Group #26136763 — subgroups

Subgroups — #26136763

Order 12032.

206 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 123 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×#15688957	C₂	1	1	yes	maximal, characteristic
2	#20244984	C₂	1	1	yes	maximal, characteristic
3	Dic₄₇⋊C₃₂	C₂	1	4	yes	maximal, complemented
4	C₂²×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093964	C₄	1	1	yes	characteristic
6	#15689078	C₄	1	1	yes	characteristic
7	#15688957	—	2	2	no	—
8	C₂×C₄₇⋊C₃₂	C₂²	1	2	yes	—
9	#15688898	C₄	1	2	yes	—
10	C₁₆×Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₃₂×C₄₇	—	2	2	no	—
13	C₂×C₃₂×C₄₇	C₂²	1	2	yes	—
14	C₂×#10625329	C₈	1	1	yes	characteristic
15	#13093983	C₈	1	1	yes	characteristic
16	#13093964	—	2	2	no	—
17	C₂×C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
18	#13093934	C₈	1	2	yes	—
19	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
20	C₄₇⋊C₃₂	—	2	2	no	—
21	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
24	C₂×C₁₆×C₄₇	Q₈	1	2	yes	—
25	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
26	C₃₂×C₄₇	—	2	2	no	—
27	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₈×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₈×C₄₇	M₁₆	1	2	yes	—
31	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂²⋊Dic₄₇	C₁₆	1	2	yes	—
33	C₄⋊Dic₄₇	C₁₆	1	2	yes	—
34	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
35	#10625329	—	2	2	no	—
36	C₂×C₄₇⋊C₈	C₂×C₈	1	2	yes	—
37	C₁₆×C₄₇	C₄⋊C₄	1	2	yes	—
38	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₁₆×C₄₇	C₂×Q₈	1	1	yes	characteristic
40	C₄₇⋊C₁₆	—	2	2	no	—
41	C₂³×C₄₇	C₂×C₁₆	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₄⋊C₈	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
44	C₂×C₄×C₄₇	M₃₂	1	2	yes	—
45	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
46	C₂×Dic₄₇	C₂×C₁₆	1	4	yes	—
47	C₈×C₄₇	C₄⋊C₈	1	2	yes	—
48	C₈×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₄₇	C₂×M₁₆	1	1	yes	characteristic
50	C₄₇⋊C₈	—	2	2	no	—
51	#13628	—	47	1	no	maximal, Sylow
52	C₂²×C₄₇	—	2	2	no	—
53	C₂²×C₄₇	C₄⋊C₁₆	1	2	yes	—
54	C₂²×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
55	C₄×C₄₇	C₄⋊C₁₆	1	2	yes	—
56	C₄×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
