Group #16815742 — subgroups

Subgroups — C₂₉×#2028 #16815742

Order 3712.

246 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 84 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	C₂₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#419	C₂	1	2	yes	maximal
3	C₂₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#343	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#339	C₂	1	2	yes	maximal
6	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	C₂₉×C₄⋊Q₈	—	2	2	no	—
9	C₂₉×#125	—	2	2	no	—
10	C₂₉×C₂²⋊Q₈	—	2	2	no	—
11	C₂₉×#117	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×#103	—	2	2	no	—
15	C₂₉×#103	—	2	2	no	—
16	C₂₉×#95	—	2	2	no	—
17	C₂×Q₈×C₂₉	—	2	2	no	—
18	C₂×Q₈×C₂₉	—	2	1	no	—
19	C₂×Q₈×C₂₉	—	2	2	no	—
20	C₂×Q₈×C₂₉	—	2	2	no	—
21	C₂×Q₈×C₂₉	Q₈	1	2	yes	complemented
22	C₂²×C₄×C₂₉	—	2	1	no	—
23	C₂²×C₄×C₂₉	—	2	1	no	—
24	C₂²×C₄×C₂₉	D₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	M₁₆×C₂₉	—	2	2	no	—
27	M₁₆×C₂₉	—	2	2	no	—
28	C₂×C₈×C₂₉	—	2	2	no	—
29	C₄⋊C₄×C₂₉	—	2	2	no	—
30	C₄⋊C₄×C₂₉	—	2	4	no	—
31	C₄⋊C₄×C₂₉	—	2	2	no	—
32	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
33	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
34	C₂²⋊C₄×C₂₉	—	2	2	no	—
35	C₄²×C₂₉	—	2	2	no	—
36	C₄²×C₂₉	—	2	2	no	—
37	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₂₉	—	2	4	no	—
39	Q₈×C₂₉	—	4	2	no	—
40	Q₈×C₂₉	—	8	2	no	—
41	C₂×C₄×C₂₉	—	2	2	no	—
42	C₂×C₄×C₂₉	—	2	2	no	—
43	C₂×C₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	—	4	1	no	—
47	C₂×C₄×C₂₉	—	4	1	no	—
48	C₂×C₄×C₂₉	—	4	1	no	—
49	C₂×C₄×C₂₉	—	4	1	no	—
50	C₂×C₄×C₂₉	—	4	2	no	—
51	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₄×C₂₉	#41	1	2	yes	—
54	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
55	C₈×C₂₉	—	4	2	no	—
56	#2028	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂²×C₂₉	—	2	1	no	—
58	C₂²×C₂₉	—	2	1	no	—
59	C₂²×C₂₉	#120	1	1	yes	characteristic
60	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂²×C₂₉	#124	1	1	yes	characteristic
62	C₄×C₂₉	—	4	2	no	—
63	C₄×C₂₉	—	4	2	no	—
64	C₄×C₂₉	—	4	2	no	—
65	C₄×C₂₉	—	4	2	no	—
66	C₄×C₂₉	—	4	2	no	—
67	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
68	C₄×C₂₉	#124	1	2	yes	—
69	#544	C₂×C₂₉	1	1	yes	characteristic
70	#419	C₂×C₂₉	1	2	yes	—
71	#391	C₂×C₂₉	1	1	yes	characteristic
72	#343	C₂×C₂₉	1	1	yes	characteristic
73	#339	C₂×C₂₉	1	2	yes	—
74	C₂×C₂₉	—	2	1	no	—
75	C₂×C₂₉	—	2	1	no	—
76	C₂×C₂₉	#393	1	1	yes	characteristic
77	C₂×C₂₉	#455	1	1	yes	characteristic
78	C₂×C₂₉	#456	1	1	yes	characteristic
79	C₂²×Q₈	C₂²×C₂₉	1	1	yes	characteristic
80	C₂×M₁₆	C₂²×C₂₉	1	2	yes	—
81	C₄⋊Q₈	—	2	2	no	—
82	#125	—	2	2	no	—
83	C₂²⋊Q₈	—	2	2	no	—
84	#117	C₂²×C₂₉	1	2	yes	—
85	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
86	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
87	#103	—	2	2	no	—
88	#103	—	2	2	no	—
89	#95	—	2	2	no	—
90	C₂₉	#2028	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×Q₈	—	2	2	no	—
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	—	2	2	no	—
95	C₂×Q₈	Q₈×C₂₉	1	2	yes	complemented
96	C₂²×C₄	—	2	1	no	—
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	D₄×C₂₉	1	2	yes	—
99	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
100	M₁₆	—	2	2	no	—
101	M₁₆	—	2	2	no	—
102	C₂×C₈	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	2	4	no	—
105	C₄⋊C₄	—	2	2	no	—
106	C₄⋊C₄	D₄×C₂₉	1	2	yes	—
107	C₄⋊C₄	D₄×C₂₉	1	2	yes	—
108	C₂²⋊C₄	—	2	2	no	—
109	C₄²	—	2	2	no	—
110	C₄²	—	2	2	no	—
111	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
112	Q₈	—	2	4	no	—
113	Q₈	—	4	2	no	—
114	Q₈	—	8	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
126	C₂×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
127	C₂×C₄	#41×C₂₉	1	2	yes	—
128	C₂×C₄	#41×C₂₉	1	1	yes	characteristic
129	C₈	—	4	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	C₂₉×#120	1	1	yes	characteristic
133	C₂²	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
134	C₂²	C₂₉×#124	1	1	yes	characteristic
135	C₄	—	4	2	no	—
136	C₄	—	4	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	4	2	no	—
139	C₄	—	4	2	no	—
140	C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
141	C₄	C₂₉×#124	1	2	yes	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	C₂₉×#393	1	1	yes	characteristic
145	C₂	C₂₉×#455	1	1	yes	characteristic
146	C₂	C₂₉×#456	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#544

