Group #16790233 — subgroups

Subgroups — #16790233

Order 3328.

282 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 104 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	#13130776	C₂	1	2	yes	maximal
2	#13129896	C₂	1	4	yes	maximal
3	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#88104	C₂²	1	4	yes	—
5	C₂×#88103	—	2	2	no	—
6	#11719053	—	2	2	no	—
7	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
8	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
10	C₁₆×Dic₁₃	C₄	1	2	yes	—
11	C₄×#6090	C₄	1	1	yes	characteristic
12	C₂×#6118	—	2	4	no	—
13	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
14	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
15	C₄²×D₁₃	D₄	1	1	yes	characteristic
16	#88112	—	4	4	no	—
17	#88104	—	2	8	no	—
18	#88103	—	4	4	no	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
23	C₂×#6090	C₂×C₄	1	2	yes	—
24	C₄×#1055	Q₈	1	1	yes	characteristic
25	C₁₆×D₁₃	—	2	4	no	—
26	#12891	—	13	1	no	maximal, Sylow
27	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
28	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×#1057	—	4	4	no	—
30	#6118	—	4	4	no	—
31	#6118	—	4	4	no	—
32	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
36	C₄×Dic₁₃	D₈	1	2	yes	—
37	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
38	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
39	C₈×D₁₃	SD₁₆	1	4	yes	—
40	C₈×D₁₃	#41	1	4	yes	—
41	C₁₃×C₁₆	—	2	2	no	—
42	#6090	—	2	2	no	—
43	C₂×C₄×C₁₆	—	13	1	no	—
44	#1848	—	13	2	no	—
45	#1381	—	13	4	no	—
46	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₃	#107	1	2	yes	—
48	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×Dic₁₃	#107	1	2	yes	—
50	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
51	C₄×D₁₃	—	2	4	no	—
52	C₄×D₁₃	#124	1	2	yes	—
53	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
54	#1057	—	8	4	no	—
55	C₈×C₁₃	#106	1	2	yes	—
56	C₈×C₁₃	#117	1	2	yes	—
57	#1055	#106	1	2	yes	—
58	#1055	#125	1	2	yes	—
59	C₂²×C₁₆	—	13	2	no	—
60	C₂×#108	—	13	4	no	—
61	C₂×#108	—	26	2	no	—
62	#423	—	26	2	no	—
63	C₂×C₄×C₈	—	13	1	no	—
64	C₄×C₁₆	—	13	2	no	—
65	C₄×C₁₆	—	13	1	no	—
66	C₄×C₁₆	#261	1	1	yes	characteristic
67	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
68	C₂×D₁₃	—	2	2	no	—
69	C₂×D₁₃	#487	1	2	yes	—
70	C₄×C₁₃	—	2	2	no	—
71	C₄×C₁₃	#382	1	1	yes	characteristic
72	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
73	Dic₁₃	#368	1	4	yes	—
74	Dic₁₃	#486	1	2	yes	—
75	C₂×M₁₆	—	26	4	no	—
76	C₂²×C₈	—	13	1	no	—
77	C₂²×C₈	—	13	1	no	—
78	C₂×C₄²	—	13	1	no	—
79	C₂×C₁₆	—	13	2	no	—
80	C₂×C₁₆	—	26	4	no	—
81	C₂×C₁₆	C₂×#261	1	2	yes	—
82	#108	—	26	8	no	—
83	#108	—	52	4	no	—
84	C₄⋊C₈	—	52	4	no	—
85	C₄×C₈	—	13	1	no	—
86	C₄×C₈	—	13	1	no	—
87	C₄×C₈	—	13	1	no	—
88	C₄×C₈	C₂×#261	1	1	yes	characteristic
89	C₂×C₁₃	#1834	1	1	yes	characteristic
90	C₂×C₁₃	C₂×#368	1	2	yes	—
91	D₁₃	—	2	2	no	—
92	C₂²×C₄	—	13	1	no	—
93	C₂²×C₄	—	13	2	no	—
94	M₁₆	—	52	4	no	—
95	M₁₆	—	52	4	no	—
96	C₂×C₈	—	13	1	no	—
97	C₂×C₈	—	13	1	no	—
98	C₂×C₈	—	13	4	no	—
99	C₂×C₈	—	13	4	no	—
100	C₂×C₈	—	52	4	no	—
101	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
102	C₂×C₈	C₂²×#261	1	1	yes	characteristic
103	C₄²	—	13	2	no	—
104	C₄²	—	13	1	no	—
105	C₄²	C₄⋊#261	1	1	yes	characteristic
106	C₁₆	—	2	2	no	—
107	C₁₆	—	26	2	no	—
108	C₁₃	#12891	1	1	yes	characteristic, complemented, Sylow
109	C₂³	—	13	1	no	—
110	C₂×C₄	—	13	1	no	—
111	C₂×C₄	—	13	2	no	—
112	C₂×C₄	—	13	2	no	—
113	C₂×C₄	—	13	2	no	—
114	C₂×C₄	—	26	4	no	—
115	C₂×C₄	#88102	1	2	yes	—
116	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
117	C₈	—	13	2	no	—
118	C₈	—	13	2	no	—
119	C₈	—	104	4	no	—
120	C₈	#88101	1	2	yes	—
121	C₈	#88237	1	2	yes	—
122	C₂²	—	13	2	no	—
123	C₂²	—	26	2	no	—
124	C₂²	C₂×#88102	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	13	2	no	—
127	C₄	—	13	4	no	—
128	C₄	#11719060	1	1	yes	characteristic
129	C₄	C₂×#88101	1	1	yes	characteristic
130	C₂	—	26	2	no	—
131	C₂	#13130757	1	1	yes	characteristic
132	C₂	D₁₃⋊#368	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130776