57	C₄×C₄₇	C₂×M₃₂	1	1	yes	characteristic
58	Dic₄₇	—	2	4	no	—
59	C₂×M₆₄	—	47	1	no	—
60	C₂²×C₃₂	D₄₇	1	1	yes	characteristic
61	#2108	—	47	1	no	—
62	C₄⋊C₃₂	—	47	4	no	—
63	C₂×C₄₇	—	2	2	no	—
64	C₂×C₄₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
65	C₂×C₄₇	#2258	1	2	yes	—
66	C₂×M₃₂	—	47	1	no	—
67	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
68	#405	—	47	1	no	—
69	M₆₄	—	94	2	no	—
70	C₂×C₃₂	—	2	2	no	—
71	C₂×C₃₂	—	47	2	no	—
72	C₂×C₃₂	C₂×D₄₇	1	2	yes	—
73	#346	—	47	2	no	—
74	C₄×C₁₆	—	47	2	no	—
75	C₄₇	#13628	1	1	yes	characteristic, complemented, Sylow
76	C₂×M₁₆	—	47	1	no	—
77	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
78	#117	—	47	1	no	—
79	M₃₂	—	94	2	no	—
80	C₂×C₁₆	—	47	2	no	—
81	C₂×C₁₆	Dic₉₄	1	2	yes	—
82	C₂×C₁₆	C₄×D₄₇	1	1	yes	characteristic
83	C₂×C₁₆	C₂²⋊D₄₇	1	2	yes	—
84	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
85	#97	—	47	2	no	—
86	C₄×C₈	—	47	2	no	—
87	C₃₂	—	2	2	no	—
88	C₃₂	—	94	2	no	—
89	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
90	M₁₆	—	94	2	no	—
91	C₂×C₈	—	47	2	no	—
92	C₂×C₈	C₈×D₄₇	1	1	yes	characteristic
93	C₂×C₈	#10625324	1	2	yes	—
94	C₂×C₈	Dic₄₇⋊C₄	1	2	yes	—
95	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
96	C₄⋊C₄	—	47	2	no	—
97	C₂²⋊C₄	—	47	2	no	—
98	C₄²	—	47	2	no	—
99	C₁₆	—	94	2	no	—
100	C₁₆	Dic₄₇⋊C₄	1	2	yes	—
101	C₁₆	C₂×Dic₉₄	1	1	yes	characteristic
102	C₁₆	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
103	C₂³	C₁₆×D₄₇	1	1	yes	characteristic
104	C₂×C₄	—	47	4	no	—
105	C₂×C₄	Dic₄₇⋊C₈	1	2	yes	—
106	C₂×C₄	C₁₆×D₄₇	1	1	yes	characteristic
107	C₂×C₄	#13093963	1	2	yes	—
108	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
109	C₈	—	94	2	no	—
110	C₈	Dic₄₇⋊C₈	1	2	yes	—
111	C₈	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
112	C₈	C₂×#10625324	1	1	yes	characteristic
113	C₂²	—	2	2	no	—
114	C₂²	Dic₄₇⋊C₁₆	1	2	yes	—
115	C₂²	C₂×C₁₆×D₄₇	1	1	yes	characteristic
116	C₄	—	94	4	no	—
117	C₄	Dic₄₇⋊C₁₆	1	2	yes	—
118	C₄	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
119	C₄	C₂×#13093963	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×Dic₄₇⋊C₁₆	1	1	yes	characteristic
122	C₂	#20245681	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15688957

