Group #20251579 — subgroups

Subgroups — #20251579

Order 6016.

380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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	#15689065	C₂	1	6	yes	maximal, complemented
2	#15689048	C₂	1	3	yes	maximal
3	#15689042	C₂	1	2	yes	maximal, complemented
4	#15688995	C₂	1	3	yes	maximal
5	C₄₇×#393	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
9	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
10	C₄₇⋊#95	C₂²	1	6	yes	—
11	C₄₇⋊#95	C₂²	1	6	yes	—
12	C₄₇⋊#95	C₂²	1	3	yes	—
13	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
15	#95×C₄₇	C₂²	1	3	yes	—
16	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	—	4	3	no	—
18	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
19	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
20	C₂²×Dic₄₇	—	4	3	no	—
21	C₂²×Dic₄₇	C₂³	1	6	yes	—
22	C₂²×Dic₄₇	C₂³	1	2	yes	—
23	C₂²⋊C₄×C₄₇	—	4	3	no	—
24	C₂²⋊Dic₄₇	—	2	6	no	—
25	C₄⋊Dic₄₇	—	4	3	no	—
26	Dic₄₇⋊C₄	—	4	6	no	—
27	C₂³×C₄₇	—	2	3	no	—
28	C₂³×C₄₇	—	2	3	no	—
29	C₂³×C₄₇	#41	1	2	yes	—
30	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
31	Q₈×C₄₇	—	4	4	no	—
32	C₂×C₄×C₄₇	—	2	6	no	—
33	C₂×C₄×C₄₇	—	2	3	no	—
34	C₂×C₄×C₄₇	—	2	3	no	—
35	C₂×C₄×C₄₇	—	2	6	no	—
36	C₂×Dic₄₇	—	2	6	no	—
37	C₂×Dic₄₇	—	2	6	no	—
38	C₂×Dic₄₇	—	2	6	no	—
39	C₂×Dic₄₇	—	2	6	no	—
40	C₂×Dic₄₇	—	4	4	no	—
41	C₂²×C₄₇	—	2	6	no	—
42	C₂²×C₄₇	—	4	1	no	—
43	C₂²×C₄₇	—	4	3	no	—
44	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
45	C₂²×C₄₇	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₄₇	2₋¹⁺⁴	1	3	yes	—
47	C₄×C₄₇	—	4	3	no	—
48	C₄×C₄₇	—	4	3	no	—
49	Dic₄₇	—	4	6	no	—
50	Dic₄₇	—	4	2	no	—
51	#2835	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	—	4	2	no	—
53	C₂×C₄₇	#539	1	3	yes	—
54	C₂×C₄₇	H(3,𝔽₄)	1	1	yes	characteristic
55	C₂×C₄₇	#563	1	3	yes	—
56	#400	—	47	6	no	—
57	#397	—	47	3	no	—
58	#395	—	47	2	no	—
59	#393	D₄₇	1	1	yes	characteristic
60	#385	—	47	3	no	—
61	C₄₇	#2835	1	1	yes	characteristic, complemented, Sylow
62	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
63	C₂³×C₄	—	47	1	no	—
64	C₂×C₄⋊C₄	—	47	6	no	—
65	C₂×C₄⋊C₄	—	47	3	no	—
66	C₂×C₂²⋊C₄	—	47	3	no	—
67	C₂×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
68	#95	—	47	6	no	—
69	#95	—	47	6	no	—
70	#95	—	47	3	no	—
71	#95	C₂×D₄₇	1	3	yes	—
72	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
73	C₂×Q₈	—	4	3	no	—
74	C₂²×C₄	—	47	6	no	—
75	C₂²×C₄	—	47	2	no	—
76	C₂²×C₄	—	188	3	no	—
77	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
78	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
79	C₄⋊C₄	—	188	6	no	—
80	C₄⋊C₄	—	188	3	no	—
81	C₂²⋊C₄	—	4	3	no	—
82	C₂²⋊C₄	—	94	6	no	—
83	C₂³	—	2	3	no	—
84	C₂³	—	2	3	no	—
85	C₂³	#10625354	1	2	yes	—
86	C₂³	C₂³×D₄₇	1	1	yes	characteristic
87	Q₈	—	4	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	6	no	—
91	C₂×C₄	—	2	6	no	—
92	C₂×C₄	—	94	6	no	—
93	C₂×C₄	—	94	6	no	—
94	C₂×C₄	—	94	6	no	—
95	C₂×C₄	—	94	6	no	—
96	C₂×C₄	—	188	4	no	—
97	C₂²	—	2	6	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	4	3	no	—
100	C₂²	C₂×#10625354	1	1	yes	characteristic
101	C₂²	#13094069	1	3	yes	—
102	C₂²	#13094071	1	3	yes	—
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	188	2	no	—
106	C₄	—	188	6	no	—
107	C₂	—	4	2	no	—
108	C₂	#15689722	1	3	yes	—
109	C₂	#15689866	1	1	yes	characteristic
110	C₂	#15689873	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689065

C₂

yes

maximal, complemented

#15689048

C₂

yes

maximal

#15689042

C₂

yes

maximal, complemented

#15688995

C₂

yes

maximal

C₄₇×#393

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2835

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#539

yes

—

C₂×C₄₇

H(3,𝔽₄)

yes

characteristic

C₂×C₄₇

#563

yes

—

—

—

—

D₄₇

yes

characteristic

#385

—

C₄₇

#2835

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

—

—

—

C₂×D₄₇

yes

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

188

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

#10625354

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#10625354

yes

characteristic

101

C₂²

#13094069

yes

—

102

C₂²

#13094071

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

188

—

106

C₄

—

188

—

107

C₂

—

108

C₂

#15689722

yes

—

109

C₂

#15689866

yes

characteristic

110

C₂

#15689873

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#393	C₂
hypercenter	#393	D₄₇
hypocenter	C₄₇	#2835
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #393

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#393

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #393

N	H ≅ G/N	type
1. #15689065	C₂	semidirect
3. #15689042	C₂	semidirect
61. C₄₇	#2835	semidirect

H ≅ G/N

type

1. #15689065

C₂

semidirect

3. #15689042

C₂

semidirect

61. C₄₇

#2835

semidirect

Subgroups — #20251579

Conjugacy classes of subgroups

Complements