Group #15778335 — subgroups

Subgroups — #15778335

Order 3328.

306 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11718098	C₂	1	2	yes	maximal
2	C₄×#88059	C₂	1	2	yes	maximal
3	#13112930	C₂	1	2	yes	maximal
4	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88059	C₂²	1	4	yes	—
9	C₄×#6099	—	2	2	no	—
10	C₁₃×#346	C₄	1	4	yes	—
11	#11718144	—	2	2	no	—
12	#11718098	C₄	1	8	yes	complemented
13	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
16	C₂×#6099	—	2	4	no	—
17	C₂×C₁₃×C₁₆	—	2	2	no	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₃	Q₈	1	2	yes	—
23	#88059	—	2	4	no	—
24	#88059	C₂×C₄	1	8	yes	—
25	#88043	—	4	2	no	—
26	C₄×#1055	—	4	2	no	—
27	#12676	—	13	1	no	maximal, Sylow
28	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
29	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
34	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	#41	1	2	yes	—
36	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
37	C₄²×C₁₃	D₈	1	2	yes	—
38	#6099	—	2	8	no	—
39	#6099	—	4	4	no	—
40	C₂×#1055	—	4	4	no	—
41	C₁₃×C₁₆	—	2	2	no	—
42	C₁₃×C₁₆	C₄²	1	4	yes	—
43	C₂×#368	—	13	2	no	—
44	C₂×#346	D₁₃	1	1	yes	characteristic
45	C₄×#108	—	13	2	no	—
46	#1381	—	13	2	no	—
47	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₃	—	4	2	no	—
49	C₂×C₄×C₁₃	#107	1	4	yes	—
50	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
53	C₂×C₄×C₁₃	#135	1	2	yes	—
54	C₈×C₁₃	—	2	2	no	—
55	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
56	C₈×C₁₃	#117	1	1	yes	characteristic
57	C₈×C₁₃	C₄×Q₈	1	2	yes	—
58	#1055	—	4	8	no	—
59	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
60	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
61	C₂×#108	—	13	4	no	—
62	C₄×M₁₆	—	26	2	no	—
63	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
64	#368	—	13	8	no	—
65	#346	Dic₁₃	1	4	yes	—
66	#341	—	26	2	no	—
67	C₂²×C₁₃	—	2	2	no	—
68	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
69	C₂²×C₁₃	C₄×Q₁₆	1	2	yes	—
70	C₄×C₁₃	—	2	4	no	—
71	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
72	C₄×C₁₃	#427	1	1	yes	characteristic
73	C₄×C₁₃	C₄×D₈	1	2	yes	—
74	C₂×M₁₆	—	26	4	no	—
75	C₂²×C₈	D₅₂	1	1	yes	characteristic
76	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
77	C₂×C₄²	D₅₂	1	1	yes	characteristic
78	C₂×C₁₆	—	2	2	no	—
79	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
80	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
81	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
82	#108	—	13	8	no	—
83	#108	—	26	4	no	—
84	#97	—	52	2	no	—
85	C₄×C₈	—	52	2	no	—
86	C₄×C₈	Dic₂₆	1	2	yes	—
87	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
88	C₂×C₁₃	—	2	2	no	—
89	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
90	C₂×C₁₃	#2161	1	2	yes	—
91	C₂²×C₄	Dic₅₂	1	2	yes	—
92	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
93	M₁₆	—	26	8	no	—
94	M₁₆	—	52	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	52	4	no	—
97	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
98	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
99	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
100	C₂×C₈	#6127	1	2	yes	—
101	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
102	C₄²	D₁₀₄	1	2	yes	—
103	C₄²	C₄⋊Dic₁₃	1	2	yes	—
104	C₁₆	—	2	2	no	—
105	C₁₆	C₄×Dic₁₃	1	4	yes	—
106	C₁₃	#12676	1	1	yes	characteristic, complemented, Sylow
107	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	#88058	1	4	yes	—
110	C₂×C₄	C₄×D₅₂	1	2	yes	—
111	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
112	C₂×C₄	#88158	1	2	yes	—
113	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	52	8	no	—
116	C₈	C₄×Dic₂₆	1	2	yes	—
117	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
118	C₈	#88180	1	1	yes	characteristic
119	C₂²	—	2	2	no	—
120	C₂²	C₄×Dic₅₂	1	2	yes	—
121	C₂²	C₂×#88058	1	1	yes	characteristic
122	C₄	—	2	4	no	—
123	C₄	C₄×D₁₀₄	1	2	yes	—
124	C₄	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
125	C₄	#11718767	1	1	yes	characteristic
126	C₂	—	2	2	no	—
127	C₂	C₄×#88058	1	1	yes	characteristic
128	C₂	#13116631	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718098

