Group #20241253 — subgroups

Subgroups — #20241253

Order 6016.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689180	C₂	1	1	yes	maximal, characteristic
2	#15688991	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
5	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
6	#13093935	C₄	1	2	yes	complemented
7	C₄₇⋊#95	—	2	1	no	—
8	C₄₇⋊#95	—	2	1	no	—
9	C₄₇⋊#95	C₄	1	2	yes	—
10	C₂×M₁₆×C₄₇	—	2	1	no	—
11	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	#97×C₄₇	—	2	1	no	—
13	C₄×C₈×C₄₇	C₄	1	2	yes	complemented
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	2	no	—
18	M₁₆×C₄₇	—	2	4	no	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₄₇	D₄	1	1	yes	characteristic
23	C₄²×C₄₇	Q₈	1	1	yes	characteristic
24	C₂×C₄₇⋊C₈	—	2	2	no	—
25	C₂³×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇	—	2	2	no	—
27	C₂×C₄×C₄₇	—	4	1	no	—
28	C₂×C₄×C₄₇	—	4	1	no	—
29	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₄₇	—	4	2	no	—
36	C₂×Dic₄₇	—	4	2	no	—
37	C₂×Dic₄₇	—	4	2	no	—
38	C₈×C₄₇	—	2	4	no	—
39	C₄₇⋊C₈	—	4	2	no	—
40	C₂²×C₄₇	—	2	1	no	—
41	C₂²×C₄₇	—	2	1	no	—
42	C₂²×C₄₇	#95	1	1	yes	characteristic
43	C₂²×C₄₇	#104	1	2	yes	—
44	C₄×C₄₇	—	2	1	no	—
45	C₄×C₄₇	—	2	1	no	—
46	C₄×C₄₇	—	2	1	no	—
47	C₄×C₄₇	—	2	1	no	—
48	C₄×C₄₇	—	2	1	no	—
49	C₄×C₄₇	—	2	1	no	—
50	Dic₄₇	—	8	2	no	—
51	#1288	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	—	2	2	no	—
53	C₂×C₄₇	H(3,ℤ/4)	1	1	yes	characteristic
54	C₂×C₄₇	#339	1	1	yes	characteristic
55	C₂×C₄₇	#344	1	1	yes	characteristic
56	#432	—	47	1	no	—
57	C₄×M₁₆	D₄₇	1	1	yes	characteristic
58	#383	—	47	1	no	—
59	C₄₇	#1288	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₁₆	—	2	1	no	—
61	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
62	C₄⋊C₈	—	94	1	no	—
63	C₂²⋊C₈	—	94	1	no	—
64	#97	—	2	1	no	—
65	#97	—	47	2	no	—
66	C₄×C₈	Dic₄₇	1	2	yes	complemented
67	#95	—	47	2	no	—
68	#95	—	94	1	no	—
69	#95	—	94	1	no	—
70	C₂²×C₄	—	94	2	no	—
71	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
72	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
73	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
74	M₁₆	—	2	4	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	94	2	no	—
77	C₄²	Dic₉₄	1	1	yes	characteristic
78	C₄²	C₄×D₄₇	1	1	yes	characteristic
79	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
80	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
81	C₂³	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	—	188	2	no	—
86	C₂×C₄	—	188	2	no	—
87	C₂×C₄	—	188	2	no	—
88	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
89	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
90	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
92	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
93	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
94	C₈	—	2	4	no	—
95	C₈	—	188	2	no	—
96	C₂²	—	2	1	no	—
97	C₂²	—	2	1	no	—
98	C₂²	C₄₇⋊#95	1	1	yes	characteristic
99	C₂²	#13093952	1	2	yes	—
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	376	2	no	—
107	C₂	—	2	2	no	—
108	C₂	#15688880	1	1	yes	characteristic
109	C₂	#15688883	1	1	yes	characteristic
110	C₂	#15688894	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689180

C₂

yes

maximal, characteristic

#15688991

C₂

yes

maximal, characteristic

C₄×M₁₆×C₄₇

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

C₄

yes

complemented

C₄₇⋊#95

—

C₄₇⋊#95

—

C₄₇⋊#95

C₄

yes

—

C₂×M₁₆×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

—

C₄×C₈×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

Q₈

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#95

yes

characteristic

C₂²×C₄₇

#104

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#1288

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₄×M₁₆

D₄₇

yes

characteristic

#383

—

C₄₇

#1288

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

Dic₄₇

yes

—

—

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₉₄

yes

characteristic

C₄²

C₄×D₄₇

yes

characteristic

C₄²

C₂×Dic₄₇

yes

characteristic

C₄²

C₂²⋊D₄₇

yes

characteristic

C₂³

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

Dic₄₇⋊C₄

yes

characteristic

C₂×C₄

Dic₄₇⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₄₇

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

C₄₇⋊#95

yes

characteristic

C₂²

#13093952

yes

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

376

—

107

C₂

—

108

C₂

#15688880

yes

characteristic

109

C₂

#15688883

yes

characteristic

110

C₂

#15688894

yes

characteristic

	subgroup	G/H
center	C₂²	C₄₇⋊#95
commutator	C₂×C₄×C₄₇	C₄²
Frattini	C₂×C₄²	C₂×D₄₇
Fitting	C₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	#95
hypercenter	C₄×M₁₆	D₄₇
hypocenter	C₄₇	#1288
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₄₇⋊#95

commutator

C₂×C₄×C₄₇

C₄²

Frattini

C₂×C₄²

C₂×D₄₇

Fitting

C₄×M₁₆×C₄₇

C₂

socle

C₂²×C₄₇

#95

hypercenter

C₄×M₁₆

D₄₇

hypocenter

C₄₇

#1288

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
6. #13093935	C₄	semidirect
13. C₄×C₈×C₄₇	C₄	semidirect
59. C₄₇	#1288	semidirect
66. C₄×C₈	Dic₄₇	semidirect

H ≅ G/N

type

6. #13093935

C₄

semidirect

13. C₄×C₈×C₄₇

C₄

semidirect

59. C₄₇

#1288

semidirect

66. C₄×C₈

Dic₄₇

semidirect

Subgroups — #20241253

Conjugacy classes of subgroups

Complements