Group #16789267 — subgroups

Subgroups — #16789267

Order 3328.

354 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 156 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	C₄×#88106	C₂	1	2	yes	maximal
2	#13129878	C₂	1	4	yes	maximal
3	C₄×#88055	C₂	1	1	yes	maximal, characteristic
4	C₂×#88106	C₂²	1	4	yes	—
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×#88055	C₄	1	2	yes	—
7	C₂×#88055	C₂²	1	2	yes	—
8	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
9	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
10	#11718231	C₄	1	4	yes	complemented
11	C₄×#6092	C₄	1	4	yes	complemented
12	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₃	—	2	2	no	—
15	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
16	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
17	C₂²×#1055	C₂³	1	1	yes	characteristic
18	#88106	—	2	8	no	—
19	C₂×#6092	C₂×C₄	1	8	yes	—
20	C₄×C₈×C₁₃	—	2	2	no	—
21	#88055	—	2	4	no	—
22	#88055	C₈	1	8	yes	—
23	C₄×#1055	C₂×C₄	1	2	yes	—
24	C₄×#1055	C₂×C₄	1	2	yes	—
25	#12594	—	13	1	no	maximal, Sylow
26	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
27	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×Dic₁₃	—	2	2	no	—
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
32	C₄²×C₁₃	C₄²	1	1	yes	characteristic
33	C₄²×C₁₃	C₄²	1	1	yes	characteristic
34	C₄²×C₁₃	M₁₆	1	2	yes	—
35	C₄×Dic₁₃	—	2	2	no	—
36	C₄×Dic₁₃	—	4	4	no	—
37	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
38	C₂×#1055	C₄²	1	2	yes	—
39	C₂×#1055	C₂×C₈	1	4	yes	—
40	C₂×#1055	C₂²×C₄	1	2	yes	—
41	C₂×#1055	#41	1	4	yes	—
42	#6092	—	2	8	no	—
43	C₄×M₃₂	—	13	2	no	—
44	C₄×#97	—	13	1	no	—
45	#1375	—	13	4	no	—
46	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₃	—	2	4	no	—
48	C₂×C₄×C₁₃	#97	1	2	yes	—
49	C₂×C₄×C₁₃	#97	1	2	yes	—
50	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
51	C₂×C₄×C₁₃	#117	1	2	yes	—
52	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
53	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
54	C₂×Dic₁₃	—	2	4	no	—
55	C₂×Dic₁₃	—	4	4	no	—
56	C₈×C₁₃	—	2	4	no	—
57	#1055	C₄×C₈	1	4	yes	—
58	#1055	#117	1	4	yes	—
59	C₂×M₃₂	—	13	4	no	—
60	C₂×#97	—	13	2	no	—
61	C₂×#97	—	13	2	no	—
62	C₂×C₄×C₈	—	13	1	no	—
63	C₂×C₄×C₈	#261	1	1	yes	characteristic
64	C₄³	—	13	1	no	—
65	#346	—	13	4	no	—
66	C₄×C₁₆	—	13	4	no	—
67	C₂²×C₁₃	—	2	2	no	—
68	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
69	C₂²×C₁₃	#431	1	2	yes	—
70	C₄×C₁₃	—	2	2	no	—
71	C₄×C₁₃	#347	1	4	yes	—
72	C₄×C₁₃	#376	1	1	yes	characteristic
73	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
74	C₄×C₁₃	#431	1	2	yes	—
75	Dic₁₃	—	4	4	no	—
76	C₂²×C₈	—	13	1	no	—
77	C₂²×C₈	—	13	1	no	—
78	C₂²×C₈	C₂×#261	1	2	yes	—
79	C₂×C₄²	—	13	2	no	—
80	C₂×C₄²	—	26	2	no	—
81	C₂×C₄²	C₂×#261	1	1	yes	characteristic
82	M₃₂	—	26	8	no	—
83	C₂×C₁₆	—	13	8	no	—
84	#97	—	13	8	no	—
85	#97	—	26	4	no	—
86	C₄×C₈	—	2	2	no	—
87	C₄×C₈	—	13	2	no	—
88	C₄×C₈	—	13	2	no	—
89	C₂×C₁₃	—	2	2	no	—
90	C₂×C₁₃	#1744	1	1	yes	characteristic
91	C₂×C₁₃	C₂×#347	1	2	yes	—
92	C₂²×C₄	—	26	2	no	—
93	C₂²×C₄	#6118	1	2	yes	—
94	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	13	4	no	—
98	C₂×C₈	—	13	2	no	—
99	C₂×C₈	—	13	2	no	—
100	C₂×C₈	—	13	4	no	—
101	C₂×C₈	D₁₃⋊C₈	1	4	yes	—
102	C₄²	—	13	4	no	—
103	C₄²	—	26	2	no	—
104	C₄²	—	52	4	no	—
105	C₄²	C₄×#261	1	1	yes	characteristic
106	C₄²	C₄×#261	1	1	yes	characteristic
107	C₄²	#6122	1	2	yes	—
108	C₁₆	—	26	8	no	—
109	C₁₃	#12594	1	1	yes	characteristic, complemented, Sylow
110	C₂³	C₂×#6118	1	1	yes	characteristic
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	26	4	no	—
113	C₂×C₄	—	52	4	no	—
114	C₂×C₄	#88110	1	2	yes	—
115	C₂×C₄	#88110	1	2	yes	—
116	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
117	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
118	C₂×C₄	#88237	1	2	yes	—
119	C₂×C₄	C₂×#6122	1	1	yes	characteristic
120	C₈	—	2	4	no	—
121	C₈	—	13	4	no	—
122	C₈	—	13	4	no	—
123	C₂²	—	2	2	no	—
124	C₂²	#11719051	1	2	yes	—
125	C₂²	C₂×#88110	1	1	yes	characteristic
126	C₄	—	2	2	no	—
127	C₄	—	52	4	no	—
128	C₄	#11718262	1	4	yes	—
129	C₄	C₄×D₁₃⋊C₈	1	1	yes	characteristic
130	C₄	#11719057	1	1	yes	characteristic
131	C₄	#11719125	1	2	yes	—
132	C₂	—	2	2	no	—
133	C₂	#13130551	1	1	yes	characteristic
134	C₂	C₂×#11718262	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#88106

