Group #16780307 — subgroups

Subgroups — #16780307

Order 3328.

294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 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	#13130554	C₂	1	1	yes	maximal, characteristic
2	#13130050	C₂	1	1	yes	maximal, characteristic
3	#13129661	C₂	1	2	yes	maximal
4	#13129659	C₂	1	2	yes	maximal
5	#13113118	C₂	1	1	yes	maximal, characteristic
6	#11719057	C₂²	1	1	yes	characteristic
7	#11719049	C₂²	1	2	yes	—
8	#11719047	C₂²	1	1	yes	characteristic
9	#11718346	C₂²	1	2	yes	—
10	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	(C₂×#261)⋊C₈	C₄	1	4	yes	—
12	#1057⋊C₈	C₄	1	4	yes	complemented
13	C₈²×C₁₃	C₄	1	1	yes	characteristic, complemented
14	#11718046	C₄	1	2	yes	complemented
15	C₈×#1055	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×#261	C₂×C₄	1	2	yes	—
17	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
18	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
19	C₄²×D₁₃	C₂³	1	1	yes	characteristic
20	(C₂×#261)⋊C₄	—	2	2	no	—
21	#88112	—	2	2	no	—
22	#88111	—	2	2	no	—
23	#88110	—	2	2	no	—
24	C₄×#1057	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	#88060	—	2	2	no	—
28	#88054	—	2	2	no	—
29	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
30	C₄×#1055	C₂×C₄	1	2	yes	—
31	C₄×#1055	C₂×C₄	1	1	yes	characteristic
32	#8141	—	13	1	no	maximal, Sylow
33	C₂²×#261	—	2	2	no	—
34	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×D₁₃	#41	1	2	yes	—
36	C₂×#1057	—	2	4	no	—
37	C₂×#1057	—	2	2	no	—
38	C₄×#261	—	2	4	no	—
39	D₁₃⋊C₈	—	2	4	no	—
40	C₂×C₈×C₁₃	—	2	2	no	—
41	C₂×C₈×C₁₃	C₄²	1	2	yes	—
42	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₄×Dic₁₃	#41	1	2	yes	—
45	C₂×#1055	—	2	2	no	—
46	C₂×#1055	C₄²	1	2	yes	—
47	C₈×D₁₃	—	2	4	no	—
48	#1746	—	13	1	no	—
49	#1452	—	13	1	no	—
50	#1450	—	13	1	no	—
51	#1275	—	13	2	no	—
52	#1274	—	13	2	no	—
53	C₂²×D₁₃	#117	1	1	yes	characteristic
54	C₂×#261	—	4	4	no	—
55	C₂×#261	—	4	2	no	—
56	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₁₃	#117	1	2	yes	—
58	C₂×Dic₁₃	#117	1	2	yes	—
59	C₂×Dic₁₃	#117	1	1	yes	characteristic
60	C₄×D₁₃	—	4	2	no	—
61	C₄×D₁₃	#131	1	4	yes	—
62	#1057	—	4	4	no	—
63	#1057	—	4	2	no	—
64	C₈×C₁₃	—	2	2	no	—
65	C₈×C₁₃	—	4	2	no	—
66	#1055	—	2	2	no	—
67	#1055	—	4	2	no	—
68	#431	—	13	2	no	—
69	#431	—	13	2	no	—
70	C₂×#97	—	13	1	no	—
71	C₂×C₄×C₈	—	13	1	no	—
72	#376	—	13	1	no	—
73	#336	—	13	4	no	—
74	#322	—	13	4	no	—
75	#322	—	13	2	no	—
76	C₈²	—	13	1	no	—
77	C₈²	#261	1	1	yes	characteristic, complemented
78	C₂²×C₁₃	#376	1	1	yes	characteristic
79	C₂×D₁₃	—	2	2	no	—
80	C₂×D₁₃	#433	1	2	yes	—
81	#261	—	8	2	no	—
82	C₄×C₁₃	—	2	2	no	—
83	C₄×C₁₃	#405	1	2	yes	—
84	Dic₁₃	—	2	2	no	—
85	Dic₁₃	#433	1	2	yes	—
86	C₂²×C₈	—	13	2	no	—
87	C₂²×C₈	—	13	2	no	—
88	C₂×C₄²	—	13	1	no	—
89	C₂×C₄²	—	13	2	no	—
90	C₄⋊C₈	—	26	2	no	—
91	C₄⋊C₈	—	26	2	no	—
92	C₂²⋊C₈	—	26	2	no	—
93	C₂²⋊C₈	—	26	2	no	—
94	#97	—	26	2	no	—
95	C₄×C₈	—	13	2	no	—
96	C₄×C₈	—	13	4	no	—
97	C₄×C₈	—	13	1	no	—
98	C₄×C₈	—	13	2	no	—
99	C₄×C₈	C₂×#261	1	2	yes	—
100	C₄×C₈	C₂×#261	1	1	yes	characteristic
101	#95	—	26	2	no	—
102	C₂×C₁₃	#1746	1	1	yes	characteristic
103	C₂×C₁₃	#1747	1	2	yes	—
104	D₁₃	—	2	2	no	—
105	C₂²×C₄	—	13	1	no	—
106	C₂²×C₄	—	13	2	no	—
107	C₂²×C₄	—	26	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	13	2	no	—
110	C₂×C₈	—	26	4	no	—
111	C₂×C₈	—	26	4	no	—
112	C₂×C₈	—	26	2	no	—
113	C₂×C₈	—	26	4	no	—
114	C₂×C₈	—	26	2	no	—
115	C₂×C₈	C₄×#261	1	2	yes	—
116	C₄²	—	13	1	no	—
117	C₄²	—	13	2	no	—
118	C₄²	—	26	4	no	—
119	C₄²	C₂²×#261	1	1	yes	characteristic
120	C₁₃	#8141	1	1	yes	characteristic, complemented, Sylow
121	C₂³	—	13	1	no	—
122	C₂×C₄	—	13	1	no	—
123	C₂×C₄	—	13	4	no	—
124	C₂×C₄	—	13	2	no	—
125	C₂×C₄	—	52	2	no	—
126	C₂×C₄	—	52	2	no	—
127	C₂×C₄	—	52	4	no	—
128	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
129	C₂×C₄	#88237	1	2	yes	—
130	C₈	—	2	2	no	—
131	C₈	—	4	2	no	—
132	C₈	—	26	2	no	—
133	C₈	—	52	2	no	—
134	C₈	—	52	2	no	—
135	C₈	—	52	4	no	—
136	C₂²	—	13	2	no	—
137	C₂²	—	26	2	no	—
138	C₂²	#11719057	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	13	2	no	—
141	C₄	—	26	2	no	—
142	C₄	—	104	2	no	—
143	C₄	#11719089	1	2	yes	—
144	C₂	—	26	2	no	—
145	C₂	#13130554	1	1	yes	characteristic
146	C₂	#13130557	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130554

