Group #20249490 — subgroups

Subgroups — #20249490

Order 6016.

804 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13093998	C₂	1	6	yes	maximal, complemented
2	#15689060	C₂	1	4	yes	maximal, complemented
3	#15689033	C₂	1	4	yes	maximal, complemented
4	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₈₈	C₂²	1	6	yes	—
6	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	—
7	#13093998	—	2	24	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	6	yes	—
9	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	12	yes	—
10	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
11	#95×C₄₇	C₂²	1	4	yes	—
12	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
13	C₂³×D₄₇	C₂³	1	4	yes	—
14	C₂²×C₄×C₄₇	—	4	6	no	—
15	C₂²×C₄×C₄₇	D₄	1	12	yes	complemented
16	C₂²×C₄×C₄₇	C₂³	1	6	yes	—
17	C₂×C₂²⋊D₄₇	—	2	24	no	—
18	C₂²×Dic₄₇	C₂³	1	4	yes	—
19	C₂×D₁₈₈	—	2	12	no	—
20	C₂×D₁₈₈	—	4	12	no	—
21	(C₂×D₄₇)⋊C₄	—	2	24	no	—
22	C₄⋊Dic₄₇	—	2	12	no	—
23	C₂³×C₄₇	—	2	3	no	—
24	C₂³×C₄₇	—	2	1	no	—
25	C₂³×C₄₇	C₂×D₄	1	6	yes	—
26	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
27	C₂²×D₄₇	—	2	12	no	—
28	C₂²×D₄₇	—	2	12	no	—
29	C₂²×D₄₇	—	2	4	no	—
30	C₂×C₄×C₄₇	—	2	12	no	—
31	C₂×C₄×C₄₇	—	4	12	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	12	yes	—
33	C₂²⋊D₄₇	—	4	16	no	—
34	C₂×Dic₄₇	—	2	12	no	—
35	D₁₈₈	—	4	24	no	—
36	C₂²×C₄₇	—	2	6	no	—
37	C₂²×C₄₇	—	2	6	no	—
38	C₂²×C₄₇	#127	1	4	yes	—
39	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
40	C₂²×C₄₇	H(5,𝔽₂)	1	3	yes	—
41	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
42	C₂×D₄₇	—	4	4	no	—
43	C₂×D₄₇	—	4	12	no	—
44	C₂×D₄₇	—	4	12	no	—
45	C₄×C₄₇	—	2	12	no	—
46	Dic₄₇	—	4	4	no	—
47	#2656	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	4	no	—
49	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
50	C₂×C₄₇	#534	1	3	yes	—
51	C₂×C₄₇	#537	1	3	yes	—
52	D₄₇	—	8	4	no	—
53	C₂×#121	—	47	6	no	—
54	#399	—	47	4	no	—
55	#392	—	47	4	no	—
56	C₂×#95	D₄₇	1	1	yes	characteristic, complemented
57	C₄₇	#2656	1	1	yes	characteristic, complemented, Sylow
58	C₂²×D₄	—	47	4	no	—
59	C₂²×D₄	—	47	6	no	—
60	C₂³×C₄	C₂×D₄₇	1	3	yes	—
61	#121	—	94	24	no	—
62	C₂×C₄⋊C₄	—	47	6	no	—
63	C₂×C₂²⋊C₄	—	47	12	no	—
64	#95	C₂×D₄₇	1	4	yes	—
65	C₂⁴	—	47	4	no	—
66	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
67	C₂×D₄	—	94	24	no	—
68	C₂×D₄	—	94	12	no	—
69	C₂×D₄	—	188	12	no	—
70	C₂²×C₄	—	4	6	no	—
71	C₂²×C₄	—	47	4	no	—
72	C₂²×C₄	D₁₈₈	1	12	yes	complemented
73	C₂²×C₄	C₂²×D₄₇	1	6	yes	—
74	C₄⋊C₄	—	94	12	no	—
75	C₂²⋊C₄	—	94	24	no	—
76	C₂³	—	2	3	no	—
77	C₂³	—	2	1	no	—
78	C₂³	—	94	12	no	—
79	C₂³	—	94	12	no	—
80	C₂³	—	94	4	no	—
81	C₂³	C₂×D₁₈₈	1	6	yes	—
82	C₂³	C₂³×D₄₇	1	1	yes	characteristic
83	D₄	—	188	24	no	—
84	D₄	—	188	16	no	—
85	C₂×C₄	—	2	12	no	—
86	C₂×C₄	—	4	12	no	—
87	C₂×C₄	—	94	12	no	—
88	C₂×C₄	C₂×D₁₈₈	1	12	yes	—
89	C₂²	—	2	6	no	—
90	C₂²	—	2	6	no	—
91	C₂²	—	188	4	no	—
92	C₂²	—	188	12	no	—
93	C₂²	—	188	12	no	—
94	C₂²	#13094021	1	4	yes	—
95	C₂²	C₂²×D₁₈₈	1	3	yes	—
96	C₂²	#13094069	1	3	yes	—
97	C₂²	#13094072	1	1	yes	characteristic
98	C₄	—	2	12	no	—
99	C₄	—	188	4	no	—
100	C₂	—	2	4	no	—
101	C₂	—	376	4	no	—
102	C₂	C₂×#13094021	1	1	yes	characteristic
103	C₂	#15689685	1	3	yes	—
104	C₂	#15689704	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093998

C₂

yes

maximal, complemented

#15689060

C₂

yes

maximal, complemented

#15689033

C₂

yes

maximal, complemented

C₂×#95×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

C₂²×C₂²⋊D₄₇

C₂²

yes

—

#13093998

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

—

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#127

yes

—

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#2656

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#127

yes

characteristic

C₂×C₄₇

#534

yes

—

C₂×C₄₇

#537

yes

—

D₄₇

—

C₂×#121

—

#399

—

#392

—

C₂×#95

D₄₇

yes

characteristic, complemented

C₄₇

#2656

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

C₂×D₄₇

yes

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#95

C₂×D₄₇

yes

—

C₂⁴

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

complemented

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×D₁₈₈

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂²

—

C₂²

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

#13094021

yes

—

C₂²

C₂²×D₁₈₈

yes

—

C₂²

#13094069

yes

—

C₂²

#13094072

yes

characteristic

C₄

—

C₄

—

188

—

100

C₂

—

101

C₂

—

376

—

102

C₂

C₂×#13094021

yes

characteristic

103

C₂

#15689685

yes

—

104

C₂

#15689704

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#95×C₄₇	C₂
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#2656
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#95×C₄₇

C₂

hypercenter

C₂×#95

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
1. C₂×#13093998	C₂	semidirect
2. #15689060	C₂	semidirect
3. #15689033	C₂	semidirect
4. C₂×#95×C₄₇	C₂	semidirect
15. C₂²×C₄×C₄₇	D₄	semidirect
56. C₂×#95	D₄₇	semidirect
57. C₄₇	#2656	semidirect
72. C₂²×C₄	D₁₈₈	semidirect

H ≅ G/N

type

1. C₂×#13093998

C₂

semidirect

2. #15689060

C₂

semidirect

3. #15689033

C₂

semidirect

4. C₂×#95×C₄₇

C₂

semidirect

15. C₂²×C₄×C₄₇

D₄

semidirect

56. C₂×#95

D₄₇

semidirect

57. C₄₇

#2656

semidirect

72. C₂²×C₄

D₁₈₈

semidirect

Subgroups — #20249490

Conjugacy classes of subgroups

Complements