Group #16819536 — subgroups

Subgroups — #16819536

Order 3712.

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

normal subgroups only

This group has 260 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	C₂×#11745310	C₂	1	1	yes	maximal, characteristic
2	#14271199	C₂	1	2	yes	maximal, complemented
3	#14271137	C₂	1	1	yes	maximal, characteristic
4	#14270919	C₂	1	2	yes	maximal, complemented
5	C₂₉×#410	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#117	C₂²	1	2	yes	—
8	#11745310	—	2	2	no	—
9	#11745310	—	2	2	no	—
10	#11745288	C₂²	1	2	yes	—
11	C₂×#90777	C₄	1	2	yes	complemented
12	C₂×#90777	C₂²	1	1	yes	characteristic
13	C₂²×#6597	C₄	1	2	yes	complemented
14	C₂²×#6597	C₂²	1	1	yes	characteristic
15	C₂₉×#99	—	2	2	no	—
16	#11745182	—	2	2	no	—
17	#11745156	—	2	2	no	—
18	#11745155	—	2	2	no	—
19	#41×C₂₉	—	2	2	no	—
20	#41×C₂₉	—	2	2	no	—
21	C₂×Q₈×C₂₉	Q₈	1	1	yes	characteristic
22	C₂×D₄×C₂₉	D₄	1	2	yes	—
23	C₂×D₄×C₂₉	Q₈	1	1	yes	characteristic
24	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₂₉	—	2	2	no	—
27	C₂²⋊C₄×C₂₉	—	2	2	no	—
28	C₄²×C₂₉	—	2	2	no	—
29	C₂²⋊Dic₂₉	—	2	2	no	—
30	C₄⋊Dic₂₉	—	2	2	no	—
31	C₄×Dic₂₉	—	2	2	no	—
32	#90777	—	2	2	no	—
33	#90777	—	2	4	no	—
34	C₂×#6597	—	2	2	no	—
35	C₂×#6597	—	2	2	no	—
36	C₂×#6597	C₂×C₄	1	2	yes	—
37	C₂×#6597	C₂×C₄	1	1	yes	characteristic
38	C₂×#6597	C₂×C₄	1	1	yes	characteristic
39	C₂×#6597	D₄	1	2	yes	—
40	C₂×#6597	D₄	1	2	yes	—
41	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
42	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₂₉	—	2	2	no	—
44	D₄×C₂₉	—	2	4	no	—
45	D₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	—	2	2	no	—
47	C₂×C₄×C₂₉	—	2	2	no	—
48	C₂×C₄×C₂₉	—	4	2	no	—
49	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
50	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₄×C₂₉	#41	1	2	yes	—
54	C₂×Dic₂₉	—	4	2	no	—
55	#6597	—	2	2	no	—
56	#6597	C₂²⋊C₄	1	1	yes	characteristic
57	#6597	C₂²⋊C₄	1	1	yes	characteristic
58	#6597	C₂²⋊C₄	1	2	yes	—
59	#1812	—	29	1	no	maximal, Sylow
60	C₂²×C₂₉	—	2	2	no	—
61	C₂²×C₂₉	—	4	1	no	—
62	C₂²×C₂₉	—	4	2	no	—
63	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₂₉	#121	1	2	yes	—
65	C₄×C₂₉	—	2	2	no	—
66	C₄×C₂₉	—	8	2	no	—
67	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₄×C₂₉	#117	1	1	yes	characteristic
69	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
70	Dic₂₉	—	8	2	no	—
71	C₂×#131	—	29	1	no	—
72	#427	—	29	2	no	—
73	#410	—	29	1	no	—
74	#410	D₂₉	1	1	yes	characteristic
75	H(3,ℤ/4)	—	29	2	no	—
76	C₂×C₂₉	—	2	2	no	—
77	C₂×C₂₉	—	2	1	no	—
78	C₂×C₂₉	—	4	2	no	—
79	C₂×C₂₉	#380	1	1	yes	characteristic
80	C₂×#41	C₂×D₂₉	1	1	yes	characteristic
81	#131	—	58	2	no	—
82	#131	—	58	2	no	—
83	C₂×M₁₆	—	29	2	no	—
84	C₂×M₁₆	—	29	1	no	—
85	C₂²×C₈	—	29	1	no	—
86	C₂²×C₈	—	29	2	no	—
87	#117	—	29	2	no	—
88	#117	C₂×D₂₉	1	2	yes	—
89	#107	—	58	2	no	—
90	#106	—	58	2	no	—
91	#99	—	2	2	no	—
92	#99	—	58	2	no	—
93	C₂₉	#1812	1	1	yes	characteristic, complemented, Sylow
94	#41	—	2	2	no	—
95	#41	—	2	2	no	—
96	C₂×Q₈	Dic₅₈	1	1	yes	characteristic
97	C₂×D₄	Dic₅₈	1	1	yes	characteristic
98	C₂×D₄	C₂²⋊D₂₉	1	2	yes	—
99	C₂²×C₄	C₄×D₂₉	1	2	yes	—
100	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
101	M₁₆	—	58	4	no	—
102	M₁₆	—	58	2	no	—
103	C₂×C₈	—	29	1	no	—
104	C₂×C₈	—	29	1	no	—
105	C₂×C₈	—	29	2	no	—
106	C₂×C₈	—	29	2	no	—
107	C₂×C₈	—	29	2	no	—
108	C₂×C₈	—	58	2	no	—
109	C₂×C₈	—	58	2	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	—	58	2	no	—
112	C₂²⋊C₄	—	2	2	no	—
113	C₂²⋊C₄	—	58	2	no	—
114	C₄²	—	2	2	no	—
115	C₄²	—	58	2	no	—
116	C₂³	#90779	1	2	yes	—
117	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
118	Q₈	—	2	2	no	—
119	D₄	—	2	4	no	—
120	D₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	116	2	no	—
125	C₂×C₄	#90779	1	2	yes	—
126	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
127	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
128	C₂×C₄	D₄×D₂₉	1	2	yes	—
129	C₂×C₄	#90807	1	2	yes	—
130	C₈	—	29	1	no	—
131	C₈	—	29	1	no	—
132	C₈	—	29	2	no	—
133	C₈	—	58	2	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	4	1	no	—
136	C₂²	—	4	2	no	—
137	C₂²	C₂×#90779	1	1	yes	characteristic
138	C₂²	#11745301	1	2	yes	—
139	C₄	—	2	2	no	—
140	C₄	—	8	2	no	—
141	C₄	—	232	2	no	—
142	C₄	#11745239	1	1	yes	characteristic
143	C₄	#11745240	1	2	yes	—
144	C₄	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
145	C₂	—	2	2	no	—
146	C₂	—	2	1	no	—
147	C₂	—	4	2	no	—
148	C₂	#14271021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745310

