Group #16789256 — subgroups

Subgroups — #16789256

Order 3328.

358 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 168 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×#11718231	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6092	C₂	1	1	yes	maximal, characteristic
3	#13129875	C₂	1	4	yes	maximal
4	#13114524	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6092	C₂²	1	2	yes	—
6	C₂²×#6092	C₂²	1	2	yes	—
7	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
8	C₂×#88055	C₄	1	2	yes	—
9	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
10	#11718593	C₄	1	1	yes	characteristic
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	#11718231	C₄	1	4	yes	complemented
13	C₄×#6092	C₄	1	4	yes	complemented
14	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
17	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
18	C₂²×#1055	C₂³	1	1	yes	characteristic
19	C₂×#6092	—	2	4	no	—
20	C₂×#6092	—	2	4	no	—
21	C₂×#6092	C₂×C₄	1	4	yes	—
22	C₂×#6092	C₂×C₄	1	4	yes	—
23	C₁₃×#97	C₈	1	4	yes	—
24	#88071	C₈	1	4	yes	—
25	#88055	—	2	4	no	—
26	C₈×Dic₁₃	—	2	4	no	—
27	C₄×#1055	C₂×C₄	1	2	yes	—
28	C₄×#1055	C₂×C₄	1	2	yes	—
29	#12592	—	13	1	no	maximal, Sylow
30	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
31	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₃	—	2	2	no	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
36	C₄²×C₁₃	C₄²	1	2	yes	—
37	C₄²×C₁₃	C₂×C₈	1	2	yes	—
38	C₄×Dic₁₃	—	2	2	no	—
39	C₄×Dic₁₃	—	2	2	no	—
40	C₂×#1055	C₄²	1	2	yes	—
41	C₂×#1055	M₁₆	1	4	yes	—
42	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
43	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
44	C₂×#1055	#41	1	4	yes	—
45	#6092	—	2	4	no	—
46	#6092	—	2	4	no	—
47	C₂×#346	—	13	1	no	—
48	C₂×C₄×C₁₆	—	13	1	no	—
49	#1726	—	13	1	no	—
50	#1374	—	13	4	no	—
51	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	—	2	4	no	—
53	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
54	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₃	#117	1	2	yes	—
56	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
58	C₂×Dic₁₃	—	2	4	no	—
59	C₂×Dic₁₃	—	2	8	no	—
60	C₈×C₁₃	—	2	4	no	—
61	#1055	#97	1	4	yes	—
62	#1055	#117	1	2	yes	—
63	#1055	#117	1	2	yes	—
64	C₂²×C₁₆	—	13	2	no	—
65	C₂²×C₁₆	—	13	2	no	—
66	C₂×#97	—	13	2	no	—
67	C₂×#97	#261	1	1	yes	characteristic
68	C₂×C₄×C₈	—	13	1	no	—
69	C₂×C₄×C₈	—	13	2	no	—
70	#376	—	13	1	no	—
71	#346	—	13	4	no	—
72	C₄×C₁₆	—	13	4	no	—
73	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
74	C₂²×C₁₃	#431	1	2	yes	—
75	C₂²×C₁₃	#504	1	4	yes	—
76	C₄×C₁₃	—	2	4	no	—
77	C₄×C₁₃	#376	1	1	yes	characteristic
78	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
79	C₄×C₁₃	#431	1	2	yes	—
80	Dic₁₃	—	4	4	no	—
81	C₂²×C₈	—	13	1	no	—
82	C₂²×C₈	—	13	1	no	—
83	C₂²×C₈	C₂×#261	1	2	yes	—
84	C₂×C₄²	—	13	2	no	—
85	C₂×C₄²	C₂×#261	1	1	yes	characteristic
86	C₂×C₁₆	—	13	4	no	—
87	C₂×C₁₆	—	13	4	no	—
88	C₂×C₁₆	—	26	4	no	—
89	C₂×C₁₆	—	26	4	no	—
90	#97	—	26	4	no	—
91	#97	#1057	1	4	yes	—
92	C₄×C₈	—	13	2	no	—
93	C₄×C₈	—	13	2	no	—
94	C₄×C₈	—	26	4	no	—
95	#95	—	13	4	no	—
96	C₂×C₁₃	#1744	1	1	yes	characteristic
97	C₂×C₁₃	#2108	1	2	yes	—
98	C₂×C₁₃	#2164	1	4	yes	—
99	C₂²×C₄	—	13	4	no	—
100	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
101	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	13	4	no	—
105	C₂×C₈	—	13	1	no	—
106	C₂×C₈	—	13	1	no	—
107	C₂×C₈	—	13	2	no	—
108	C₂×C₈	—	13	4	no	—
109	C₂×C₈	C₂×#1057	1	4	yes	—
110	C₄²	—	26	2	no	—
111	C₄²	—	26	2	no	—
112	C₄²	C₄×#261	1	2	yes	—
113	C₄²	C₂×#1057	1	2	yes	—
114	C₁₆	—	26	4	no	—
115	C₁₆	—	26	4	no	—
116	C₁₃	#12592	1	1	yes	characteristic, complemented, Sylow
117	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	26	4	no	—
120	C₂×C₄	—	26	8	no	—
121	C₂×C₄	C₄×#1057	1	4	yes	—
122	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
123	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
124	C₂×C₄	#88237	1	2	yes	—
125	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
126	C₈	—	2	4	no	—
127	C₈	—	13	4	no	—
128	C₈	—	13	2	no	—
129	C₈	—	13	2	no	—
130	C₂²	#11719049	1	2	yes	—
131	C₂²	#11719096	1	4	yes	—
132	C₂²	C₂×C₄×#1057	1	1	yes	characteristic
133	C₄	—	2	4	no	—
134	C₄	—	52	4	no	—
135	C₄	#11719047	1	1	yes	characteristic
136	C₄	#11719057	1	1	yes	characteristic
137	C₄	#11719119	1	2	yes	—
138	C₂	#13130550	1	1	yes	characteristic
139	C₂	#13131047	1	2	yes	—
140	C₂	#13131203	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718231

