Group #20241494 — subgroups

Subgroups — #20241494

Order 6016.

140 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 73 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	#15689161	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093956	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093983	—	2	1	no	—
5	C₂×C₄⋊Dic₄₇	—	2	1	no	—
6	#13093958	C₄	1	2	yes	complemented
7	#13093956	—	2	1	no	—
8	#13093956	—	2	1	no	—
9	#13093956	C₄	1	2	yes	complemented
10	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	M₃₂×C₄₇	—	2	1	no	—
12	M₃₂×C₄₇	C₄	1	2	yes	complemented
13	C₂×C₁₆×C₄₇	—	2	1	no	—
14	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂²×Dic₄₇	—	4	1	no	—
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
22	C₂²⋊Dic₄₇	—	4	1	no	—
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	—	4	1	no	—
26	C₄×Dic₄₇	—	4	1	no	—
27	C₁₆×C₄₇	—	2	2	no	—
28	C₂³×C₄₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
33	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₄₇	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₄₇	—	4	2	no	—
36	C₂×Dic₄₇	—	4	2	no	—
37	C₂×Dic₄₇	—	8	2	no	—
38	C₈×C₄₇	C₄²	1	1	yes	characteristic
39	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄₇	—	2	2	no	—
43	C₂²×C₄₇	#102	1	1	yes	characteristic
44	C₂²×C₄₇	#102	1	1	yes	characteristic
45	C₂²×C₄₇	#107	1	1	yes	characteristic
46	C₄×C₄₇	#95	1	1	yes	characteristic
47	C₄×C₄₇	#103	1	1	yes	characteristic
48	C₄×C₄₇	#103	1	1	yes	characteristic
49	C₄×C₄₇	#106	1	1	yes	characteristic
50	Dic₄₇	—	8	2	no	—
51	Dic₄₇	—	8	2	no	—
52	#1386	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	—	2	1	no	—
54	C₂×C₄₇	—	2	1	no	—
55	C₂×C₄₇	#340	1	1	yes	characteristic
56	C₂×C₄₇	#360	1	2	yes	—
57	C₂×M₃₂	D₄₇	1	1	yes	characteristic
58	#427	—	47	1	no	—
59	C₂×#106	—	47	1	no	—
60	C₄₇	#1386	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
62	#117	—	94	1	no	—
63	C₂×C₄⋊C₄	—	94	1	no	—
64	M₃₂	—	2	1	no	—
65	M₃₂	Dic₄₇	1	2	yes	complemented
66	C₂×C₁₆	—	2	1	no	—
67	#107	—	47	2	no	—
68	#106	—	47	2	no	—
69	#106	—	94	1	no	—
70	#106	—	94	1	no	—
71	C₂²×C₄	—	188	1	no	—
72	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
73	C₂×C₈	Dic₉₄	1	1	yes	characteristic
74	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
75	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
77	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
79	C₄⋊C₄	—	94	2	no	—
80	C₄⋊C₄	—	94	2	no	—
81	C₄⋊C₄	—	188	1	no	—
82	C₂²⋊C₄	—	188	1	no	—
83	C₄²	—	188	1	no	—
84	C₁₆	—	2	2	no	—
85	C₂³	D₃₇₆	1	1	yes	characteristic
86	C₂×C₄	—	376	2	no	—
87	C₂×C₄	—	188	2	no	—
88	C₂×C₄	—	188	2	no	—
89	C₂×C₄	#10625325	1	1	yes	characteristic
90	C₂×C₄	#10625325	1	1	yes	characteristic
91	C₂×C₄	Dic₁₈₈	1	1	yes	characteristic
92	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
93	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
94	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
95	C₈	C₄×Dic₄₇	1	1	yes	characteristic
96	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
97	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
98	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
99	C₂²	—	2	2	no	—
100	C₂²	#13093946	1	1	yes	characteristic
101	C₂²	#13093946	1	1	yes	characteristic
102	C₂²	#13093958	1	1	yes	characteristic
103	C₄	—	376	2	no	—
104	C₄	—	376	2	no	—
105	C₄	C₄₇⋊#95	1	1	yes	characteristic
106	C₄	#13093949	1	1	yes	characteristic
107	C₄	#13093949	1	1	yes	characteristic
108	C₄	#13093956	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	#15688886	1	1	yes	characteristic
112	C₂	#15688934	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689161

C₂

yes

maximal, characteristic

C₂×#13093956

C₂

yes

maximal, characteristic

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic

#13093983

—

C₂×C₄⋊Dic₄₇

—

#13093958

C₄

yes

—

—

C₄

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

C₄

yes

complemented

C₂×C₁₆×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₁₆×C₄₇

—

C₂³×C₄₇

D₈

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

SD₁₆

yes

characteristic

C₂×C₄×C₄₇

SD₁₆

yes

characteristic

C₂×C₄×C₄₇

Q₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

C₄²

yes

characteristic

C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

#1386

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#340

yes

characteristic

C₂×C₄₇

#360

yes

—

C₂×M₃₂

D₄₇

yes

characteristic

#427

—

C₂×#106

—

C₄₇

#1386

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

M₃₂

—

M₃₂

Dic₄₇

yes

complemented

C₂×C₁₆

—

—

—

—

—

C₂²×C₄

—

188

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂×C₈

Dic₉₄

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₄²

—

188

—

C₁₆

—

C₂³

D₃₇₆

yes

characteristic

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

Dic₁₈₈

yes

characteristic

C₂×C₄

C₄⋊Dic₄₇

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

C₄×Dic₄₇

yes

characteristic

C₈

Dic₄₇⋊C₄

yes

characteristic

C₈

Dic₄₇⋊C₄

yes

characteristic

C₈

C₂²⋊Dic₄₇

yes

characteristic

C₂²

—

100

C₂²

#13093946

yes

characteristic

101

C₂²

#13093946

yes

characteristic

102

C₂²

#13093958

yes

characteristic

103

C₄

—

376

—

104

C₄

—

376

—

105

C₄

C₄₇⋊#95

yes

characteristic

106

C₄

#13093949

yes

characteristic

107

C₄

#13093949

yes

characteristic

108

C₄

#13093956

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

#15688886

yes

characteristic

112

C₂

#15688934

yes

—

	subgroup	G/H
center	C₂²	#13093946
commutator	C₈×C₄₇	C₄²
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂×M₃₂×C₄₇	C₂
socle	C₂²×C₄₇	#102
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	#1386
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

#13093946

commutator

C₈×C₄₇

C₄²

Frattini

C₂²×C₈

C₂×D₄₇

Fitting

C₂×M₃₂×C₄₇

C₂

socle

C₂²×C₄₇

#102

hypercenter

C₂×M₃₂

D₄₇

hypocenter

C₄₇

#1386

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
6. #13093958	C₄	semidirect
9. #13093956	C₄	semidirect
12. M₃₂×C₄₇	C₄	semidirect
60. C₄₇	#1386	semidirect
65. M₃₂	Dic₄₇	semidirect

H ≅ G/N

type

6. #13093958

C₄

semidirect

9. #13093956

C₄

semidirect

12. M₃₂×C₄₇

C₄

semidirect

60. C₄₇

#1386

semidirect

65. M₃₂

Dic₄₇

semidirect

Subgroups — #20241494

Conjugacy classes of subgroups

Complements