Group #20241298 — subgroups

Subgroups — #20241298

Order 6016.

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

normal subgroups only

This group has 130 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	#15689147	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#432	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625329	C₄	1	2	yes	—
5	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
6	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
7	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₂²⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
9	#13093935	—	2	1	no	—
10	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₄₇	—	2	1	no	—
12	C₂²⋊C₈×C₄₇	C₄	1	2	yes	—
13	#97×C₄₇	—	2	1	no	—
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₄²×C₄₇	D₄	1	1	yes	characteristic
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	C₄²×C₄₇	D₄	1	1	yes	characteristic
21	C₄²×C₄₇	Q₈	1	1	yes	characteristic
22	#10625329	—	4	2	no	—
23	C₂×C₄₇⋊C₈	—	2	2	no	—
24	C₂×C₄₇⋊C₈	—	2	2	no	—
25	C₂³×C₄₇	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	4	1	no	—
29	C₂×C₄×C₄₇	—	4	1	no	—
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂²⋊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×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₄₇	—	4	2	no	—
37	C₄₇⋊C₈	—	4	2	no	—
38	C₄₇⋊C₈	—	4	2	no	—
39	C₂²×C₄₇	—	2	1	no	—
40	C₂²×C₄₇	—	2	1	no	—
41	C₂²×C₄₇	—	2	1	no	—
42	C₂²×C₄₇	#95	1	1	yes	characteristic
43	C₄×C₄₇	—	2	1	no	—
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	#100	1	1	yes	characteristic
49	C₄×C₄₇	#101	1	1	yes	characteristic
50	#1307	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	—	4	1	no	—
52	C₂×C₄₇	#343	1	1	yes	characteristic
53	C₂×C₄₇	#344	1	1	yes	characteristic
54	C₂×C₄₇	#344	1	1	yes	characteristic
55	#432	—	47	1	no	—
56	#432	D₄₇	1	1	yes	characteristic
57	#423	—	47	1	no	—
58	C₄₇	#1307	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	47	2	no	—
60	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
61	C₄⋊C₈	—	2	1	no	—
62	C₄⋊C₈	—	94	1	no	—
63	C₄⋊C₈	—	94	1	no	—
64	C₄⋊C₈	—	94	1	no	—
65	C₂²⋊C₈	—	47	2	no	—
66	C₂²⋊C₈	Dic₄₇	1	2	yes	—
67	#97	—	2	1	no	—
68	#97	—	94	1	no	—
69	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
70	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
71	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
72	M₁₆	—	188	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	94	2	no	—
75	C₂×C₈	—	94	2	no	—
76	C₄²	Dic₉₄	1	1	yes	characteristic
77	C₄²	D₁₈₈	1	1	yes	characteristic
78	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
79	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
80	C₂³	C₄×Dic₄₇	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
86	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
88	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
89	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	188	2	no	—
93	C₈	—	188	2	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	2	1	no	—
96	C₂²	—	2	1	no	—
97	C₂²	C₄₇⋊#95	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	2	1	no	—
103	C₄	#13093940	1	1	yes	characteristic
104	C₄	#13093942	1	1	yes	characteristic
105	C₂	—	4	1	no	—
106	C₂	#15688891	1	1	yes	characteristic
107	C₂	#15688893	1	1	yes	characteristic
108	C₂	#15688894	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689180

C₂

yes

maximal, characteristic

#15689147

C₂

yes

maximal, characteristic

C₄₇×#432

C₂

yes

maximal, characteristic

C₂×#10625329

C₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

C₄

yes

—

#13093935

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

C₄

yes

—

#97×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

Q₈

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

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

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#95

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

yes

characteristic

#423

—

C₄₇

#1307

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₄₇

yes

—

#97

—

#97

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₉₄

yes

characteristic

C₄²

D₁₈₈

yes

characteristic

C₄²

C₂²⋊D₄₇

yes

characteristic

C₄²

C₂²⋊D₄₇

yes

characteristic

C₂³

C₄×Dic₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

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

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₈

—

188

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄₇⋊#95

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#13093940

yes

characteristic

104

C₄

#13093942

yes

characteristic

105

C₂

—

106

C₂

#15688891

yes

characteristic

107

C₂

#15688893

yes

characteristic

108

C₂

#15688894

yes

characteristic

	subgroup	G/H
center	C₂²	C₄₇⋊#95
commutator	C₂³×C₄₇	C₄²
Frattini	C₂×C₄²	C₂×D₄₇
Fitting	C₄₇×#432	C₂
socle	C₂²×C₄₇	#95
hypercenter	#432	D₄₇
hypocenter	C₄₇	#1307
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₄₇⋊#95

commutator

C₂³×C₄₇

C₄²

Frattini

C₂×C₄²

C₂×D₄₇

Fitting

C₄₇×#432

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
58. C₄₇	#1307	semidirect

H ≅ G/N

type

58. C₄₇

#1307

semidirect

Subgroups — #20241298

Conjugacy classes of subgroups

Complements