Group #15779309 — subgroups

Subgroups — #15779309

Order 3328.

282 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 155 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	#13115008	C₂	1	2	yes	maximal
2	#13112930	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88059	—	2	2	no	—
7	C₂×#88059	C₂²	1	4	yes	—
8	#11718585	—	2	2	no	—
9	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
10	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
11	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
14	C₂×#6099	—	2	4	no	—
15	C₂×C₁₃×C₁₆	—	2	4	no	—
16	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
20	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
21	#88059	—	2	8	no	—
22	#88059	—	4	4	no	—
23	C₄⋊#1055	—	4	4	no	—
24	#12891	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
26	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
27	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
30	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₈×C₁₃	#41	1	4	yes	—
33	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
34	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	C₄²×C₁₃	D₈	1	2	yes	—
36	#6099	—	4	4	no	—
37	#6099	—	4	4	no	—
38	C₂×#1055	—	4	4	no	—
39	C₁₃×C₁₆	—	2	4	no	—
40	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
41	#1848	—	13	2	no	—
42	#1381	—	13	4	no	—
43	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
44	C₂×C₄×C₁₃	—	2	4	no	—
45	C₂×C₄×C₁₃	#107	1	2	yes	—
46	C₂×C₄×C₁₃	#107	1	2	yes	—
47	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₃	#124	1	2	yes	—
49	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
51	C₈×C₁₃	#106	1	2	yes	—
52	C₈×C₁₃	#106	1	2	yes	—
53	C₈×C₁₃	#117	1	2	yes	—
54	C₈×C₁₃	#125	1	2	yes	—
55	#1055	—	8	4	no	—
56	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
57	C₂×#108	—	13	4	no	—
58	C₂×#108	—	26	2	no	—
59	#423	—	26	2	no	—
60	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
61	C₄×C₁₆	Dic₁₃	1	2	yes	—
62	C₄×C₁₆	Dic₁₃	1	2	yes	—
63	C₂²×C₁₃	—	2	2	no	—
64	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
65	C₂²×C₁₃	#487	1	2	yes	—
66	C₄×C₁₃	—	2	2	no	—
67	C₄×C₁₃	#368	1	4	yes	—
68	C₄×C₁₃	#382	1	1	yes	characteristic
69	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
70	C₄×C₁₃	#486	1	2	yes	—
71	C₂×M₁₆	—	26	4	no	—
72	C₂²×C₈	D₅₂	1	1	yes	characteristic
73	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
74	C₂×C₄²	D₅₂	1	1	yes	characteristic
75	C₂×C₁₆	—	2	4	no	—
76	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
77	#108	—	26	8	no	—
78	#108	—	52	4	no	—
79	C₄⋊C₈	—	52	4	no	—
80	C₄×C₈	Dic₂₆	1	1	yes	characteristic
81	C₄×C₈	Dic₂₆	1	1	yes	characteristic
82	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
83	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
84	C₂×C₁₃	—	2	2	no	—
85	C₂×C₁₃	#1834	1	1	yes	characteristic
86	C₂×C₁₃	C₂×#368	1	2	yes	—
87	C₂²×C₄	Dic₅₂	1	2	yes	—
88	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
89	M₁₆	—	52	4	no	—
90	M₁₆	—	52	4	no	—
91	C₂×C₈	—	52	4	no	—
92	C₂×C₈	#6095	1	4	yes	—
93	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
94	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
95	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
96	C₂×C₈	#6127	1	4	yes	—
97	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
98	C₄²	D₁₀₄	1	2	yes	—
99	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
100	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
101	C₁₆	—	2	4	no	—
102	C₁₃	#12891	1	1	yes	characteristic, complemented, Sylow
103	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	#88058	1	2	yes	—
106	C₂×C₄	#88058	1	2	yes	—
107	C₂×C₄	#88129	1	2	yes	—
108	C₂×C₄	C₂×#6095	1	2	yes	—
109	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
110	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
111	C₈	—	104	4	no	—
112	C₈	#88057	1	2	yes	—
113	C₈	#88057	1	2	yes	—
114	C₈	#88124	1	2	yes	—
115	C₈	#88180	1	2	yes	—
116	C₂²	—	2	2	no	—
117	C₂²	#11718342	1	2	yes	—
118	C₂²	C₂×#88058	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	#11718098	1	4	yes	—
121	C₄	#11718355	1	2	yes	—
122	C₄	#11718597	1	1	yes	characteristic
123	C₄	C₂×#88057	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	#13114964	1	1	yes	characteristic
126	C₂	C₂×#11718098	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13115008

