Group #16821050 — subgroups

Subgroups — #16821050

Order 3712.

214 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14271033	C₂	1	1	yes	maximal, characteristic
2	#14270925	C₂	1	2	yes	maximal
3	#14270925	C₂	1	2	yes	maximal
4	#14270918	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#389	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
7	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	—	2	1	no	—
11	C₂×C₄⋊Dic₂₉	—	2	1	no	—
12	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
13	C₂²×#6597	C₂²	1	2	yes	—
14	C₂₉×#95	—	2	1	no	—
15	C₂²×C₄×C₂₉	—	2	1	no	—
16	C₂²×C₄×C₂₉	—	2	1	no	—
17	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₂₉	—	2	2	no	—
21	C₄⋊C₄×C₂₉	—	2	1	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	—	4	2	no	—
24	C₄⋊C₄×C₂₉	Q₈	1	2	yes	—
25	C₄²×C₂₉	—	2	2	no	—
26	C₄⋊Dic₂₉	—	2	4	no	—
27	C₄⋊Dic₂₉	—	4	2	no	—
28	C₄⋊Dic₂₉	—	4	2	no	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	—	2	1	no	—
34	C₂×C₄×C₂₉	—	2	1	no	—
35	C₂×C₄×C₂₉	—	2	1	no	—
36	C₂×C₄×C₂₉	—	2	1	no	—
37	C₂×C₄×C₂₉	—	2	2	no	—
38	C₂×C₄×C₂₉	—	4	1	no	—
39	C₂×C₄×C₂₉	—	4	1	no	—
40	C₂×C₄×C₂₉	—	4	1	no	—
41	C₂×C₄×C₂₉	—	4	1	no	—
42	C₂×C₄×C₂₉	—	4	1	no	—
43	C₂×C₄×C₂₉	D₈	1	2	yes	—
44	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
45	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
47	C₂×C₄×C₂₉	#41	1	2	yes	—
48	C₂×C₄×C₂₉	#41	1	2	yes	—
49	C₂×Dic₂₉	—	4	2	no	—
50	C₂×Dic₂₉	—	4	2	no	—
51	C₂×Dic₂₉	—	4	2	no	—
52	#6597	—	4	2	no	—
53	#2099	—	29	1	no	maximal, Sylow
54	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₂²×C₂₉	#123	1	1	yes	characteristic
56	C₂²×C₂₉	#124	1	1	yes	characteristic
57	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
58	C₂²×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
59	C₂²×C₂₉	#137	1	1	yes	characteristic
60	C₂²×C₂₉	#137	1	1	yes	characteristic
61	C₄×C₂₉	—	2	2	no	—
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	—	4	2	no	—
64	C₄×C₂₉	—	8	1	no	—
65	C₄×C₂₉	#125	1	2	yes	—
66	C₄×C₂₉	#126	1	2	yes	—
67	Dic₂₉	—	8	2	no	—
68	#389	D₂₉	1	1	yes	characteristic
69	#384	—	29	1	no	—
70	#340	—	29	2	no	—
71	#340	—	29	2	no	—
72	#336	—	29	1	no	—
73	C₂×C₂₉	#400	1	1	yes	characteristic
74	C₂×C₂₉	#474	1	1	yes	characteristic
75	C₂×C₂₉	#475	1	1	yes	characteristic
76	C₂×C₂₉	#480	1	1	yes	characteristic
77	C₂×C₂₉	#483	1	1	yes	characteristic
78	C₂×C₂₉	#486	1	1	yes	characteristic
79	C₂×C₂₉	#491	1	1	yes	characteristic
80	C₂²×C₈	—	29	2	no	—
81	C₂×C₄⋊C₄	—	2	1	no	—
82	C₂×C₄⋊C₄	—	29	2	no	—
83	C₂×C₄⋊C₄	—	58	1	no	—
84	C₂×C₄⋊C₄	—	58	1	no	—
85	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
86	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
87	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
88	#95	—	2	1	no	—
89	C₂₉	#2099	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	2	1	no	—
91	C₂²×C₄	—	2	1	no	—
92	C₂²×C₄	—	58	2	no	—
93	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
94	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
95	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
96	C₂×C₈	—	58	2	no	—
97	C₂×C₈	—	58	2	no	—
98	C₂×C₈	—	58	2	no	—
99	C₄⋊C₄	—	2	1	no	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	—	4	2	no	—
102	C₄⋊C₄	—	58	4	no	—
103	C₄⋊C₄	—	116	2	no	—
104	C₄⋊C₄	—	116	2	no	—
105	C₄⋊C₄	Dic₅₈	1	2	yes	—
106	C₄²	—	2	2	no	—
107	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	116	2	no	—
119	C₂×C₄	—	116	2	no	—
120	C₂×C₄	—	116	2	no	—
121	C₂×C₄	#90782	1	2	yes	—
122	C₂×C₄	#90784	1	2	yes	—
123	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
124	C₂×C₄	#90805	1	1	yes	characteristic
125	C₂×C₄	#90807	1	2	yes	—
126	C₂×C₄	#90809	1	2	yes	—
127	C₈	—	116	2	no	—
128	C₂²	#11745286	1	1	yes	characteristic
129	C₂²	C₂×#90782	1	1	yes	characteristic
130	C₂²	#11745297	1	1	yes	characteristic
131	C₂²	C₂×#90784	1	1	yes	characteristic
132	C₂²	#11745309	1	1	yes	characteristic
133	C₂²	#11745313	1	1	yes	characteristic
134	C₂²	#11745313	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	8	1	no	—
139	C₄	—	232	2	no	—
140	C₄	#11745252	1	2	yes	—
141	C₄	#11745260	1	2	yes	—
142	C₂	#14271102	1	1	yes	characteristic
143	C₂	#14271443	1	1	yes	characteristic
144	C₂	#14271448	1	1	yes	characteristic
145	C₂	#14271474	1	1	yes	characteristic
146	C₂	#14271491	1	1	yes	characteristic
147	C₂	#14271511	1	1	yes	characteristic
148	C₂	#14271533	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271033

