Group #20245294 — subgroups

Subgroups — #20245294

Order 6016.

126 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 71 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	C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	#15688898	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#346	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₉₄	C₄	1	1	yes	characteristic
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
12	Dic₄₇⋊C₈	C₄	1	1	yes	characteristic
13	Dic₄₇⋊C₈	C₄	1	1	yes	characteristic
14	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Dic₉₄	C₈	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
24	Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
25	Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
26	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₁₆×C₄₇	—	2	1	no	—
31	C₁₆×C₄₇	Q₈	1	2	yes	complemented
32	C₄₇⋊C₁₆	—	2	1	no	—
33	C₄₇⋊C₁₆	—	2	1	no	—
34	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
41	Dic₉₄	—	2	2	no	—
42	C₈×C₄₇	—	2	1	no	—
43	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
44	C₈×C₄₇	#41	1	1	yes	characteristic
45	C₄₇⋊C₈	—	2	1	no	—
46	C₄₇⋊C₈	—	2	1	no	—
47	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
48	C₄×C₄₇	—	2	1	no	—
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
51	C₄×C₄₇	#131	1	1	yes	characteristic
52	Dic₄₇	—	2	1	no	—
53	Dic₄₇	—	2	1	no	—
54	Dic₄₇	—	2	1	no	—
55	Dic₄₇	M₃₂	1	2	yes	—
56	#2183	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	C₈×Q₈	1	1	yes	characteristic
58	C₂×C₄₇	C₂×M₃₂	1	1	yes	characteristic
59	C₂×C₄₇	#504	1	1	yes	characteristic
60	C₈×Q₈	—	47	1	no	—
61	C₄⋊C₁₆	—	47	1	no	—
62	C₄⋊C₁₆	—	47	1	no	—
63	C₄⋊C₁₆	—	47	1	no	—
64	#346	—	47	1	no	—
65	#346	D₄₇	1	1	yes	characteristic
66	C₄×C₁₆	—	47	1	no	—
67	C₄₇	#2183	1	1	yes	characteristic, complemented, Sylow
68	C₄×Q₈	—	47	1	no	—
69	C₂×C₁₆	—	47	1	no	—
70	C₂×C₁₆	—	47	1	no	—
71	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
72	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
73	C₄⋊C₈	—	47	1	no	—
74	C₄⋊C₈	—	47	1	no	—
75	C₄⋊C₈	—	47	1	no	—
76	C₄×C₈	—	47	1	no	—
77	C₄×C₈	—	47	1	no	—
78	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
79	C₂×Q₈	—	47	1	no	—
80	C₂×C₈	—	47	1	no	—
81	C₂×C₈	—	47	1	no	—
82	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
83	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
84	C₄⋊C₄	—	47	1	no	—
85	C₄⋊C₄	—	47	1	no	—
86	C₄⋊C₄	—	47	1	no	—
87	C₄²	—	47	1	no	—
88	C₄²	—	47	1	no	—
89	C₄²	C₄×D₄₇	1	1	yes	characteristic
90	C₁₆	—	2	1	no	—
91	C₁₆	—	94	1	no	—
92	C₁₆	—	94	1	no	—
93	C₁₆	Dic₉₄	1	2	yes	complemented
94	Q₈	—	94	2	no	—
95	C₂×C₄	—	47	1	no	—
96	C₂×C₄	—	47	1	no	—
97	C₂×C₄	—	47	1	no	—
98	C₂×C₄	—	47	1	no	—
99	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
100	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	94	1	no	—
104	C₈	—	94	1	no	—
105	C₈	C₂×Dic₉₄	1	1	yes	characteristic
106	C₈	#10625350	1	1	yes	characteristic
107	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	47	2	no	—
111	C₄	—	94	1	no	—
112	C₄	—	94	1	no	—
113	C₄	—	94	1	no	—
114	C₄	C₄×Dic₉₄	1	1	yes	characteristic
115	C₄	#13094030	1	1	yes	characteristic
116	C₂	C₈×Dic₉₄	1	1	yes	characteristic
117	C₂	M₃₂×D₄₇	1	1	yes	characteristic
118	C₂	#15689541	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₉₄

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic

#15688898

C₂

yes

maximal, characteristic

C₁₆×Dic₄₇

C₂

yes

maximal, characteristic

C₄₇×#346

C₂

yes

maximal, characteristic

C₄×Dic₉₄

C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₄

yes

characteristic

Dic₄₇⋊C₈

C₄

yes

characteristic

Dic₄₇⋊C₈

C₄

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

C₈

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄⋊Dic₄₇

C₈

yes

characteristic

Dic₄₇⋊C₄

C₈

yes

characteristic

Dic₄₇⋊C₄

C₈

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₁₆×C₄₇

—

C₁₆×C₄₇

Q₈

yes

complemented

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×Q₈

yes

characteristic

C₄×C₄₇

#131

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

M₃₂

yes

—

#2183

—

maximal, Sylow

C₂×C₄₇

C₈×Q₈

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

characteristic

C₂×C₄₇

#504

yes

characteristic

C₈×Q₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

#346

D₄₇

yes

characteristic

C₄×C₁₆

—

C₄₇

#2183

yes

characteristic, complemented, Sylow

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

Dic₉₄

yes

complemented

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

characteristic

100

C₂×C₄

C₈×D₄₇

yes

characteristic

101

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

C₂×Dic₉₄

yes

characteristic

106

C₈

#10625350

yes

characteristic

107

C₂²

C₂×C₈×D₄₇

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

C₄×Dic₉₄

yes

characteristic

115

C₄

#13094030

yes

characteristic

116

C₂

C₈×Dic₉₄

yes

characteristic

117

C₂

M₃₂×D₄₇

yes

characteristic

118

C₂

#15689541

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₄₇×#346	C₂
hypercenter	#346	D₄₇
hypocenter	C₄₇	#2183
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₈

Fitting

C₄₇×#346

C₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
31. C₁₆×C₄₇	Q₈	semidirect
67. C₄₇	#2183	semidirect
93. C₁₆	Dic₉₄	semidirect

H ≅ G/N

type

31. C₁₆×C₄₇

Q₈

semidirect

67. C₄₇

#2183

semidirect

93. C₁₆

Dic₉₄

semidirect

Subgroups — #20245294

Conjugacy classes of subgroups

Complements