Group #13114987 — subgroups

Subgroups — #13114987

Order 1664.

300 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 153 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×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#88054	C₂	1	4	yes	maximal
3	C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₄	1	2	yes	—
9	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
11	C₂²×#1055	C₂²	1	2	yes	—
12	C₁₃×C₄⋊C₈	—	2	2	no	—
13	#88054	—	2	8	no	—
14	C₄⋊#1055	—	2	2	no	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
19	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	—	2	4	no	—
22	C₄²×C₁₃	D₄	1	2	yes	—
23	C₄²×C₁₃	Q₈	1	2	yes	—
24	C₄×Dic₁₃	—	2	2	no	—
25	C₄×Dic₁₃	—	2	4	no	—
26	C₄×Dic₁₃	C₈	1	4	yes	complemented
27	C₄×Dic₁₃	D₄	1	4	yes	—
28	C₄×Dic₁₃	Q₈	1	4	yes	—
29	C₂×#1055	—	2	2	no	—
30	C₂×#1055	—	2	4	no	—
31	#1842	—	13	1	no	maximal, Sylow
32	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	—	2	2	no	—
34	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
37	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
38	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
42	C₂×Dic₁₃	—	2	2	no	—
43	C₂×Dic₁₃	—	2	2	no	—
44	C₂×Dic₁₃	C₄⋊C₄	1	4	yes	—
45	C₂×Dic₁₃	C₄⋊C₄	1	4	yes	—
46	C₂×Dic₁₃	C₂×C₈	1	4	yes	—
47	C₂×Dic₁₃	M₁₆	1	4	yes	—
48	C₈×C₁₃	—	4	2	no	—
49	#1055	—	4	2	no	—
50	C₂×C₄⋊C₈	—	13	4	no	—
51	C₂×C₄⋊C₈	—	13	1	no	—
52	C₂×C₄⋊C₈	D₁₃	1	1	yes	characteristic
53	C₄³	—	13	1	no	—
54	C₂²×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
55	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
57	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
58	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
59	C₄×C₁₃	—	2	2	no	—
60	C₄×C₁₃	C₄⋊C₈	1	4	yes	complemented
61	C₄×C₁₃	#127	1	1	yes	characteristic
62	C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
63	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
64	Dic₁₃	—	2	4	no	—
65	Dic₁₃	C₄⋊C₈	1	8	yes	complemented
66	C₂²×C₈	—	13	2	no	—
67	C₂²×C₈	C₂×D₁₃	1	2	yes	—
68	C₂×C₄²	—	13	1	no	—
69	C₂×C₄²	—	13	2	no	—
70	C₂×C₄²	—	13	2	no	—
71	C₂×C₄²	—	13	1	no	—
72	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
73	C₄⋊C₈	—	2	2	no	—
74	C₄⋊C₈	—	26	8	no	—
75	C₄⋊C₈	—	26	2	no	—
76	C₂×C₁₃	#384	1	1	yes	characteristic
77	C₂×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
78	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
79	C₂×C₁₃	#423	1	2	yes	—
80	C₂×C₁₃	#423	1	1	yes	characteristic
81	C₂²×C₄	—	13	2	no	—
82	C₂²×C₄	—	13	2	no	—
83	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
84	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
85	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
86	C₂×C₈	—	2	4	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	26	4	no	—
89	C₂×C₈	—	26	2	no	—
90	C₄²	—	13	4	no	—
91	C₄²	—	13	4	no	—
92	C₄²	—	13	4	no	—
93	C₄²	—	26	4	no	—
94	C₄²	—	26	2	no	—
95	C₄²	Dic₂₆	1	2	yes	—
96	C₄²	C₂²⋊D₁₃	1	2	yes	—
97	C₁₃	#1842	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	13	4	no	—
101	C₂×C₄	—	13	4	no	—
102	C₂×C₄	—	13	4	no	—
103	C₂×C₄	—	13	4	no	—
104	C₂×C₄	—	26	2	no	—
105	C₂×C₄	—	26	2	no	—
106	C₂×C₄	C₈×D₁₃	1	2	yes	—
107	C₂×C₄	#6094	1	2	yes	—
108	C₂×C₄	#6101	1	2	yes	—
109	C₂×C₄	#6101	1	2	yes	—
110	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
111	C₂×C₄	D₄×D₁₃	1	2	yes	—
112	C₂×C₄	Q₈×D₁₃	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
114	C₈	—	4	2	no	—
115	C₈	—	52	2	no	—
116	C₂²	C₄⋊C₄×D₁₃	1	2	yes	—
117	C₂²	C₂×C₈×D₁₃	1	1	yes	characteristic
118	C₂²	C₂×#6094	1	1	yes	characteristic
119	C₂²	M₁₆×D₁₃	1	2	yes	—
120	C₂²	C₂×#6101	1	1	yes	characteristic
121	C₄	—	2	2	no	—
122	C₄	—	13	8	no	—
123	C₄	—	26	4	no	—
124	C₄	#88054	1	4	yes	complemented
125	C₄	#88142	1	2	yes	—
126	C₄	#88194	1	1	yes	characteristic
127	C₄	#88198	1	1	yes	characteristic
128	C₂	D₁₃×C₄⋊C₈	1	2	yes	—
129	C₂	#11718498	1	2	yes	—
130	C₂	#11718637	1	1	yes	characteristic
131	C₂	C₂×#88054	1	1	yes	characteristic
132	C₂	#11718779	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#88054

