Group #16821035 — subgroups

Subgroups — #16821035

Order 3712.

254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11745156	C₂	1	2	yes	maximal
2	C₂×#11745183	C₂	1	2	yes	maximal
3	#14271033	C₂	1	1	yes	maximal, characteristic
4	#14270918	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₂₉	—	2	2	no	—
10	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
11	C₂²×#6597	C₂²	1	2	yes	—
12	C₂₉×#95	—	2	2	no	—
13	#11745183	—	2	4	no	—
14	#11745156	—	2	4	no	—
15	C₂×Q₈×C₂₉	—	2	1	no	—
16	C₂×Q₈×C₂₉	—	2	2	no	—
17	C₂×Q₈×C₂₉	—	2	2	no	—
18	C₂×Q₈×C₂₉	Q₈	1	2	yes	—
19	C₂²×C₄×C₂₉	—	2	1	no	—
20	C₂²×C₄×C₂₉	—	2	1	no	—
21	C₂²×C₄×C₂₉	D₄	1	2	yes	—
22	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₂₉	—	2	2	no	—
24	C₄⋊C₄×C₂₉	—	2	2	no	—
25	C₄²×C₂₉	—	2	2	no	—
26	C₄⋊Dic₂₉	—	2	2	no	—
27	C₄⋊Dic₂₉	—	2	2	no	—
28	C₄⋊Dic₂₉	—	4	4	no	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	D₄	1	4	yes	—
32	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₂₉	—	2	4	no	—
34	Q₈×C₂₉	—	4	2	no	—
35	C₂×C₄×C₂₉	—	2	2	no	—
36	C₂×C₄×C₂₉	—	2	2	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	2	no	—
42	C₂×C₄×C₂₉	SD₁₆	1	4	yes	—
43	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₂₉	#41	1	2	yes	—
47	C₂×Dic₂₉	—	4	2	no	—
48	C₂×Dic₂₉	—	4	4	no	—
49	#6597	—	2	4	no	—
50	#2096	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₂²×C₂₉	#123	1	1	yes	characteristic
53	C₂²×C₂₉	#127	1	1	yes	characteristic
54	C₂²×C₂₉	C₂×SD₁₆	1	2	yes	—
55	C₂²×C₂₉	#137	1	2	yes	—
56	C₄×C₂₉	—	2	4	no	—
57	C₄×C₂₉	—	4	2	no	—
58	C₄×C₂₉	—	8	1	no	—
59	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
60	C₄×C₂₉	#123	1	2	yes	—
61	Dic₂₉	—	8	2	no	—
62	C₂×#106	—	29	2	no	—
63	C₂×#103	—	29	2	no	—
64	#391	D₂₉	1	1	yes	characteristic
65	#384	—	29	1	no	—
66	#336	—	29	1	no	—
67	C₂×C₂₉	#399	1	1	yes	characteristic
68	C₂×C₂₉	#475	1	2	yes	—
69	C₂×C₂₉	#483	1	2	yes	—
70	C₂×C₂₉	#492	1	1	yes	characteristic
71	C₂×C₂₉	#497	1	1	yes	characteristic
72	C₂²×Q₈	C₂×D₂₉	1	1	yes	characteristic
73	C₂²×C₈	—	29	2	no	—
74	C₂×C₄⋊C₄	—	29	2	no	—
75	C₂×C₄⋊C₄	—	58	2	no	—
76	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
77	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
78	#106	—	58	4	no	—
79	#103	—	58	4	no	—
80	#95	—	2	2	no	—
81	C₂₉	#2096	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₈	—	2	1	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	—	2	2	no	—
85	C₂×Q₈	Dic₅₈	1	2	yes	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	58	2	no	—
89	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
91	C₂×C₈	—	29	4	no	—
92	C₂×C₈	—	58	2	no	—
93	C₂×C₈	—	58	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	58	2	no	—
96	C₄⋊C₄	—	58	2	no	—
97	C₄⋊C₄	—	116	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	116	2	no	—
110	C₂×C₄	—	116	4	no	—
111	C₂×C₄	#90784	1	4	yes	—
112	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
113	C₂×C₄	#90805	1	1	yes	characteristic
114	C₂×C₄	D₄×D₂₉	1	2	yes	—
115	C₂×C₄	#90807	1	2	yes	—
116	C₈	—	58	4	no	—
117	C₂²	#11745286	1	1	yes	characteristic
118	C₂²	#11745297	1	1	yes	characteristic
119	C₂²	#11745302	1	1	yes	characteristic
120	C₂²	C₂×#90784	1	2	yes	—
121	C₂²	#11745313	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	4	2	no	—
124	C₄	—	8	1	no	—
125	C₄	—	232	2	no	—
126	C₄	#11745240	1	2	yes	—
127	C₄	#11745245	1	2	yes	—
128	C₂	#14271099	1	1	yes	characteristic
129	C₂	#14271448	1	2	yes	—
130	C₂	#14271491	1	2	yes	—
131	C₂	#14271537	1	1	yes	characteristic
132	C₂	#14271558	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745156

C₂

yes

maximal

C₂×#11745183

C₂

yes

maximal

#14271033

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

C₂₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

C₂₉×#95

—

#11745183

—

#11745156

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

Q₈

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

D₄

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

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

SD₁₆

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#2096

—

maximal, Sylow

C₂²×C₂₉

C₂²⋊Q₈

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

C₂×SD₁₆

yes

—

C₂²×C₂₉

#137

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#123

yes

—

Dic₂₉

—

C₂×#106

—

C₂×#103

—

#391

D₂₉

yes

characteristic

#384

—

#336

—

C₂×C₂₉

#399

yes

characteristic

C₂×C₂₉

#475

yes

—

C₂×C₂₉

#483

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

C₂×D₂₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₂×C₄²

C₂×D₂₉

yes

—

—

—

C₂₉

#2096

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₅₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄²

—

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

116

—

110

C₂×C₄

—

116

—

111

C₂×C₄

#90784

yes

—

112

C₂×C₄

C₂×Dic₅₈

yes

characteristic

113

C₂×C₄

#90805

yes

characteristic

114

C₂×C₄

D₄×D₂₉

yes

—

115

C₂×C₄

#90807

yes

—

116

C₈

—

117

C₂²

#11745286

yes

characteristic

118

C₂²

#11745297

yes

characteristic

119

C₂²

#11745302

yes

characteristic

120

C₂²

C₂×#90784

yes

—

121

C₂²

#11745313

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

232

—

126

C₄

#11745240

yes

—

127

C₄

#11745245

yes

—

128

C₂

#14271099

yes

characteristic

129

C₂

#14271448

yes

—

130

C₂

#14271491

yes

—

131

C₂

#14271537

yes

characteristic

132

C₂

#14271558

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#391	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
hypercenter	#391	D₂₉
hypocenter	C₂₉	#2096
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#391

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

D₂₉

C₂₉

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
81. C₂₉	#2096	semidirect

H ≅ G/N

type

81. C₂₉

#2096

semidirect

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

subgroup	index
C₂×#11745156	2
C₂×#11745183	2
#14271033	2
#14270918	2
C₂₉×#391	2
#2096	29

subgroup

index

C₂₉×#391

Subgroups — #16821035

Conjugacy classes of subgroups

Complements

Maximal subgroups