C₂

yes

maximal

#13129896

C₂

yes

maximal

C₄×C₁₆×D₁₃

C₂

yes

maximal, characteristic

C₂×#88104

C₂²

yes

—

C₂×#88103

—

#11719053

—

C₂×C₁₆×D₁₃

C₂²

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₄×C₁₃×C₁₆

C₄

yes

characteristic

C₁₆×Dic₁₃

C₄

yes

—

C₄×#6090

C₄

yes

characteristic

C₂×#6118

—

C₂×C₈×D₁₃

D₄

yes

characteristic

C₂×C₈×D₁₃

C₂³

yes

characteristic

C₄²×D₁₃

D₄

yes

—

—

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

Q₈

yes

characteristic

C₂×#6090

C₂×C₄

yes

—

C₄×#1055

Q₈

yes

characteristic

C₁₆×D₁₃

—

#12891

—

maximal, Sylow

C₂×C₄×D₁₃

Q₁₆

yes

—

C₂×C₄×D₁₃

C₂×D₄

yes

—

—

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

D₈

yes

—

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

C₂×Q₈

yes

characteristic

C₈×D₁₃

SD₁₆

yes

—

C₈×D₁₃

#41

yes

—

C₁₃×C₁₆

—

#6090

—

C₂×C₄×C₁₆

—

#1848

—

#1381

—

C₂²×D₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₁₃

#107

yes

—

C₂×Dic₁₃

C₂×D₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

#124

yes

—

C₄×D₁₃

C₂×SD₁₆

yes

—

#1057

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#117

yes

—

#1055

#106

yes

—

#1055

#125

yes

—

C₂²×C₁₆

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

yes

C₂²×C₁₃

yes

C₂×D₁₃

—

C₂×D₁₃

#487

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

yes

—

Dic₁₃

#486

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#261

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₄⋊#261

yes

characteristic

102

C₂×C₈

C₂²×#261

yes

characteristic

103

C₄²

—

104

C₄²

—

105

C₄²

C₄⋊#261

yes

characteristic

106

C₁₆

—

107

C₁₆

—

108

C₁₃

#12891

yes

characteristic, complemented, Sylow

109

C₂³

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

#88102

yes

—

116

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

104

—

120

C₈

#88101

yes

—

121

C₈

#88237

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

C₂×#88102

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

#11719060

yes

characteristic

129

C₄

C₂×#88101

yes

characteristic

130

C₂

—

131

C₂

#13130757

yes

characteristic

132

C₂

D₁₃⋊#368

yes

—

	subgroup	G/H
center	C₂²	C₂×#88102
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂²×D₁₃	C₂×Q₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#12891
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×#88102

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×#261

Fitting

C₄×C₁₃×C₁₆

C₄

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂²×D₁₃

C₂×Q₁₆

cosocle

C₂×C₈×D₁₃

C₂³

C₄×C₁₆

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
108. C₁₃	#12891	semidirect

H ≅ G/N

type

108. C₁₃

#12891

semidirect

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

subgroup	index
#13130776	2
#13129896	2
C₄×C₁₆×D₁₃	2
#12891	13

subgroup

index

#13130776

#13129896

C₄×C₁₆×D₁₃

#12891

Subgroups — #16790233

Conjugacy classes of subgroups

Complements

Maximal subgroups