C₂

yes

maximal, characteristic

#13130050

C₂

yes

maximal, characteristic

#13129661

C₂

yes

maximal

#13129659

C₂

yes

maximal

#13113118

C₂

yes

maximal, characteristic

#11719057

C₂²

yes

characteristic

#11719049

C₂²

yes

—

#11719047

C₂²

yes

characteristic

#11718346

C₂²

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

(C₂×#261)⋊C₈

C₄

yes

—

#1057⋊C₈

C₄

yes

complemented

C₈²×C₁₃

C₄

yes

characteristic, complemented

#11718046

C₄

yes

complemented

C₈×#1055

C₄

yes

characteristic, complemented

C₂×C₄×#261

C₂×C₄

yes

—

C₂×D₁₃⋊C₈

C₂×C₄

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₄²×D₁₃

C₂³

yes

characteristic

(C₂×#261)⋊C₄

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

#88060

—

#88054

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

characteristic

#8141

—

maximal, Sylow

C₂²×#261

—

C₂×C₄×D₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₁₃

#41

yes

—

C₂×#1057

—

C₂×#1057

—

C₄×#261

—

D₁₃⋊C₈

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

#41

yes

—

C₂×#1055

—

C₂×#1055

C₄²

yes

—

C₈×D₁₃

—

—

—

—

—

—

C₂²×D₁₃

yes

—

—

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×Dic₁₃

#117

yes

—

C₂×Dic₁₃

#117

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

#131

yes

—

#1057

—

#1057

—

C₈×C₁₃

—

C₈×C₁₃

—

—

—

—

—

C₂×#97

—

C₂×C₄×C₈

—

—

—

—

—

C₈²

—

C₈²

#261

yes

characteristic, complemented

C₂²×C₁₃

#376

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

#433

yes

—

#261

—

C₄×C₁₃

—

C₄×C₁₃

#405

yes

—

Dic₁₃

—

Dic₁₃

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#261

yes

—

100

C₄×C₈

C₂×#261

yes

characteristic

101

#95

—

102

C₂×C₁₃

#1746

yes

characteristic

103

C₂×C₁₃

#1747

yes

—

104

D₁₃

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₄×#261

yes

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

C₂²×#261

yes

characteristic

120

C₁₃

#8141

yes

characteristic, complemented, Sylow

121

C₂³

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×C₄×#261

yes

characteristic

129

C₂×C₄

#88237

yes

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

—

138

C₂²

#11719057

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

104

—

143

C₄

#11719089

yes

—

144

C₂

—

145

C₂

#13130554

yes

characteristic

146

C₂

#13130557

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×#261
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	#376
prime radical	C₂²×D₁₃	#117
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#8141
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈²

subgroup

G/H

center

C₂×C₄

C₂×C₄×#261

commutator

C₂×C₄×C₁₃

C₂×C₄²

Frattini

C₄²

C₂²×#261

Fitting

C₈²×C₁₃

C₄

C₂²×C₁₃

C₂²×D₁₃

C₄²×D₁₃

C₂³

C₈²

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ C₈²

N	H ≅ G/N	type
12. #1057⋊C₈	C₄	semidirect
13. C₈²×C₁₃	C₄	semidirect
14. #11718046	C₄	semidirect
15. C₈×#1055	C₄	semidirect
77. C₈²	#261	semidirect
120. C₁₃	#8141	semidirect

H ≅ G/N

type

12. #1057⋊C₈

C₄

semidirect

13. C₈²×C₁₃

C₄

semidirect

14. #11718046

C₄

semidirect

15. C₈×#1055

C₄

semidirect

77. C₈²

#261

semidirect

120. C₁₃

#8141

semidirect

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

subgroup	index
#13130554	2
#13130050	2
#13129661	2
#13129659	2
#13113118	2
#8141	13

subgroup

index

Subgroups — #16780307

Conjugacy classes of subgroups

Complements

Maximal subgroups