Group #16835130 — subgroups

Subgroups — #16835130

Order 3712.

152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 56 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	#14272214	C₂	1	1	yes	maximal, characteristic
2	#14272213	C₂	1	1	yes	maximal, characteristic
3	#14272027	C₂	1	1	yes	maximal, characteristic
4	#14272013	C₂	1	1	yes	maximal, characteristic
5	Q₈⋊#6599	C₂	1	1	yes	maximal, characteristic
6	C₈×#6599	C₂	1	1	yes	maximal, characteristic
7	#14271255	C₂	1	1	yes	maximal, characteristic
8	Q₈×Dic₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90785	C₄	1	1	yes	characteristic
10	#11745249	C₂²	1	1	yes	characteristic
11	#11745220	—	2	1	no	—
12	#11745218	—	2	1	no	—
13	#11745218	—	2	1	no	—
14	C₄⋊#6599	—	2	1	no	—
15	C₄⋊#6599	C₂²	1	1	yes	characteristic
16	C₄⋊#6599	C₂²	1	1	yes	characteristic
17	C₄×#6599	C₂²	1	1	yes	characteristic
18	C₄×#6599	C₂²	1	1	yes	characteristic
19	C₂₉×#103	C₄	1	1	yes	characteristic
20	#11745164	C₄	1	1	yes	characteristic
21	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
22	#11745155	C₄	1	1	yes	characteristic
23	C₂×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
25	C₂×#6599	—	2	1	no	—
26	C₂×#6599	—	2	1	no	—
27	C₂×#6599	—	2	1	no	—
28	C₂×#6599	D₄	1	1	yes	characteristic
29	C₂×#6599	D₄	1	1	yes	characteristic
30	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
31	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
32	#90785	—	2	2	no	—
33	C₄⋊Dic₂₉	—	2	1	no	—
34	C₄⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
35	#90779	—	2	1	no	—
36	C₄×Dic₂₉	—	2	1	no	—
37	C₄×Dic₂₉	—	2	1	no	—
38	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
39	C₂×#6597	C₂×C₄	1	1	yes	characteristic
40	Q₈×C₂₉	—	2	1	no	—
41	Q₈×C₂₉	—	2	1	no	—
42	C₂×C₄×C₂₉	—	2	1	no	—
43	C₂×C₄×C₂₉	—	2	1	no	—
44	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×Dic₂₉	—	2	1	no	—
46	C₂×Dic₂₉	—	2	1	no	—
47	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₂₉	#41	1	1	yes	characteristic
49	Dic₅₈	—	2	1	no	—
50	Dic₅₈	—	2	1	no	—
51	#6599	—	2	2	no	—
52	#6599	—	2	1	no	—
53	#6599	—	4	1	no	—
54	#6599	—	4	1	no	—
55	#6599	Q₁₆	1	2	yes	complemented
56	C₈×C₂₉	—	2	1	no	—
57	#6597	M₁₆	1	2	yes	—
58	#1591	—	29	1	no	maximal, Sylow
59	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
60	C₄×C₂₉	—	4	1	no	—
61	C₄×C₂₉	—	4	1	no	—
62	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
63	C₄×C₂₉	#131	1	1	yes	characteristic
64	Dic₂₉	—	2	1	no	—
65	Dic₂₉	—	4	1	no	—
66	Dic₂₉	—	4	1	no	—
67	Dic₂₉	C₂×Q₁₆	1	1	yes	characteristic
68	Dic₂₉	#135	1	1	yes	characteristic
69	#446	—	29	1	no	—
70	#446	—	29	1	no	—
71	C₄×Q₁₆	—	29	1	no	—
72	#335	—	29	1	no	—
73	Q₈⋊C₈	—	29	1	no	—
74	Q₈⋊C₈	—	29	1	no	—
75	C₈²	—	29	1	no	—
76	C₂×C₂₉	#436	1	1	yes	characteristic
77	C₂×C₂₉	C₄×Q₁₆	1	1	yes	characteristic
78	C₂×C₂₉	#443	1	1	yes	characteristic
79	C₂×Q₁₆	—	29	1	no	—
80	C₄×Q₈	—	29	1	no	—
81	C₄×Q₈	—	29	1	no	—
82	#107	—	29	1	no	—
83	C₄⋊C₈	—	29	1	no	—
84	C₄⋊C₈	—	29	1	no	—
85	C₄⋊C₈	—	58	1	no	—
86	C₄⋊C₈	—	58	1	no	—
87	#103	—	29	1	no	—
88	#103	#1181	1	1	yes	characteristic
89	#97	—	58	1	no	—
90	#97	—	58	1	no	—
91	C₄×C₈	—	29	1	no	—
92	C₄×C₈	—	29	1	no	—
93	C₄×C₈	—	29	1	no	—
94	C₂₉	#1591	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	29	1	no	—
96	C₂×Q₈	C₂×#1181	1	1	yes	characteristic
97	Q₁₆	—	58	2	no	—
98	C₂×C₈	—	29	1	no	—
99	C₂×C₈	—	29	1	no	—
100	C₂×C₈	—	29	1	no	—
101	C₂×C₈	—	58	1	no	—
102	C₂×C₈	—	58	1	no	—
103	C₂×C₈	—	58	1	no	—
104	C₂×C₈	C₂×#1181	1	1	yes	characteristic
105	C₄⋊C₄	—	29	1	no	—
106	C₄⋊C₄	—	58	1	no	—
107	C₄⋊C₄	—	58	1	no	—
108	C₄⋊C₄	C₂×#1181	1	1	yes	characteristic
109	C₄²	—	29	1	no	—
110	C₄²	—	58	1	no	—
111	C₄²	—	58	1	no	—
112	Q₈	—	2	1	no	—
113	Q₈	—	2	1	no	—
114	Q₈	—	58	1	no	—
115	Q₈	—	58	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	29	1	no	—
119	C₂×C₄	—	29	1	no	—
120	C₂×C₄	—	58	1	no	—
121	C₂×C₄	—	58	1	no	—
122	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	29	2	no	—
125	C₈	—	29	2	no	—
126	C₈	—	58	1	no	—
127	C₈	—	58	2	no	—
128	C₈	—	116	1	no	—
129	C₈	—	116	1	no	—
130	C₂²	D₄×#1181	1	1	yes	characteristic
131	C₄	—	4	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	29	1	no	—
134	C₄	—	29	1	no	—
135	C₄	—	58	1	no	—
136	C₄	—	116	1	no	—
137	C₄	—	116	1	no	—
138	C₄	D₂₉⋊M₁₆	1	1	yes	characteristic
139	C₄	#11745346	1	1	yes	characteristic
140	C₂	#14272196	1	1	yes	characteristic
141	C₂	Q₁₆×#1181	1	1	yes	characteristic
142	C₂	#14272206	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272214

