉	#1857	semidirect

H ≅ G/N

type

14. C₂₉×#101

C₄

semidirect

89. #101

Dic₂₉

semidirect

91. C₂₉

#1857

semidirect

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

subgroup	index
#14271641	2
#14271205	2
#14271070	2
#14270924	2
C₂×C₂₉×#101	2
#1857	29

subgroup

index

C₂×C₂₉×#101

Subgroups — #16819709

Conjugacy classes of subgroups

Complements

Maximal subgroups