Group #16829807 — subgroups

Subgroups — C₂×#14271517 #16829807

Order 3712.

412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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, complemented
2	#14271517	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11745183	C₂	1	2	yes	maximal, complemented
4	C₂×#11745180	C₂	1	2	yes	maximal
5	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#124	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂₉×#124	—	2	2	no	—
10	C₂₉×#124	C₂²	1	4	yes	—
11	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
14	C₂×#90779	—	2	2	no	—
15	C₂²×#6597	C₂²	1	2	yes	—
16	#11745232	—	2	2	no	—
17	#11745232	C₂²	1	4	yes	complemented
18	#11745183	C₂²	1	8	yes	complemented
19	#11745180	C₂²	1	8	yes	—
20	C₄×#6597	C₂²	1	4	yes	complemented
21	C₂⁴×C₂₉	—	2	1	no	—
22	C₂×Q₈×C₂₉	—	2	1	no	—
23	C₂×Q₈×C₂₉	—	2	4	no	—
24	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
25	C₂×D₄×C₂₉	—	2	1	no	—
26	C₂×D₄×C₂₉	—	2	4	no	—
27	C₂×D₄×C₂₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₂₉	—	2	1	no	—
29	C₂²×C₄×C₂₉	D₄	1	2	yes	—
30	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₂₉	—	2	2	no	—
32	C₂²⋊C₄×C₂₉	—	2	8	no	—
33	C₄²×C₂₉	D₄	1	2	yes	—
34	C₄²×C₂₉	C₂³	1	2	yes	—
35	C₄⋊Dic₂₉	—	2	2	no	—
36	C₄⋊Dic₂₉	C₂³	1	4	yes	—
37	#90779	—	2	8	no	—
38	C₂×#6597	—	2	4	no	—
39	C₂×#6597	C₂³	1	4	yes	—
40	C₂³×C₂₉	—	2	2	no	—
41	C₂³×C₂₉	—	4	2	no	—
42	C₂³×C₂₉	—	4	4	no	—
43	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₂₉	—	2	4	no	—
45	Q₈×C₂₉	—	4	2	no	—
46	D₄×C₂₉	—	2	4	no	—
47	D₄×C₂₉	—	4	2	no	—
48	C₂×C₄×C₂₉	—	2	4	no	—
49	C₂×C₄×C₂₉	—	2	2	no	—
50	C₂×C₄×C₂₉	—	4	2	no	—
51	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
52	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₂₉	#41	1	4	yes	—
54	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
55	C₂×Dic₂₉	—	2	4	no	—
56	C₂×Dic₂₉	—	4	4	no	—
57	#6597	—	2	4	no	—
58	C₂×#488	—	29	1	no	maximal, Sylow
59	C₂²×C₂₉	—	4	2	no	—
60	C₂²×C₂₉	—	4	4	no	—
61	C₂²×C₂₉	—	8	4	no	—
62	C₂²×C₂₉	#124	1	2	yes	—
63	C₂²×C₂₉	#135	1	4	yes	—
64	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
65	C₄×C₂₉	—	2	4	no	—
66	C₄×C₂₉	—	4	2	no	—
67	C₄×C₂₉	#124	1	2	yes	—
68	C₄×C₂₉	C₂×#41	1	2	yes	—
69	Dic₂₉	—	4	4	no	—
70	C₂×#125	—	29	1	no	—
71	C₂×#124	D₂₉	1	1	yes	characteristic
72	#488	—	29	8	no	—
73	C₂×#103	—	29	2	no	—
74	C₂×#102	—	29	2	no	—
75	C₂×C₄×C₈	—	29	1	no	—
76	C₂×C₂₉	—	8	2	no	—
77	C₂×C₂₉	#488	1	4	yes	complemented
78	C₂×C₂₉	C₂×#124	1	1	yes	characteristic
79	C₂×C₂₉	C₂×#135	1	2	yes	—
80	C₂²×Q₈	C₂×D₂₉	1	1	yes	characteristic
81	C₂²×D₄	C₂×D₂₉	1	1	yes	characteristic
82	C₂²×C₈	—	29	2	no	—
83	#125	—	29	4	no	—
84	#125	—	58	2	no	—
85	#124	—	2	2	no	—
86	#124	C₂×D₂₉	1	4	yes	—
87	C₂×C₄⋊C₄	—	29	2	no	—
88	C₂×C₄⋊C₄	—	58	2	no	—
89	C₂×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
91	#103	—	29	8	no	—
92	#102	—	29	8	no	—
93	C₄×C₈	—	29	4	no	—
94	C₂₉	C₂×#488	1	1	yes	characteristic, complemented, Sylow
95	C₂⁴	—	2	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	2	4	no	—
98	C₂×Q₈	C₂²×D₂₉	1	2	yes	—
99	C₂×D₄	—	2	4	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	C₂²×D₂₉	1	2	yes	—
102	C₂²×C₄	—	2	1	no	—
103	C₂²×C₄	—	58	2	no	—
104	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
105	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
106	C₂×C₈	—	29	4	no	—
107	C₂×C₈	—	58	4	no	—
108	C₄⋊C₄	—	29	4	no	—
109	C₄⋊C₄	—	58	2	no	—
110	C₄⋊C₄	—	58	8	no	—
111	C₂²⋊C₄	—	2	8	no	—
112	C₄²	C₂²⋊D₂₉	1	2	yes	—
113	C₄²	C₂²×D₂₉	1	2	yes	—
114	C₂³	—	2	2	no	—
115	C₂³	—	4	2	no	—
116	C₂³	—	4	4	no	—
117	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
118	Q₈	—	2	4	no	—
119	Q₈	—	4	2	no	—
120	D₄	—	2	4	no	—
121	D₄	—	4	2	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	58	4	no	—
126	C₂×C₄	—	116	4	no	—
127	C₂×C₄	#90807	1	4	yes	—
128	C₂×C₄	C₂×C₂²⋊D₂₉	1	4	yes	—
129	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
130	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
131	C₈	—	58	4	no	—
132	C₂²	—	4	2	no	—
133	C₂²	—	4	4	no	—
134	C₂²	—	8	4	no	—
135	C₂²	#11745298	1	2	yes	—
136	C₂²	#11745312	1	4	yes	—
137	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
138	C₄	—	2	4	no	—
139	C₄	—	4	2	no	—
140	C₄	—	116	4	no	—
141	C₄	#11745298	1	2	yes	—
142	C₄	C₂×#90807	1	2	yes	—
143	C₂	—	8	2	no	—
144	C₂	#14271517	1	4	yes	direct product factor
145	C₂	C₂×#11745298	1	1	yes	characteristic
146	C₂	C₂×#11745312	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal, characteristic, complemented

