Group #13116324 — subgroups

Subgroups — #13116324

Order 1664.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88058	C₂	1	1	yes	maximal, characteristic
3	#11718589	C₂	1	2	yes	maximal
4	#11718143	C₂	1	2	yes	maximal
5	#11718143	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×#6101	—	2	2	no	—
12	C₁₃×C₄⋊C₈	—	2	2	no	—
13	#88071	—	2	2	no	—
14	#88058	—	2	2	no	—
15	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₃	—	2	2	no	—
19	C₂²×Dic₁₃	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	—	2	1	no	—
22	C₂×C₈×C₁₃	—	2	2	no	—
23	C₂×C₈×C₁₃	D₄	1	2	yes	—
24	C₄²×C₁₃	—	2	1	no	—
25	C₄²×C₁₃	—	2	1	no	—
26	C₄⋊Dic₁₃	—	2	2	no	—
27	C₄⋊Dic₁₃	—	2	2	no	—
28	C₄⋊Dic₁₃	—	2	2	no	—
29	C₄⋊Dic₁₃	Q₈	1	4	yes	—
30	#6101	—	4	4	no	—
31	#2086	—	13	1	no	maximal, Sylow
32	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	—	2	1	no	—
34	C₂×C₄×C₁₃	—	2	1	no	—
35	C₂×C₄×C₁₃	—	2	1	no	—
36	C₂×C₄×C₁₃	—	2	2	no	—
37	C₂×C₄×C₁₃	D₈	1	2	yes	—
38	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₁₃	#41	1	2	yes	—
41	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
42	C₂×Dic₁₃	—	2	4	no	—
43	C₂×Dic₁₃	—	4	2	no	—
44	C₂×Dic₁₃	—	4	2	no	—
45	C₂×Dic₁₃	—	4	2	no	—
46	C₂×Dic₁₃	—	4	2	no	—
47	C₂×Dic₁₃	—	4	2	no	—
48	C₈×C₁₃	—	2	2	no	—
49	C₈×C₁₃	—	4	1	no	—
50	C₂×#107	—	13	1	no	—
51	C₂×C₄⋊C₈	D₁₃	1	1	yes	characteristic
52	#389	—	13	2	no	—
53	#340	—	13	1	no	—
54	#340	—	13	2	no	—
55	C₂²×C₁₃	#121	1	1	yes	characteristic
56	C₂²×C₁₃	C₂²⋊Q₈	1	2	yes	—
57	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
58	C₂²×C₁₃	#135	1	1	yes	characteristic
59	C₂²×C₁₃	#137	1	2	yes	—
60	C₄×C₁₃	—	2	2	no	—
61	C₄×C₁₃	—	4	1	no	—
62	C₄×C₁₃	#123	1	1	yes	characteristic
63	C₄×C₁₃	#125	1	2	yes	—
64	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
65	Dic₁₃	—	4	4	no	—
66	Dic₁₃	—	8	2	no	—
67	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
68	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	13	2	no	—
70	C₂×C₄⋊C₄	—	13	2	no	—
71	C₂×C₄⋊C₄	—	26	2	no	—
72	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
73	#107	—	26	2	no	—
74	C₄⋊C₈	—	2	2	no	—
75	#95	—	26	2	no	—
76	C₂×C₁₃	#398	1	1	yes	characteristic
77	C₂×C₁₃	#466	1	1	yes	characteristic
78	C₂×C₁₃	#470	1	1	yes	characteristic
79	C₂×C₁₃	#474	1	2	yes	—
80	C₂×C₁₃	#479	1	2	yes	—
81	C₂²×C₄	—	26	2	no	—
82	C₂²×C₄	—	26	2	no	—
83	C₂²×C₄	D₅₂	1	1	yes	characteristic
84	C₂²×C₄	D₅₂	1	1	yes	characteristic
85	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
90	C₄⋊C₄	—	13	4	no	—
91	C₄⋊C₄	—	26	2	no	—
92	C₄⋊C₄	—	26	2	no	—
93	C₄⋊C₄	—	26	2	no	—
94	C₄⋊C₄	—	52	4	no	—
95	C₄²	—	2	1	no	—
96	C₄²	—	2	1	no	—
97	C₁₃	#2086	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₂×D₅₂	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	26	4	no	—
104	C₂×C₄	—	52	2	no	—
105	C₂×C₄	—	52	2	no	—
106	C₂×C₄	—	52	2	no	—
107	C₂×C₄	—	52	2	no	—
108	C₂×C₄	—	52	2	no	—
109	C₂×C₄	D₁₀₄	1	2	yes	—
110	C₂×C₄	#6127	1	1	yes	characteristic
111	C₂×C₄	#6129	1	2	yes	—
112	C₂×C₄	Q₈×D₁₃	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	4	1	no	—
116	C₂²	#88151	1	2	yes	—
117	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
118	C₂²	#88158	1	1	yes	characteristic
119	C₂²	#88163	1	2	yes	—
120	C₂²	#88184	1	1	yes	characteristic
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	52	4	no	—
124	C₄	—	104	2	no	—
125	C₄	#88143	1	2	yes	—
126	C₄	#88189	1	1	yes	characteristic
127	C₄	#88198	1	1	yes	characteristic
128	C₂	#11718490	1	2	yes	—
129	C₂	#11718507	1	2	yes	—
130	C₂	#11718644	1	1	yes	characteristic
131	C₂	#11718776	1	1	yes	characteristic
132	C₂	#11718798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#88058