C₂

yes

maximal, characteristic

#14270925

C₂

yes

maximal

#14270925

C₂

yes

maximal

#14270918

C₂

yes

maximal, characteristic

C₂₉×#389

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

C₂₉×#95

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

Q₈

yes

—

C₄²×C₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

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

D₈

yes

—

C₂×C₄×C₂₉

SD₁₆

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#2099

—

maximal, Sylow

C₂²×C₂₉

C₂²⋊Q₈

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

C₂×D₈

yes

characteristic

C₂²×C₂₉

C₂×SD₁₆

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#125

yes

—

C₄×C₂₉

#126

yes

—

Dic₂₉

—

#389

D₂₉

yes

—

—

—

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₂×C₄²

C₂×D₂₉

yes

characteristic

#95

—

C₂₉

#2099

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

116

—

104

C₄⋊C₄

—

116

—

105

C₄⋊C₄

Dic₅₈

yes

—

106

C₄²

—

107

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

116

—

119

C₂×C₄

—

116

—

120

C₂×C₄

—

116

—

121

C₂×C₄

#90782

yes

—

122

C₂×C₄

#90784

yes

—

123

C₂×C₄

C₂×Dic₅₈

yes

characteristic

124

C₂×C₄

#90805

yes

characteristic

125

C₂×C₄

#90807

yes

—

126

C₂×C₄

#90809

yes

—

127

C₈

—

116

—

128

C₂²

#11745286

yes

characteristic

129

C₂²

C₂×#90782

yes

characteristic

130

C₂²

#11745297

yes

characteristic

131

C₂²

C₂×#90784

yes

characteristic

132

C₂²

#11745309

yes

characteristic

133

C₂²

#11745313

yes

characteristic

134

C₂²

#11745313

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

232

—

140

C₄

#11745252

yes

—

141

C₄

#11745260

yes

—

142

C₂

#14271102

yes

characteristic

143

C₂

#14271443

yes

characteristic

144

C₂

#14271448

yes

characteristic

145

C₂

#14271474

yes

characteristic

146

C₂

#14271491

yes

characteristic

147

C₂

#14271511

yes

characteristic

148

C₂

#14271533

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#389	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
hypercenter	#389	D₂₉
hypocenter	C₂₉	#2099
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#389

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

D₂₉

C₂₉

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #389

N	H ≅ G/N	type
89. C₂₉	#2099	semidirect

H ≅ G/N

type

89. C₂₉

#2099

semidirect

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

subgroup	index
#14271033	2
#14270925	2
#14270918	2
C₂₉×#389	2
#2099	29

subgroup

index

C₂₉×#389

Subgroups — #16821050

Conjugacy classes of subgroups

Complements

Maximal subgroups