C₂

yes

maximal

#13129878

C₂

yes

maximal

C₄×#88055

C₂

yes

maximal, characteristic

C₂×#88106

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₄

yes

characteristic

C₂×#88055

C₄

yes

—

C₂×#88055

C₂²

yes

—

C₄²×Dic₁₃

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×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

characteristic

#88106

—

C₂×#6092

C₂×C₄

yes

—

C₄×C₈×C₁₃

—

#88055

—

#88055

C₈

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

—

#12594

—

maximal, Sylow

C₂²×C₄×C₁₃

M₁₆

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

C₄²

yes

characteristic

C₄²×C₁₃

C₄²

yes

characteristic

C₄²×C₁₃

M₁₆

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

C₄²

yes

—

C₂×#1055

C₂×C₈

yes

—

C₂×#1055

C₂²×C₄

yes

—

C₂×#1055

#41

yes

—

#6092

—

C₄×M₃₂

—

C₄×#97

—

#1375

—

C₂³×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#97

yes

—

C₂×C₄×C₁₃

#97

yes

—

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

#1055

C₄×C₈

yes

—

#1055

#117

yes

—

C₂×M₃₂

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

#261

yes

characteristic

C₄³

—

#346

—

C₄×C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×#97

yes

characteristic

C₂²×C₁₃

#431

yes

—

C₄×C₁₃

—

C₄×C₁₃

#347

yes

—

C₄×C₁₃

#376

yes

characteristic

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

#431

yes

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×#261

yes

characteristic

M₃₂

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#1744

yes

characteristic

C₂×C₁₃

C₂×#347

yes

—

C₂²×C₄

—

C₂²×C₄

#6118

yes

—

C₂²×C₄

C₂²×#261

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

D₁₃⋊C₈

yes

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

C₄×#261

yes

characteristic

106

C₄²

C₄×#261

yes

characteristic

107

C₄²

#6122

yes

—

108

C₁₆

—

109

C₁₃

#12594

yes

characteristic, complemented, Sylow

110

C₂³

C₂×#6118

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#88110

yes

—

115

C₂×C₄

#88110

yes

—

116

C₂×C₄

C₂×D₁₃⋊C₈

yes

—

117

C₂×C₄

C₂×C₄×#261

yes

characteristic

118

C₂×C₄

#88237

yes

—

119

C₂×C₄

C₂×#6122

yes

characteristic

120

C₈

—

121

C₈

—

122

C₈

—

123

C₂²

—

124

C₂²

#11719051

yes

—

125

C₂²

C₂×#88110

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

#11718262

yes

—

129

C₄

C₄×D₁₃⋊C₈

yes

characteristic

130

C₄

#11719057

yes

characteristic

131

C₄

#11719125

yes

—

132

C₂

—

133

C₂

#13130551

yes

characteristic

134

C₂

C₂×#11718262

yes

—

	subgroup	G/H
center	C₄²	C₄×#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#12594
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₄²

C₄×#261

commutator

C₄×C₁₃

C₂×C₄×C₈

Frattini

C₂²×C₄

C₂²×#261

Fitting

C₂×C₄×C₈×C₁₃

C₄

socle

C₂²×C₁₃

C₂×#97

prime radical

C₂³×C₁₃

C₂×M₁₆

cosocle

C₂²×#1055

C₂³

C₂×C₄×C₈

C₁₃

G ▷ C₄×C₁₃ ▷ C₁₃

C₁ ◁ C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
10. #11718231	C₄	semidirect
11. C₄×#6092	C₄	semidirect
109. C₁₃	#12594	semidirect

H ≅ G/N

type

10. #11718231

C₄

semidirect

11. C₄×#6092

C₄

semidirect

109. C₁₃

#12594

semidirect

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

subgroup	index
C₄×#88106	2
#13129878	2
C₄×#88055	2
#12594	13

subgroup

index

Subgroups — #16789267

Conjugacy classes of subgroups

Complements

Maximal subgroups