C₂

yes

maximal, characteristic

#11718589

C₂

yes

maximal

#11718143

C₂

yes

maximal

#11718143

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

—

C₁₃×C₄⋊C₈

—

#88071

—

#88058

—

C₂²×C₄×C₁₃

D₄

yes

characteristic

C₂²×C₄×C₁₃

D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

Q₈

yes

—

#6101

—

#2086

—

maximal, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

D₈

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

C₂×#107

—

C₂×C₄⋊C₈

D₁₃

yes

—

—

—

C₂²×C₁₃

#121

yes

characteristic

C₂²×C₁₃

C₂²⋊Q₈

yes

—

C₂²×C₁₃

C₂×D₈

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#123

yes

characteristic

C₄×C₁₃

#125

yes

—

C₄×C₁₃

C₄⋊Q₈

yes

characteristic

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

#107

—

C₄⋊C₈

—

#95

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#479

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₅₂

yes

characteristic

C₂²×C₄

D₅₂

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₁₃

#2086

yes

characteristic, complemented, Sylow

C₂³

C₂×D₅₂

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

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

D₁₀₄

yes

—

110

C₂×C₄

#6127

yes

characteristic

111

C₂×C₄

#6129

yes

—

112

C₂×C₄

Q₈×D₁₃

yes

—

113

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#88151

yes

—

117

C₂²

C₂×D₁₀₄

yes

characteristic

118

C₂²

#88158

yes

characteristic

119

C₂²

#88163

yes

—

120

C₂²

#88184

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

104

—

125

C₄

#88143

yes

—

126

C₄

#88189

yes

characteristic

127

C₄

#88198

yes

characteristic

128

C₂

#11718490

yes

—

129

C₂

#11718507

yes

—

130

C₂

#11718644

yes

characteristic

131

C₂

#11718776

yes

characteristic

132

C₂

#11718798

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₅₂
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₁₃
hypocenter	C₁₃	#2086
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₅₂

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₃

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₁₃

hypocenter

C₁₃

#2086

LCS

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
97. C₁₃	#2086	semidirect

H ≅ G/N

type

97. C₁₃

#2086

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×#88058	2
#11718589	2
#11718143	2
#2086	13

subgroup

index

C₂×C₁₃×C₄⋊C₈

Subgroups — #13116324

Conjugacy classes of subgroups

Complements

Maximal subgroups