C₂

yes

maximal, characteristic

#20244984

C₂

yes

maximal, characteristic

Dic₄₇⋊C₃₂

C₂

yes

maximal, complemented

C₂²×C₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂×#13093964

C₄

yes

characteristic

#15689078

C₄

yes

characteristic

#15688957

—

C₂×C₄₇⋊C₃₂

C₂²

yes

—

#15688898

C₄

yes

—

C₁₆×Dic₄₇

C₂²

yes

—

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₃₂×C₄₇

—

C₂×C₃₂×C₄₇

C₂²

yes

—

C₂×#10625329

C₈

yes

characteristic

#13093983

C₈

yes

characteristic

#13093964

—

C₂×C₄₇⋊C₁₆

C₂×C₄

yes

—

#13093934

C₈

yes

—

C₈×Dic₄₇

C₂×C₄

yes

—

C₄₇⋊C₃₂

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₇

D₄

yes

—

C₂×C₁₆×C₄₇

Q₈

yes

—

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₃₂×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₈×C₄₇

C₄⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×C₈

yes

characteristic

C₂×C₈×C₄₇

M₁₆

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂²⋊Dic₄₇

C₁₆

yes

—

C₄⋊Dic₄₇

C₁₆

yes

—

C₄×Dic₄₇

C₂×C₈

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×C₈

yes

—

C₁₆×C₄₇

C₄⋊C₄

yes

—

C₁₆×C₄₇

C₂×D₄

yes

characteristic

C₁₆×C₄₇

C₂×Q₈

yes

characteristic

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₈

yes

—

C₂×C₄×C₄₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₄₇

M₃₂

yes

—

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₁₆

yes

—

C₈×C₄₇

C₄⋊C₈

yes

—

C₈×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₂×M₁₆

yes

characteristic

C₄₇⋊C₈

—

#13628

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

C₄⋊C₁₆

yes

—

C₂²×C₄₇

C₂²×C₁₆

yes

characteristic

C₄×C₄₇

C₄⋊C₁₆

yes

—

C₄×C₄₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₄₇

C₂×M₃₂

yes

characteristic

Dic₄₇

—

C₂×M₆₄

—

C₂²×C₃₂

D₄₇

yes

characteristic

#2108

—

C₄⋊C₃₂

—

C₂×C₄₇

—

C₂×C₄₇

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₄₇

#2258

yes

—

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

#405

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₄₇

yes

—

#346

—

C₄×C₁₆

—

C₄₇

#13628

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₄×D₄₇

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

Dic₉₄

yes

—

C₂×C₁₆

C₄×D₄₇

yes

characteristic

C₂×C₁₆

C₂²⋊D₄₇

yes

—

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

#97

—

C₄×C₈

—

C₃₂

—

C₃₂

—

C₂²×C₄

C₈×D₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₈×D₄₇

yes

characteristic

C₂×C₈

#10625324

yes

—

C₂×C₈

Dic₄₇⋊C₄

yes

—

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

100

C₁₆

Dic₄₇⋊C₄

yes

—

101

C₁₆

C₂×Dic₉₄

yes

characteristic

102

C₁₆

C₂×C₂²⋊D₄₇

yes

characteristic

103

C₂³

C₁₆×D₄₇

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

Dic₄₇⋊C₈

yes

—

106

C₂×C₄

C₁₆×D₄₇

yes

characteristic

107

C₂×C₄

#13093963

yes

—

108

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

109

C₈

—

110

C₈

Dic₄₇⋊C₈

yes

—

111

C₈

C₂×Dic₄₇⋊C₄

yes

characteristic

112

C₈

C₂×#10625324

yes

characteristic

113

C₂²

—

114

C₂²

Dic₄₇⋊C₁₆

yes

—

115

C₂²

C₂×C₁₆×D₄₇

yes

characteristic

116

C₄

—

117

C₄

Dic₄₇⋊C₁₆

yes

—

118

C₄

C₂×Dic₄₇⋊C₈

yes

characteristic

119

C₄

C₂×#13093963

yes

characteristic

120

C₂

—

121

C₂

C₂×Dic₄₇⋊C₁₆

yes

characteristic

122

C₂

#20245681

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₁₆
Fitting	C₂²×C₃₂×C₄₇	C₂
prime radical	C₂³×C₄₇	C₂×C₁₆
cosocle	C₂×C₁₆×C₄₇	C₂³
hypercenter	C₂²×C₃₂	D₄₇
hypocenter	C₄₇	#13628
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₃₂

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₁₆

Fitting

C₂²×C₃₂×C₄₇

C₂

prime radical

C₂³×C₄₇

C₂×C₁₆

cosocle

C₂×C₁₆×C₄₇

C₂³

hypercenter

C₂²×C₃₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₁₆ ◁ C₂²×C₃₂

N	H ≅ G/N	type
3. Dic₄₇⋊C₃₂	C₂	semidirect
75. C₄₇	#13628	semidirect

H ≅ G/N

type

3. Dic₄₇⋊C₃₂

C₂

semidirect

75. C₄₇

#13628

semidirect

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

subgroup	index
C₂×#15688957	2
#20244984	2
Dic₄₇⋊C₃₂	2
C₂²×C₃₂×C₄₇	2
#13628	47

subgroup

index

C₂×#15688957

#20244984

Dic₄₇⋊C₃₂

C₂²×C₃₂×C₄₇

#13628

Subgroups — #26136763

Conjugacy classes of subgroups

Complements

Maximal subgroups