Group #16818922 — subgroups

Subgroups — #16818922

Order 3712.

150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271514	C₂	1	1	yes	maximal, characteristic
2	#14271448	C₂	1	1	yes	maximal, characteristic
3	#14271373	C₂	1	1	yes	maximal, characteristic
4	#14270914	C₂	1	1	yes	maximal, characteristic
5	#14270910	C₂	1	1	yes	maximal, characteristic
6	#14270908	C₂	1	1	yes	maximal, characteristic
7	C₈×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
8	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90785	—	2	1	no	—
10	#11745231	C₂²	1	1	yes	characteristic
11	#11745231	C₂²	1	1	yes	characteristic
12	C₂₉×C₄⋊C₈	—	2	1	no	—
13	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₉	—	2	1	no	—
15	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	#11745183	—	2	1	no	—
17	#11745164	—	2	1	no	—
18	#11745164	—	2	1	no	—
19	#11745158	—	2	1	no	—
20	#11745156	—	2	1	no	—
21	C₄⋊#6597	C₂²	1	1	yes	characteristic
22	C₄⋊#6597	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
24	C₂×Dic₅₈	—	2	1	no	—
25	C₂×Dic₅₈	—	2	1	no	—
26	C₂×C₈×C₂₉	—	2	1	no	—
27	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
29	C₄⋊C₄×C₂₉	—	2	1	no	—
30	C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
31	C₄²×C₂₉	—	2	1	no	—
32	C₄²×C₂₉	C₂³	1	1	yes	characteristic
33	#90785	—	4	2	no	—
34	C₄⋊Dic₂₉	—	2	1	no	—
35	C₄⋊Dic₂₉	—	2	1	no	—
36	C₄⋊Dic₂₉	—	2	1	no	—
37	C₄⋊Dic₂₉	—	2	1	no	—
38	C₂×#6597	—	2	1	no	—
39	C₂×#6597	—	2	1	no	—
40	Q₈×C₂₉	—	2	1	no	—
41	Q₈×C₂₉	SD₁₆	1	2	yes	—
42	C₂×C₄×C₂₉	—	2	1	no	—
43	C₂×C₄×C₂₉	—	2	1	no	—
44	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
47	C₂×Dic₂₉	—	4	1	no	—
48	C₂×Dic₂₉	—	4	1	no	—
49	Dic₅₈	—	4	1	no	—
50	Dic₅₈	—	4	1	no	—
51	Dic₅₈	—	4	1	no	—
52	Dic₅₈	—	4	1	no	—
53	C₈×C₂₉	—	2	1	no	—
54	C₈×C₂₉	—	2	1	no	—
55	C₈×C₂₉	—	4	1	no	—
56	#6597	—	4	1	no	—
57	#6597	—	4	1	no	—
58	#1680	—	29	1	no	maximal, Sylow
59	C₂²×C₂₉	#121	1	1	yes	characteristic
60	C₄×C₂₉	—	2	2	no	—
61	C₄×C₂₉	—	2	1	no	—
62	C₄×C₂₉	—	4	1	no	—
63	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
64	C₄×C₂₉	#135	1	1	yes	characteristic
65	C₄×C₂₉	#135	1	1	yes	characteristic
66	C₄×C₂₉	#137	1	1	yes	characteristic
67	Dic₂₉	—	8	1	no	—
68	Dic₂₉	—	8	1	no	—
69	#487	—	29	1	no	—
70	#475	—	29	1	no	—
71	#462	—	29	1	no	—
72	C₈×Q₈	D₂₉	1	1	yes	characteristic
73	#334	—	29	1	no	—
74	#332	—	29	1	no	—
75	#332	—	29	1	no	—
76	C₂×C₂₉	#464	1	1	yes	characteristic
77	C₂×C₂₉	#465	1	1	yes	characteristic
78	C₂×C₂₉	#473	1	1	yes	characteristic
79	C₂×Q₁₆	—	58	1	no	—
80	C₄⋊Q₈	—	29	1	no	—
81	C₄⋊Q₈	—	29	1	no	—
82	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic
83	#106	—	58	1	no	—
84	C₄⋊C₈	—	2	1	no	—
85	C₄⋊C₈	—	29	1	no	—
86	C₄⋊C₈	—	29	1	no	—
87	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic
88	#103	—	58	1	no	—
89	#103	—	58	1	no	—
90	#103	—	58	1	no	—
91	#103	—	58	1	no	—
92	C₄×C₈	—	2	1	no	—
93	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
94	C₂₉	#1680	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	58	1	no	—
96	C₂×Q₈	—	58	1	no	—
97	C₂×Q₈	D₁₁₆	1	1	yes	characteristic
98	Q₁₆	—	116	2	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	58	1	no	—
101	C₂×C₈	—	58	1	no	—
102	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
103	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	58	1	no	—
106	C₄⋊C₄	—	58	1	no	—
107	C₄⋊C₄	—	58	1	no	—
108	C₄⋊C₄	—	58	1	no	—
109	C₄⋊C₄	D₁₁₆	1	1	yes	characteristic
110	C₄²	—	2	1	no	—
111	C₄²	C₂²×D₂₉	1	1	yes	characteristic
112	Q₈	—	2	1	no	—
113	Q₈	—	116	1	no	—
114	Q₈	—	116	1	no	—
115	Q₈	—	116	1	no	—
116	Q₈	—	116	1	no	—
117	Q₈	#90773	1	2	yes	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	116	1	no	—
121	C₂×C₄	—	116	1	no	—
122	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
123	C₂×C₄	#90805	1	1	yes	characteristic
124	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	2	1	no	—
127	C₈	—	4	1	no	—
128	C₈	—	116	1	no	—
129	C₈	—	116	1	no	—
130	C₂²	#11745292	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	232	1	no	—
135	C₄	—	232	1	no	—
136	C₄	C₂×#90773	1	1	yes	characteristic
137	C₄	#11745266	1	1	yes	characteristic
138	C₄	#11745304	1	1	yes	characteristic
139	C₄	#11745312	1	1	yes	characteristic
140	C₂	#14271385	1	1	yes	characteristic
141	C₂	#14271392	1	1	yes	characteristic
142	C₂	#14271438	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271514

