Group #16836406 — subgroups

Subgroups — #16836406

Order 3712.

314 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 144 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	#14272215	C₂	1	4	yes	maximal, complemented
2	#14272214	C₂	1	4	yes	maximal, complemented
3	#14272188	C₂	1	4	yes	maximal
4	#14272186	C₂	1	1	yes	maximal, characteristic
5	#14272186	C₂	1	1	yes	maximal, characteristic
6	#14271718	C₂	1	1	yes	maximal, characteristic
7	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
8	#11745308	C₄	1	2	yes	—
9	Q₈×Dic₂₉	C₂²	1	2	yes	—
10	#11745259	C₄	1	2	yes	—
11	#11745254	C₂²	1	2	yes	—
12	#11745252	C₄	1	2	yes	—
13	#11745249	C₂²	1	2	yes	—
14	C₄²×D₂₉	C₂²	1	1	yes	characteristic
15	#11745231	C₄	1	1	yes	characteristic
16	#11745220	C₂²	1	2	yes	—
17	#11745220	C₂²	1	2	yes	—
18	#11745220	C₂²	1	4	yes	—
19	#11745219	C₂²	1	2	yes	—
20	#11745219	C₂²	1	2	yes	—
21	#11745218	C₂²	1	2	yes	—
22	#11745218	C₂²	1	2	yes	—
23	#11745218	C₂²	1	4	yes	—
24	C₄⋊#6599	C₂²	1	4	yes	—
25	C₄×#6599	C₂²	1	4	yes	—
26	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
31	C₂×#6599	C₂³	1	4	yes	—
32	C₂×#6599	C₂³	1	4	yes	—
33	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
34	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
35	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
36	#90781	C₂×C₄	1	4	yes	—
37	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
38	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
39	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
40	#90779	C₂×C₄	1	4	yes	—
41	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
42	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
43	C₄×Dic₂₉	C₂³	1	4	yes	—
44	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
45	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
46	Q₈×C₂₉	—	4	2	no	—
47	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
54	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
55	C₄×D₂₉	—	2	2	no	—
56	C₄×D₂₉	—	4	1	no	—
57	C₄×D₂₉	—	4	1	no	—
58	Dic₅₈	—	4	2	no	—
59	#6599	—	2	4	no	—
60	#6599	—	2	4	no	—
61	#2987	—	29	1	no	maximal, Sylow
62	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
63	C₂×D₂₉	—	2	1	no	—
64	C₂×D₂₉	—	2	1	no	—
65	C₂×D₂₉	—	2	1	no	—
66	C₄×C₂₉	—	2	1	no	—
67	C₄×C₂₉	—	2	1	no	—
68	C₄×C₂₉	—	2	1	no	—
69	C₄×C₂₉	—	2	4	no	—
70	Dic₂₉	—	2	4	no	—
71	Dic₂₉	—	2	1	no	—
72	Dic₂₉	—	2	1	no	—
73	Dic₂₉	2₋¹⁺⁴	1	2	yes	—
74	#533	—	29	1	no	—
75	#446	—	29	4	no	—
76	#446	—	29	4	no	—
77	#433	—	29	4	no	—
78	#432	—	29	1	no	—
79	#432	—	29	1	no	—
80	C₂×C₂₉	#519	1	1	yes	characteristic
81	C₂×C₂₉	#568	1	1	yes	characteristic
82	C₂×C₂₉	#568	1	1	yes	characteristic
83	D₂₉	—	4	1	no	—
84	C₄⋊Q₈	—	29	1	no	—
85	C₄⋊Q₈	#1181	1	1	yes	characteristic
86	#125	—	29	2	no	—
87	C₂²⋊Q₈	—	29	2	no	—
88	C₂²⋊Q₈	—	29	2	no	—
89	C₄×Q₈	—	29	2	no	—
90	C₄×Q₈	—	29	2	no	—
91	#117	—	29	2	no	—
92	C₂×C₄²	—	29	1	no	—
93	C₄⋊C₈	—	29	2	no	—
94	C₄⋊C₈	—	29	2	no	—
95	C₄⋊C₈	—	29	4	no	—
96	C₄⋊C₈	—	29	4	no	—
97	C₂²⋊C₈	—	29	2	no	—
98	C₂²⋊C₈	—	29	2	no	—
99	#97	—	29	2	no	—
100	#97	—	29	2	no	—
101	#97	—	29	4	no	—
102	C₄×C₈	—	29	4	no	—
103	C₂₉	#2987	1	1	yes	characteristic, complemented, Sylow
104	C₂×Q₈	—	29	2	no	—
105	C₂×Q₈	C₂×#1181	1	2	yes	—
106	C₂²×C₄	—	29	1	no	—
107	C₂²×C₄	—	29	1	no	—
108	C₂²×C₄	—	29	1	no	—
109	C₂×C₈	—	29	4	no	—
110	C₂×C₈	—	29	4	no	—
111	C₄⋊C₄	—	29	2	no	—
112	C₄⋊C₄	—	29	4	no	—
113	C₄⋊C₄	—	29	4	no	—
114	C₄⋊C₄	—	29	2	no	—
115	C₄⋊C₄	C₂×#1181	1	2	yes	—
116	C₄⋊C₄	C₂×#1181	1	2	yes	—
117	C₂²⋊C₄	—	29	4	no	—
118	C₄²	—	29	4	no	—
119	C₄²	—	29	1	no	—
120	C₄²	—	29	1	no	—
121	C₄²	—	29	1	no	—
122	C₄²	C₂×#1181	1	1	yes	characteristic
123	C₂³	—	29	1	no	—
124	Q₈	—	4	2	no	—
125	Q₈	—	116	2	no	—
126	C₂×C₄	—	29	1	no	—
127	C₂×C₄	—	29	1	no	—
128	C₂×C₄	—	29	1	no	—
129	C₂×C₄	—	29	4	no	—
130	C₂×C₄	—	58	2	no	—
131	C₂×C₄	—	116	1	no	—
132	C₂×C₄	—	116	1	no	—
133	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
134	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
135	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
136	C₂×C₄	C₂²×#1181	1	4	yes	—
137	C₈	—	58	4	no	—
138	C₈	—	58	4	no	—
139	C₂²	—	58	1	no	—
140	C₂²	—	58	1	no	—
141	C₂²	—	58	1	no	—
142	C₂²	C₂³×#1181	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	4	no	—
146	C₄	—	2	1	no	—
147	C₄	—	29	2	no	—
148	C₄	—	58	1	no	—
149	C₄	—	58	1	no	—
150	C₄	—	58	4	no	—
151	C₂	—	116	1	no	—
152	C₂	#14272231	1	1	yes	characteristic
153	C₂	#14272241	1	1	yes	characteristic
154	C₂	#14272243	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272215