C₂

yes

maximal, characteristic

C₂×C₄×#6092

C₂

yes

maximal, characteristic

#13129875

C₂

yes

maximal

#13114524

C₂

yes

maximal, characteristic

C₂²×#6092

C₂²

yes

—

C₂²×#6092

C₂²

yes

—

C₂×C₁₃×#97

C₄

yes

characteristic

C₂×#88055

C₄

yes

—

C₂×C₈×Dic₁₃

C₂²

yes

—

#11718593

C₄

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

#11718231

C₄

yes

complemented

C₄×#6092

C₄

yes

complemented

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

—

—

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

—

C₁₃×#97

C₈

yes

—

#88071

C₈

yes

—

#88055

—

C₈×Dic₁₃

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

—

#12592

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

C₄²

yes

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₂×#1055

C₄²

yes

—

C₂×#1055

M₁₆

yes

—

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

#41

yes

—

#6092

—

#6092

—

C₂×#346

—

C₂×C₄×C₁₆

—

#1726

—

#1374

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄×C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

#1055

#97

yes

—

#1055

#117

yes

—

#1055

#117

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×#97

—

C₂×#97

#261

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

#346

—

C₄×C₁₆

—

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₃

#431

yes

—

C₂²×C₁₃

#504

yes

—

C₄×C₁₃

—

C₄×C₁₃

#376

yes

characteristic

C₄×C₁₃

C₂×#97

yes

characteristic

C₄×C₁₃

#431

yes

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×#261

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

#1057

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

#95

—

C₂×C₁₃

#1744

yes

characteristic

C₂×C₁₃

#2108

yes

—

C₂×C₁₃

#2164

yes

—

C₂²×C₄

—

100

C₂²×C₄

D₁₃⋊C₈

yes

—

101

C₂²×C₄

C₂²×#261

yes

characteristic

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂×#1057

yes

—

110

C₄²

—

111

C₄²

—

112

C₄²

C₄×#261

yes

—

113

C₄²

C₂×#1057

yes

—

114

C₁₆

—

115

C₁₆

—

116

C₁₃

#12592

yes

characteristic, complemented, Sylow

117

C₂³

C₂×D₁₃⋊C₈

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₄×#1057

yes

—

122

C₂×C₄

D₁₃⋊M₁₆

yes

—

123

C₂×C₄

C₂×C₄×#261

yes

characteristic

124

C₂×C₄

#88237

yes

—

125

C₂×C₄

C₂²×#1057

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₂²

#11719049

yes

—

131

C₂²

#11719096

yes

—

132

C₂²

C₂×C₄×#1057

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

#11719047

yes

characteristic

136

C₄

#11719057

yes

characteristic

137

C₄

#11719119

yes

—

138

C₂

#13130550

yes

characteristic

139

C₂

#13131047

yes

—

140

C₂

#13131203

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₂×C₁₃×#97	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#12592
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#261

commutator

C₂²×C₁₃

C₂×C₄×C₈

Fitting

C₂×C₁₃×#97

C₄

socle, prime radical

C₂³×C₁₃

C₂²×C₈

cosocle

C₂²×#1055

C₂³

C₂×#97

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
12. #11718231	C₄	semidirect
13. C₄×#6092	C₄	semidirect
116. C₁₃	#12592	semidirect

H ≅ G/N

type

12. #11718231

C₄

semidirect

13. C₄×#6092

C₄

semidirect

116. C₁₃

#12592

semidirect

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

subgroup	index
C₂×#11718231	2
C₂×C₄×#6092	2
#13129875	2
#13114524	2
#12592	13

subgroup

index

C₂×C₄×#6092

Subgroups — #16789256

Conjugacy classes of subgroups

Complements

Maximal subgroups