C₂

yes

maximal

#13112930

C₂

yes

maximal

C₂×C₄×C₁₃×C₁₆

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88059

—

C₂×#88059

C₂²

yes

—

#11718585

—

C₄×C₁₃×C₁₆

C₄

yes

—

C₄×C₁₃×C₁₆

C₄

yes

—

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

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

Q₈

yes

characteristic

C₄×C₈×C₁₃

Q₈

yes

—

—

—

—

C₂²×C₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₃

SD₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

characteristic

C₄²×C₁₃

C₄⋊C₄

yes

characteristic

C₄²×C₁₃

D₈

yes

—

#6099

—

#6099

—

C₂×#1055

—

C₁₃×C₁₆

—

C₂×C₄×C₁₆

D₁₃

yes

characteristic

#1848

—

#1381

—

C₂³×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#117

yes

—

C₈×C₁₃

#125

yes

—

#1055

—

C₂²×C₁₆

C₂×D₁₃

yes

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

C₄×C₁₆

Dic₁₃

yes

—

C₄×C₁₆

Dic₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×#107

yes

characteristic

C₂²×C₁₃

#487

yes

—

C₄×C₁₃

—

C₄×C₁₃

#368

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂×M₁₆

—

C₂²×C₈

D₅₂

yes

characteristic

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

D₅₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₃

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₆

yes

characteristic

C₄×C₈

Dic₂₆

yes

characteristic

C₄×C₈

C₂×Dic₁₃

yes

characteristic

C₄×C₈

C₂×Dic₁₃

yes

characteristic

C₂×C₁₃

—

C₂×C₁₃

#1834

yes

characteristic

C₂×C₁₃

C₂×#368

yes

—

C₂²×C₄

Dic₅₂

yes

—

C₂²×C₄

C₂×D₅₂

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

#6095

yes

—

C₂×C₈

C₄⋊Dic₁₃

yes

characteristic

C₂×C₈

C₄⋊Dic₁₃

yes

characteristic

C₂×C₈

C₂×Dic₂₆

yes

characteristic

C₂×C₈

#6127

yes

—

C₂×C₈

C₂²×Dic₁₃

yes

characteristic

C₄²

D₁₀₄

yes

—

C₄²

C₄⋊Dic₁₃

yes

characteristic

100

C₄²

C₄⋊Dic₁₃

yes

characteristic

101

C₁₆

—

102

C₁₃

#12891

yes

characteristic, complemented, Sylow

103

C₂³

C₂×Dic₅₂

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

#88058

yes

—

106

C₂×C₄

#88058

yes

—

107

C₂×C₄

#88129

yes

—

108

C₂×C₄

C₂×#6095

yes

—

109

C₂×C₄

C₂×D₁₀₄

yes

characteristic

110

C₂×C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

111

C₈

—

104

—

112

C₈

#88057

yes

—

113

C₈

#88057

yes

—

114

C₈

#88124

yes

—

115

C₈

#88180

yes

—

116

C₂²

—

117

C₂²

#11718342

yes

—

118

C₂²

C₂×#88058

yes

characteristic

119

C₄

—

120

C₄

#11718098

yes

—

121

C₄

#11718355

yes

—

122

C₄

#11718597

yes

characteristic

123

C₄

C₂×#88057

yes

characteristic

124

C₂

—

125

C₂

#13114964

yes

characteristic

126

C₂

C₂×#11718098

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₄
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	#12891
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂×C₄

C₂×D₁₀₄

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₂×C₄×C₁₃×C₁₆

C₂

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂³×C₁₃

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₃

C₂³

hypercenter

C₂×C₄×C₁₆

D₁₃

hypocenter

C₁₃

#12891

LCS

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

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

H ≅ G/N

type

102. C₁₃

#12891

semidirect

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

subgroup	index
#13115008	2
#13112930	2
C₂×C₄×C₁₃×C₁₆	2
#12891	13

subgroup

index

#13115008

#13112930

C₂×C₄×C₁₃×C₁₆

#12891

Subgroups — #15779309

Conjugacy classes of subgroups

Complements

Maximal subgroups