Group #20251456 — subgroups

Subgroups — #20251456

Order 6016.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₂×#13094016	C₂	1	2	yes	maximal
2	#15689063	C₂	1	4	yes	maximal
3	#15689055	C₂	1	4	yes	maximal
4	#15689053	C₂	1	4	yes	maximal
5	C₄₇×#382	C₂	1	1	yes	maximal, characteristic
6	#13094016	—	2	8	no	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
12	C₄₇⋊#95	C₂²	1	8	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	#95×C₄₇	C₂²	1	4	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
20	C₂²×Dic₄₇	C₂³	1	4	yes	—
21	C₂²×Dic₄₇	C₂³	1	4	yes	—
22	C₄⋊C₄×C₄₇	—	4	2	no	—
23	C₄²×C₄₇	D₄	1	4	yes	—
24	C₄⋊Dic₄₇	—	2	4	no	—
25	C₄⋊Dic₄₇	—	2	4	no	—
26	C₄⋊Dic₄₇	—	4	4	no	—
27	Dic₄₇⋊C₄	—	2	8	no	—
28	Dic₄₇⋊C₄	—	2	8	no	—
29	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	—	2	4	no	—
32	C₂×C₄×C₄₇	—	2	1	no	—
33	C₂×C₄×C₄₇	—	2	4	no	—
34	C₂×C₄×C₄₇	—	2	8	no	—
35	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
37	C₂×Dic₄₇	—	2	4	no	—
38	C₂×Dic₄₇	—	2	4	no	—
39	C₂×Dic₄₇	—	2	4	no	—
40	C₂×Dic₄₇	—	2	8	no	—
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
43	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
44	C₂²×C₄₇	2₋¹⁺⁴	1	4	yes	—
45	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
46	C₄×C₄₇	—	2	4	no	—
47	C₄×C₄₇	—	2	2	no	—
48	C₄×C₄₇	—	4	4	no	—
49	Dic₄₇	—	4	4	no	—
50	Dic₄₇	—	4	4	no	—
51	#2822	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	#536	1	2	yes	—
53	C₂×C₄₇	#537	1	1	yes	characteristic
54	C₂×C₄₇	#563	1	2	yes	—
55	C₂×C₄₇	#564	1	2	yes	—
56	C₂×#125	—	47	2	no	—
57	#400	—	47	4	no	—
58	#398	—	47	4	no	—
59	#398	—	47	4	no	—
60	#382	D₄₇	1	1	yes	characteristic
61	C₄₇	#2822	1	1	yes	characteristic, complemented, Sylow
62	#125	—	94	8	no	—
63	C₂×C₄⋊C₄	—	47	4	no	—
64	C₂×C₄⋊C₄	—	47	4	no	—
65	C₂×C₄⋊C₄	—	47	2	no	—
66	C₂×C₄⋊C₄	—	47	2	no	—
67	C₂×C₄⋊C₄	—	47	4	no	—
68	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
69	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
70	#95	—	47	8	no	—
71	#95	—	47	4	no	—
72	#95	C₂×D₄₇	1	4	yes	—
73	C₂²×C₄	—	47	4	no	—
74	C₂²×C₄	—	47	4	no	—
75	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
76	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
77	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
78	C₄⋊C₄	—	4	2	no	—
79	C₄⋊C₄	—	94	8	no	—
80	C₄⋊C₄	—	94	8	no	—
81	C₄⋊C₄	—	94	4	no	—
82	C₄⋊C₄	—	94	4	no	—
83	C₄⋊C₄	—	188	4	no	—
84	C₄²	D₁₈₈	1	4	yes	—
85	C₂³	C₂³×D₄₇	1	1	yes	characteristic
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	94	4	no	—
92	C₂×C₄	—	94	4	no	—
93	C₂×C₄	—	94	4	no	—
94	C₂×C₄	—	94	8	no	—
95	C₂×C₄	—	94	4	no	—
96	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
97	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
98	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
99	C₂²	#13094069	1	1	yes	characteristic
100	C₂²	#13094071	1	4	yes	—
101	C₂²	#13094072	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	2	2	no	—
104	C₄	—	4	4	no	—
105	C₄	—	188	4	no	—
106	C₄	—	188	4	no	—
107	C₂	#15689699	1	2	yes	—
108	C₂	#15689704	1	1	yes	characteristic
109	C₂	#15689873	1	2	yes	—
110	C₂	C₄₇⋊#564	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094016

C₂

yes

maximal

#15689063

C₂

yes

maximal

#15689055

C₂

yes

maximal

#15689053

C₂

yes

maximal

C₄₇×#382

C₂

yes

maximal, characteristic

#13094016

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2822

—

maximal, Sylow

C₂×C₄₇

#536

yes

—

C₂×C₄₇

#537

yes

characteristic

C₂×C₄₇

#563

yes

—

C₂×C₄₇

#564

yes

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2822

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄²

D₁₈₈

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂²

C₂²×D₁₈₈

yes

characteristic

C₂²

#13094069

yes

characteristic

100

C₂²

#13094071

yes

—

101

C₂²

#13094072

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

188

—

106

C₄

—

188

—

107

C₂

#15689699

yes

—

108

C₂

#15689704

yes

characteristic

109

C₂

#15689873

yes

—

110

C₂

C₄₇⋊#564

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#382	C₂
hypercenter	#382	D₄₇
hypocenter	C₄₇	#2822
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#382

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
61. C₄₇	#2822	semidirect

H ≅ G/N

type

61. C₄₇

#2822

semidirect

Subgroups — #20251456

Conjugacy classes of subgroups

Complements