C₂

yes

maximal, characteristic

#14271448

C₂

yes

maximal, characteristic

#14271373

C₂

yes

maximal, characteristic

#14270914

C₂

yes

maximal, characteristic

#14270910

C₂

yes

maximal, characteristic

#14270908

C₂

yes

maximal, characteristic

C₈×Q₈×C₂₉

C₂

yes

maximal, characteristic

C₄×Q₈×C₂₉

C₂²

yes

characteristic

C₂×#90785

—

#11745231

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₄⋊#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

D₄

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90785

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

Q₈×C₂₉

—

Q₈×C₂₉

SD₁₆

yes

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

#487

—

#475

—

#462

—

C₈×Q₈

D₂₉

yes

—

—

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₂₉

yes

characteristic

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₂₉

yes

—

—

—

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1680

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₁₁₆

yes

characteristic

Q₁₆

—

116

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

103

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

D₁₁₆

yes

characteristic

110

C₄²

—

111

C₄²

C₂²×D₂₉

yes

characteristic

112

Q₈

—

113

Q₈

—

116

—

114

Q₈

—

116

—

115

Q₈

—

116

—

116

Q₈

—

116

—

117

Q₈

#90773

yes

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

116

—

121

C₂×C₄

—

116

—

122

C₂×C₄

C₂×D₁₁₆

yes

characteristic

123

C₂×C₄

#90805

yes

characteristic

124

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

116

—

129

C₈

—

116

—

130

C₂²

#11745292

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

232

—

135

C₄

—

232

—

136

C₄

C₂×#90773

yes

characteristic

137

C₄

#11745266

yes

characteristic

138

C₄

#11745304

yes

characteristic

139

C₄

#11745312

yes

characteristic

140

C₂

#14271385

yes

characteristic

141

C₂

#14271392

yes

characteristic

142

C₂

#14271438

yes

characteristic

	subgroup	G/H
center	C₂²	#11745292
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₈×Q₈×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	#121
hypercenter	C₈×Q₈	D₂₉
hypocenter	C₂₉	#1680
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

subgroup

G/H

center

C₂²

#11745292

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₈×Q₈×C₂₉

C₂

socle, prime radical

C₂²×C₂₉

#121

hypercenter

C₈×Q₈

D₂₉

hypocenter

C₂₉

#1680

LCS

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

N	H ≅ G/N	type
94. C₂₉	#1680	semidirect

H ≅ G/N

type

94. C₂₉

#1680

semidirect

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

subgroup	index
#14271514	2
#14271448	2
#14271373	2
#14270914	2
#14270910	2
#14270908	2
C₈×Q₈×C₂₉	2
#1680	29

subgroup

index

C₈×Q₈×C₂₉

Subgroups — #16818922

Conjugacy classes of subgroups

Complements

Maximal subgroups