Group #20245632 — subgroups

Subgroups — #20245632

Order 6016.

132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 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	#15689524	C₂	1	1	yes	maximal, characteristic
2	#15689501	C₂	1	1	yes	maximal, characteristic
3	#15688928	C₂	1	1	yes	maximal, characteristic
4	#15688927	C₂	1	1	yes	maximal, characteristic
5	#15688926	C₂	1	1	yes	maximal, characteristic
6	#15688898	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#358	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625337	—	2	1	no	—
10	#13094022	—	2	1	no	—
11	#13094015	—	2	1	no	—
12	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13093958	C₂²	1	1	yes	characteristic
14	#13093955	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₇	—	2	1	no	—
20	C₂×Dic₉₄	—	2	1	no	—
21	Q₁₆×C₄₇	—	2	1	no	—
22	Q₁₆×C₄₇	—	2	1	no	—
23	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	1	no	—
25	#10625337	—	4	2	no	—
26	C₄⋊Dic₄₇	—	2	1	no	—
27	C₄⋊Dic₄₇	—	4	1	no	—
28	Dic₄₇⋊C₄	—	4	1	no	—
29	Dic₄₇⋊C₄	—	4	1	no	—
30	Dic₄₇⋊C₄	—	4	1	no	—
31	C₄×Dic₄₇	D₄	1	1	yes	characteristic
32	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
33	Dic₁₈₈	—	2	1	no	—
34	Dic₁₈₈	—	2	1	no	—
35	C₁₆×C₄₇	—	2	1	no	—
36	C₄₇⋊C₁₆	—	2	1	no	—
37	Q₈×C₄₇	—	4	1	no	—
38	Q₈×C₄₇	—	4	1	no	—
39	C₂×C₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	—	4	1	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₇	—	4	1	no	—
43	C₂×Dic₄₇	—	4	1	no	—
44	C₂×Dic₄₇	D₈	1	1	yes	characteristic
45	C₂×Dic₄₇	D₈	1	1	yes	characteristic
46	Dic₉₄	—	4	1	no	—
47	Dic₉₄	—	4	1	no	—
48	C₈×C₄₇	#41	1	1	yes	characteristic
49	C₈×C₄₇	#41	1	1	yes	characteristic
50	C₄₇⋊C₈	SD₁₆	1	2	yes	—
51	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
52	C₄×C₄₇	—	8	1	no	—
53	C₄×C₄₇	—	8	1	no	—
54	C₄×C₄₇	#124	1	1	yes	characteristic
55	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
56	Dic₄₇	—	2	1	no	—
57	Dic₄₇	—	2	1	no	—
58	Dic₄₇	—	8	1	no	—
59	Dic₄₇	—	8	1	no	—
60	#2245	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	#486	1	1	yes	characteristic
62	C₂×C₄₇	#510	1	1	yes	characteristic
63	C₂×C₄₇	#510	1	1	yes	characteristic
64	#499	—	47	1	no	—
65	#494	—	47	1	no	—
66	#358	—	47	1	no	—
67	#358	—	47	1	no	—
68	#358	—	47	1	no	—
69	#358	D₄₇	1	1	yes	characteristic
70	#346	—	47	1	no	—
71	C₄₇	#2245	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₁₆	—	47	1	no	—
73	C₂×Q₁₆	—	94	1	no	—
74	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
75	C₄⋊Q₈	—	94	1	no	—
76	#125	—	94	1	no	—
77	C₂×C₁₆	—	47	1	no	—
78	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
79	#107	—	47	1	no	—
80	#107	C₂×D₄₇	1	1	yes	characteristic
81	#106	—	94	1	no	—
82	C₄×C₈	—	47	1	no	—
83	C₂×Q₈	—	2	1	no	—
84	C₂×Q₈	—	94	1	no	—
85	Q₁₆	—	2	1	no	—
86	Q₁₆	—	2	1	no	—
87	Q₁₆	—	94	1	no	—
88	Q₁₆	—	94	1	no	—
89	Q₁₆	—	188	2	no	—
90	C₂×C₈	—	47	1	no	—
91	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
92	C₄⋊C₄	—	2	1	no	—
93	C₄⋊C₄	—	94	1	no	—
94	C₄⋊C₄	—	188	1	no	—
95	C₄⋊C₄	—	188	1	no	—
96	C₄⋊C₄	—	188	1	no	—
97	C₄⋊C₄	—	188	1	no	—
98	C₄²	—	47	1	no	—
99	C₁₆	—	2	1	no	—
100	C₁₆	—	94	1	no	—
101	Q₈	—	4	1	no	—
102	Q₈	—	4	1	no	—
103	Q₈	—	188	1	no	—
104	Q₈	—	188	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	47	1	no	—
108	C₂×C₄	—	47	1	no	—
109	C₂×C₄	—	188	1	no	—
110	C₂×C₄	—	188	1	no	—
111	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
112	C₈	—	47	2	no	—
113	C₈	#10625350	1	1	yes	characteristic
114	C₈	#10625352	1	1	yes	characteristic
115	C₂²	D₈×D₄₇	1	1	yes	characteristic
116	C₄	—	8	1	no	—
117	C₄	—	8	1	no	—
118	C₄	—	94	1	no	—
119	C₄	—	94	1	no	—
120	C₄	—	376	1	no	—
121	C₄	—	376	1	no	—
122	C₄	#13094010	1	1	yes	characteristic
123	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
124	C₂	#15689468	1	1	yes	characteristic
125	C₂	#15689562	1	1	yes	characteristic
126	C₂	#15689565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689524

C₂

yes

maximal, characteristic

#15689501

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, characteristic

#15688927

C₂

yes

maximal, characteristic

#15688926

C₂

yes

maximal, characteristic

#15688898

C₂

yes

maximal, characteristic

C₄₇×#358

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

—

—

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093955

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

#10625337

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

SD₁₆

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#124

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

#346

—

C₄₇

#2245

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#107

C₂×D₄₇

yes

characteristic

#106

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

188

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

C₁₆

—

100

C₁₆

—

101

Q₈

—

102

Q₈

—

103

Q₈

—

188

—

104

Q₈

—

188

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

188

—

110

C₂×C₄

—

188

—

111

C₂×C₄

D₄×D₄₇

yes

characteristic

112

C₈

—

113

C₈

#10625350

yes

characteristic

114

C₈

#10625352

yes

characteristic

115

C₂²

D₈×D₄₇

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

376

—

121

C₄

—

376

—

122

C₄

#13094010

yes

characteristic

123

C₄

SD₁₆×D₄₇

yes

characteristic

124

C₂

#15689468

yes

characteristic

125

C₂

#15689562

yes

characteristic

126

C₂

#15689565

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#358	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#358	D₄₇
hypocenter	C₄₇	#2245
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#358

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
71. C₄₇	#2245	semidirect

H ≅ G/N

type

71. C₄₇

#2245

semidirect

Subgroups — #20245632

Conjugacy classes of subgroups

Complements