C₂

yes

maximal

C₄×#88059

C₂

yes

maximal

#13112930

C₂

yes

maximal

C₂×C₁₃×#346

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88059

C₂²

yes

—

C₄×#6099

—

C₁₃×#346

C₄

yes

—

#11718144

—

#11718098

C₄

yes

complemented

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×#6099

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#88059

—

#88059

C₂×C₄

yes

—

—

—

—

C₂²×C₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

D₈

yes

—

#6099

—

#6099

—

C₂×#1055

—

C₁₃×C₁₆

—

C₁₃×C₁₆

C₄²

yes

—

C₂×#368

—

C₂×#346

D₁₃

yes

characteristic

C₄×#108

—

#1381

—

C₂³×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

#135

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₂×C₄²

yes

characteristic

C₈×C₁₃

#117

yes

characteristic

C₈×C₁₃

C₄×Q₈

yes

—

#1055

—

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

C₂×#108

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#368

—

#346

Dic₁₃

yes

—

#341

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×#107

yes

characteristic

C₂²×C₁₃

C₄×Q₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₄×C₄⋊C₄

yes

characteristic

C₄×C₁₃

#427

yes

characteristic

C₄×C₁₃

C₄×D₈

yes

—

C₂×M₁₆

—

C₂²×C₈

D₅₂

yes

characteristic

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

D₅₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₃

yes

—

C₂×C₁₆

C₂×Dic₁₃

yes

—

C₂×C₁₆

C₂×Dic₁₃

yes

—

#108

—

#108

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₂₆

yes

—

C₄×C₈

C₂×Dic₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

C₄×#107

yes

characteristic

C₂×C₁₃

#2161

yes

—

C₂²×C₄

Dic₅₂

yes

—

C₂²×C₄

C₂×D₅₂

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₃

yes

—

C₂×C₈

C₂×Dic₂₆

yes

characteristic

C₂×C₈

C₂×C₄×D₁₃

yes

—

100

C₂×C₈

#6127

yes

—

101

C₂×C₈

C₂²×Dic₁₃

yes

characteristic

102

C₄²

D₁₀₄

yes

—

103

C₄²

C₄⋊Dic₁₃

yes

—

104

C₁₆

—

105

C₁₆

C₄×Dic₁₃

yes

—

106

C₁₃

#12676

yes

characteristic, complemented, Sylow

107

C₂³

C₂×Dic₅₂

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

#88058

yes

—

110

C₂×C₄

C₄×D₅₂

yes

—

111

C₂×C₄

C₂×D₁₀₄

yes

characteristic

112

C₂×C₄

#88158

yes

—

113

C₂×C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

C₄×Dic₂₆

yes

—

117

C₈

C₂×C₄×Dic₁₃

yes

characteristic

118

C₈

#88180

yes

characteristic

119

C₂²

—

120

C₂²

C₄×Dic₅₂

yes

—

121

C₂²

C₂×#88058

yes

characteristic

122

C₄

—

123

C₄

C₄×D₁₀₄

yes

—

124

C₄

C₄×C₄⋊Dic₁₃

yes

characteristic

125

C₄

#11718767

yes

characteristic

126

C₂

—

127

C₂

C₄×#88058

yes

characteristic

128

C₂

#13116631

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#346	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#346	D₁₃
hypocenter	C₁₃	#12676
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₁₀₄

commutator

C₈×C₁₃

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₂×C₁₃×#346

C₂

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂³×C₁₃

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
12. #11718098	C₄	semidirect
106. C₁₃	#12676	semidirect

H ≅ G/N

type

12. #11718098

C₄

semidirect

106. C₁₃

#12676

semidirect

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

subgroup	index
C₂×#11718098	2
C₄×#88059	2
#13112930	2
C₂×C₁₃×#346	2
#12676	13

subgroup

index

C₂×C₁₃×#346

Subgroups — #15778335

Conjugacy classes of subgroups

Complements

Maximal subgroups