#14271517

C₂

yes

maximal, direct product factor

C₂×#11745183

C₂

yes

maximal, complemented

C₂×#11745180

C₂

yes

maximal

C₂×C₄×#6597

C₂

yes

maximal, characteristic, complemented

C₂×C₂₉×#124

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

characteristic

C₂²×D₄×C₂₉

C₂²

yes

characteristic

C₂₉×#124

—

C₂₉×#124

C₂²

yes

—

C₂×C₂²⋊C₄×C₂₉

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

—

C₂²×#6597

C₂²

yes

—

#11745232

—

#11745232

C₂²

yes

complemented

#11745183

C₂²

yes

complemented

#11745180

C₂²

yes

—

C₄×#6597

C₂²

yes

complemented

C₂⁴×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

C₂³

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

#90779

—

C₂×#6597

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

C₂×#488

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#124

yes

—

C₂²×C₂₉

#135

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#124

yes

—

C₄×C₂₉

C₂×#41

yes

—

Dic₂₉

—

C₂×#125

—

C₂×#124

D₂₉

yes

—

—

—

C₂×C₄×C₈

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂²×Q₈

C₂×D₂₉

yes

characteristic

C₂²×D₄

C₂×D₂₉

yes

characteristic

C₂²×C₈

—

—

—

—

C₂×D₂₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#103

—

#102

—

C₄×C₈

—

C₂₉

C₂×#488

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₂₉

yes

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

C₂²×D₂₉

yes

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²⋊D₂₉

yes

—

105

C₂²×C₄

C₂²×D₂₉

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

C₂²⋊D₂₉

yes

—

113

C₄²

C₂²×D₂₉

yes

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

118

Q₈

—

119

Q₈

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

116

—

127

C₂×C₄

#90807

yes

—

128

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

129

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

130

C₂×C₄

C₂³×D₂₉

yes

characteristic

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

#11745298

yes

—

136

C₂²

#11745312

yes

—

137

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

116

—

141

C₄

#11745298

yes

—

142

C₄

C₂×#90807

yes

—

143

C₂

—

144

C₂

#14271517

yes

direct product factor

145

C₂

C₂×#11745298

yes

characteristic

146

C₂

C₂×#11745312

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂×C₂₉×#124	C₂
socle	C₂³×C₂₉	C₂×D₄
prime radical	C₂²×D₄×C₂₉	C₂²
hypercenter	C₂×#124	D₂₉
hypocenter	C₂₉	C₂×#488
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂×C₂₉×#124

C₂

socle

C₂³×C₂₉

C₂×D₄

prime radical

C₂²×D₄×C₂₉

C₂²

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#11745232	C₂	semidirect
2. #14271517	C₂	direct (N × H)
3. C₂×#11745183	C₂	semidirect
5. C₂×C₄×#6597	C₂	semidirect
17. #11745232	C₂²	semidirect
18. #11745183	C₂²	semidirect
20. C₄×#6597	C₂²	semidirect
77. C₂×C₂₉	#488	semidirect
94. C₂₉	C₂×#488	semidirect
144. C₂	#14271517	direct (N × H)

H ≅ G/N

type

1. C₂×#11745232

C₂

semidirect

2. #14271517

C₂

direct (N × H)

3. C₂×#11745183

C₂

semidirect

5. C₂×C₄×#6597

C₂

semidirect

17. #11745232

C₂²

semidirect

18. #11745183

C₂²

semidirect

20. C₄×#6597

C₂²

semidirect

77. C₂×C₂₉

#488

semidirect

94. C₂₉

C₂×#488

semidirect

144. C₂

#14271517

direct (N × H)

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

subgroup	index
C₂×#11745232	2
#14271517	2
C₂×#11745183	2
C₂×#11745180	2
C₂×C₄×#6597	2
C₂×C₂₉×#124	2
C₂×#488	29

subgroup

index

C₂×C₄×#6597

C₂×C₂₉×#124

C₂×#488

Subgroups — C₂×#14271517 #16829807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#14271517 #16829807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271517 #16829807