C₂

yes

maximal, characteristic

C₂₉×#419

C₂

yes

maximal

C₂₉×#391

C₂

yes

maximal, characteristic

C₂₉×#343

C₂

yes

maximal, characteristic

C₂₉×#339

C₂

yes

maximal

C₂²×Q₈×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂₉×C₄⋊Q₈

—

C₂₉×#125

—

C₂₉×C₂²⋊Q₈

—

C₂₉×#117

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂₉×#103

—

C₂₉×#103

—

C₂₉×#95

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

Q₈

yes

complemented

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

characteristic

C₈×C₂₉

—

#2028

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₂²×C₂₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₉

#124

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#124

yes

—

#544

C₂×C₂₉

yes

characteristic

#419

C₂×C₂₉

yes

—

#391

C₂×C₂₉

yes

characteristic

#343

C₂×C₂₉

yes

characteristic

#339

C₂×C₂₉

yes

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

C₂²×C₂₉

yes

characteristic

C₂×M₁₆

C₂²×C₂₉

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

C₂²×C₂₉

yes

—

C₂×C₄⋊C₄

C₂²×C₂₉

yes

characteristic

C₂×C₄²

C₂²×C₂₉

yes

—

—

—

C₂₉

#2028

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Q₈×C₂₉

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₂₉

yes

—

C₂²×C₄

C₂³×C₂₉

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

D₄×C₂₉

yes

—

107

C₄⋊C₄

D₄×C₂₉

yes

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₂³

C₂×D₄×C₂₉

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂×D₄×C₂₉

yes

—

126

C₂×C₄

C₂×Q₈×C₂₉

yes

characteristic

127

C₂×C₄

#41×C₂₉

yes

—

128

C₂×C₄

#41×C₂₉

yes

characteristic

129

C₈

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₂₉×#120

yes

characteristic

133

C₂²

C₂₉×C₂²⋊Q₈

yes

characteristic

134

C₂²

C₂₉×#124

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

C₂₉×C₂²⋊Q₈

yes

—

141

C₄

C₂₉×#124

yes

—

142

C₂

—

143

C₂

—

144

C₂

C₂₉×#393

yes

characteristic

145

C₂

C₂₉×#455

yes

characteristic

146

C₂

C₂₉×#456

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂³×C₂₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

#120

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₂₉

prime radical

C₂³×C₂₉

C₂×D₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

N	H ≅ G/N	type
21. C₂×Q₈×C₂₉	Q₈	semidirect
56. #2028	C₂₉	direct (N × H)
90. C₂₉	#2028	direct (N × H)
95. C₂×Q₈	Q₈×C₂₉	semidirect

H ≅ G/N

type

21. C₂×Q₈×C₂₉

Q₈

semidirect

56. #2028

C₂₉

direct (N × H)

90. C₂₉

#2028

direct (N × H)

95. C₂×Q₈

Q₈×C₂₉

semidirect

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

subgroup	index
C₂₉×#544	2
C₂₉×#419	2
C₂₉×#391	2
C₂₉×#343	2
C₂₉×#339	2
#2028	29

subgroup

index

C₂₉×#544

C₂₉×#419

C₂₉×#391

C₂₉×#343

C₂₉×#339

#2028

Subgroups — C₂₉×#2028 #16815742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#2028 #16815742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2028 #16815742