C₂

yes

maximal, complemented

#14272214

C₂

yes

maximal, complemented

#14272188

C₂

yes

maximal

#14272186

C₂

yes

maximal, characteristic

#14272186

C₂

yes

maximal, characteristic

#14271718

C₂

yes

maximal, characteristic

C₂₉×C₄⋊Q₈

C₄

yes

characteristic

#11745308

C₄

yes

—

Q₈×Dic₂₉

C₂²

yes

—

#11745259

C₄

yes

—

#11745254

C₂²

yes

—

#11745252

C₄

yes

—

#11745249

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745231

C₄

yes

characteristic

#11745220

C₂²

yes

—

#11745220

C₂²

yes

—

#11745220

C₂²

yes

—

#11745219

C₂²

yes

—

#11745219

C₂²

yes

—

#11745218

C₂²

yes

—

#11745218

C₂²

yes

—

#11745218

C₂²

yes

—

C₄⋊#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×#6599

C₂³

yes

—

C₂×#6599

C₂³

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

#90781

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂³

yes

characteristic

C₄×Dic₂₉

C₂³

yes

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂²×C₄

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂⁴

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

2₋¹⁺⁴

yes

—

—

—

—

—

—

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₄⋊Q₈

—

C₄⋊Q₈

#1181

yes

characteristic

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

100

#97

—

101

#97

—

102

C₄×C₈

—

103

C₂₉

#2987

yes

characteristic, complemented, Sylow

104

C₂×Q₈

—

105

C₂×Q₈

C₂×#1181

yes

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

C₂×#1181

yes

—

116

C₄⋊C₄

C₂×#1181

yes

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

C₂×#1181

yes

characteristic

123

C₂³

—

124

Q₈

—

125

Q₈

—

116

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

116

—

132

C₂×C₄

—

116

—

133

C₂×C₄

C₂²×#1181

yes

characteristic

134

C₂×C₄

C₂²×#1181

yes

characteristic

135

C₂×C₄

C₂²×#1181

yes

characteristic

136

C₂×C₄

C₂²×#1181

yes

—

137

C₈

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₂³×#1181

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₂

—

116

—

152

C₂

#14272231

yes

characteristic

153

C₂

#14272241

yes

characteristic

154

C₂

#14272243

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×C₄⋊Q₈	C₄
prime radical	C₂²×D₂₉	C₂²×C₄
cosocle	C₂×Dic₂₉	C₂⁴
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	#2987
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×#1181

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting

C₂₉×C₄⋊Q₈

C₄

prime radical

C₂²×D₂₉

C₂²×C₄

cosocle

C₂×Dic₂₉

C₂⁴

C₄⋊Q₈

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ C₄⋊Q₈

N	H ≅ G/N	type
1. #14272215	C₂	semidirect
2. #14272214	C₂	semidirect
103. C₂₉	#2987	semidirect

H ≅ G/N

type

1. #14272215

C₂

semidirect

2. #14272214

C₂

semidirect

103. C₂₉

#2987

semidirect

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

subgroup	index
#14272215	2
#14272214	2
#14272188	2
#14272186	2
#14271718	2
#2987	29

subgroup

index

Subgroups — #16836406

Conjugacy classes of subgroups

Complements

Maximal subgroups