C₂

yes

maximal, characteristic

#14271199

C₂

yes

maximal, complemented

#14271137

C₂

yes

maximal, characteristic

#14270919

C₂

yes

maximal, complemented

C₂₉×#410

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₂²

yes

characteristic

C₂₉×#117

C₂²

yes

—

#11745310

—

#11745310

—

#11745288

C₂²

yes

—

C₂×#90777

C₄

yes

complemented

C₂×#90777

C₂²

yes

characteristic

C₂²×#6597

C₄

yes

complemented

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#99

—

#11745182

—

#11745156

—

#11745155

—

#41×C₂₉

—

#41×C₂₉

—

C₂×Q₈×C₂₉

Q₈

yes

characteristic

C₂×D₄×C₂₉

D₄

yes

—

C₂×D₄×C₂₉

Q₈

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

—

—

—

—

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂³×C₂₉

C₄⋊C₄

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

#6597

—

#6597

C₂²⋊C₄

yes

characteristic

#6597

C₂²⋊C₄

yes

characteristic

#6597

C₂²⋊C₄

yes

—

#1812

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#121

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

#117

yes

characteristic

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

—

—

—

D₂₉

yes

characteristic

H(3,ℤ/4)

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#380

yes

characteristic

C₂×#41

C₂×D₂₉

yes

characteristic

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

#117

C₂×D₂₉

yes

—

—

—

—

—

C₂₉

#1812

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

Dic₅₈

yes

characteristic

C₂×D₄

Dic₅₈

yes

characteristic

C₂×D₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₄×D₂₉

yes

—

100

C₂²×C₄

C₂²×D₂₉

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₄²

—

115

C₄²

—

116

C₂³

#90779

yes

—

117

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

118

Q₈

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

116

—

125

C₂×C₄

#90779

yes

—

126

C₂×C₄

C₂×Dic₅₈

yes

characteristic

127

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

128

C₂×C₄

D₄×D₂₉

yes

—

129

C₂×C₄

#90807

yes

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

C₂×#90779

yes

characteristic

138

C₂²

#11745301

yes

—

139

C₄

—

140

C₄

—

141

C₄

—

232

—

142

C₄

#11745239

yes

characteristic

143

C₄

#11745240

yes

—

144

C₄

C₂²⋊C₄×D₂₉

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

#14271021

yes

characteristic

	subgroup	G/H
center	C₄	#11745239
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#410	C₂
socle	C₂×C₂₉	#380
prime radical	C₂×#41×C₂₉	C₂²
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#410	D₂₉
hypocenter	C₂₉	#1812
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

subgroup

G/H

center

C₄

#11745239

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#410

C₂

socle

C₂×C₂₉

#380

prime radical

C₂×#41×C₂₉

C₂²

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

N	H ≅ G/N	type
2. #14271199	C₂	semidirect
4. #14270919	C₂	semidirect
11. C₂×#90777	C₄	semidirect
13. C₂²×#6597	C₄	semidirect
93. C₂₉	#1812	semidirect

H ≅ G/N

type

2. #14271199

C₂

semidirect

4. #14270919

C₂

semidirect

11. C₂×#90777

C₄

semidirect

13. C₂²×#6597

C₄

semidirect

93. C₂₉

#1812

semidirect

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

subgroup	index
C₂×#11745310	2
#14271199	2
#14271137	2
#14270919	2
C₂₉×#410	2
#1812	29

subgroup

index

C₂₉×#410

Subgroups — #16819536

Conjugacy classes of subgroups

Complements

Maximal subgroups