C₂

yes

maximal, characteristic

#14272213

C₂

yes

maximal, characteristic

#14272027

C₂

yes

maximal, characteristic

#14272013

C₂

yes

maximal, characteristic

Q₈⋊#6599

C₂

yes

maximal, characteristic

C₈×#6599

C₂

yes

maximal, characteristic

#14271255

C₂

yes

maximal, characteristic

Q₈×Dic₂₉

C₂²

yes

characteristic

C₂×#90785

C₄

yes

characteristic

#11745249

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₄⋊#6599

C₂²

yes

characteristic

C₄×#6599

C₂²

yes

characteristic

C₄×#6599

C₂²

yes

characteristic

C₂₉×#103

C₄

yes

characteristic

#11745164

C₄

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

#11745155

C₄

yes

characteristic

C₂×Q₈×C₂₉

C₂×C₄

yes

characteristic

C₂×Dic₅₈

C₂×C₄

yes

—

—

—

D₄

yes

characteristic

C₂×#6599

D₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₂₉

C₂×C₄

yes

characteristic

#90785

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

characteristic

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

#41

yes

characteristic

Dic₅₈

—

Dic₅₈

—

—

—

—

—

Q₁₆

yes

complemented

C₈×C₂₉

—

#6597

M₁₆

yes

—

#1591

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×M₁₆

yes

characteristic

C₄×C₂₉

#131

yes

characteristic

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

C₂×Q₁₆

yes

Dic₂₉

yes

—

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

Q₈⋊C₈

—

C₈²

—

C₂×C₂₉

#436

yes

characteristic

C₂×C₂₉

C₄×Q₁₆

yes

characteristic

C₂×C₂₉

#443

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

—

yes

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#1591

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×#1181

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×#1181

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

C₂×#1181

yes

characteristic

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₂²×#1181

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

116

—

129

C₈

—

116

—

130

C₂²

D₄×#1181

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

116

—

137

C₄

—

116

—

138

C₄

D₂₉⋊M₁₆

yes

characteristic

139

C₄

#11745346

yes

characteristic

140

C₂

#14272196

yes

characteristic

141

C₂

Q₁₆×#1181

yes

characteristic

142

C₂

#14272206

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#103	C₄
socle, prime radical	C₂²×C₂₉	C₄×D₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	#103	#1181
hypocenter	C₂₉	#1591
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#103

C₄

socle, prime radical

C₂²×C₂₉

C₄×D₄

cosocle

C₄×Dic₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
55. #6599	Q₁₆	semidirect
94. C₂₉	#1591	semidirect

H ≅ G/N

type

55. #6599

Q₁₆

semidirect

94. C₂₉

#1591

semidirect

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

subgroup	index
#14272214	2
#14272213	2
#14272027	2
#14272013	2
Q₈⋊#6599	2
C₈×#6599	2
#14271255	2
#1591	29

subgroup

index

Subgroups — #16835130

Conjugacy classes of subgroups

Complements

Maximal subgroups