C₂

yes

maximal

C₄²×Dic₁₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#1055

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

—

C₂×C₄×Dic₁₃

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

—

C₂²×#1055

C₂²

yes

—

C₁₃×C₄⋊C₈

—

#88054

—

C₄⋊#1055

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

Q₈

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₈

yes

complemented

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

Q₈

yes

—

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

M₁₆

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×C₈

yes

—

C₂×Dic₁₃

M₁₆

yes

—

C₈×C₁₃

—

#1055

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₁₃

yes

characteristic

C₄³

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

characteristic

C₂²×C₁₃

C₂×M₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₄⋊C₈

yes

complemented

C₄×C₁₃

#127

yes

characteristic

C₄×C₁₃

C₄⋊Q₈

yes

—

C₄×C₁₃

C₄⋊Q₈

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄⋊C₈

yes

complemented

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂×C₁₃

#384

yes

characteristic

C₂×C₁₃

C₂×C₄⋊C₈

yes

—

C₂×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₃

#423

yes

—

C₂×C₁₃

#423

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₂₆

yes

—

C₄²

C₂²⋊D₁₃

yes

—

C₁₃

#1842

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₁₃

yes

—

107

C₂×C₄

#6094

yes

—

108

C₂×C₄

#6101

yes

—

109

C₂×C₄

#6101

yes

—

110

C₂×C₄

C₂×Dic₂₆

yes

characteristic

111

C₂×C₄

D₄×D₁₃

yes

—

112

C₂×C₄

Q₈×D₁₃

yes

—

113

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

C₄⋊C₄×D₁₃

yes

—

117

C₂²

C₂×C₈×D₁₃

yes

characteristic

118

C₂²

C₂×#6094

yes

characteristic

119

C₂²

M₁₆×D₁₃

yes

—

120

C₂²

C₂×#6101

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#88054

yes

complemented

125

C₄

#88142

yes

—

126

C₄

#88194

yes

characteristic

127

C₄

#88198

yes

characteristic

128

C₂

D₁₃×C₄⋊C₈

yes

—

129

C₂

#11718498

yes

—

130

C₂

#11718637

yes

characteristic

131

C₂

C₂×#88054

yes

characteristic

132

C₂

#11718779

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₁₃×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	D₁₃
hypocenter	C₁₃	#1842
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₃

commutator

C₂²×C₁₃

C₂²×C₈

Fitting

C₂×C₁₃×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₃

C₂²×C₄

cosocle

C₂²×C₄×C₁₃

C₂³

hypercenter

C₂×C₄⋊C₈

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
26. C₄×Dic₁₃	C₈	semidirect
60. C₄×C₁₃	C₄⋊C₈	semidirect
65. Dic₁₃	C₄⋊C₈	semidirect
97. C₁₃	#1842	semidirect
124. C₄	#88054	semidirect

H ≅ G/N

type

26. C₄×Dic₁₃

C₈

semidirect

60. C₄×C₁₃

C₄⋊C₈

semidirect

65. Dic₁₃

C₄⋊C₈

semidirect

97. C₁₃

#1842

semidirect

124. C₄

#88054

semidirect

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

subgroup	index
C₂×C₁₃×C₄⋊C₈	2
C₂×#88054	2
C₄²×Dic₁₃	2
C₂×C₄⋊#1055	2
#1842	13

subgroup

index

C₂×C₁₃×C₄⋊C₈

C₂×#88054

C₄²×Dic₁₃

C₂×C₄⋊#1055

#1842

Subgroups — #13114987

Conjugacy classes of subgroups

Complements

Maximal subgroups