Group #20251462 — subgroups

Subgroups — #20251462

Order 6016.

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

normal subgroups only

This group has 456 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×#13094018	C₂	1	2	yes	maximal, complemented
2	#15689053	C₂	1	3	yes	maximal, complemented
3	#15689045	C₂	1	6	yes	maximal, complemented
4	#15689040	C₂	1	3	yes	maximal
5	C₄₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
7	#13094018	—	2	8	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
10	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	6	yes	—
11	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	6	yes	—
12	C₄₇⋊#95	C₂²	1	3	yes	—
13	C₄₇⋊#95	C₂²	1	3	yes	—
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
15	C₂×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
16	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄₇	C₂³	1	2	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
21	C₂²×Dic₄₇	C₂³	1	6	yes	—
22	C₂×D₁₈₈	—	4	3	no	—
23	C₄⋊C₄×C₄₇	—	4	3	no	—
24	C₄⋊C₄×C₄₇	—	4	3	no	—
25	C₄²×C₄₇	D₄	1	4	yes	complemented
26	(C₂×D₄₇)⋊C₄	—	2	12	no	—
27	(C₂×D₄₇)⋊C₄	—	4	6	no	—
28	C₄⋊Dic₄₇	—	4	3	no	—
29	Dic₄₇⋊C₄	—	2	12	no	—
30	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
31	C₂²×D₄₇	—	2	2	no	—
32	C₂²×D₄₇	—	2	6	no	—
33	C₂²×D₄₇	—	2	6	no	—
34	C₂×C₄×C₄₇	—	2	3	no	—
35	C₂×C₄×C₄₇	—	2	3	no	—
36	C₂×C₄×C₄₇	—	2	3	no	—
37	C₂×C₄×C₄₇	—	2	6	no	—
38	C₂×C₄×C₄₇	—	2	3	no	—
39	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
40	C₂×Dic₄₇	—	2	6	no	—
41	C₂×Dic₄₇	—	2	6	no	—
42	C₂×Dic₄₇	—	2	6	no	—
43	D₁₈₈	—	4	4	no	—
44	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
45	C₂²×C₄₇	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₄₇	2₋¹⁺⁴	1	3	yes	—
47	C₂×D₄₇	—	4	6	no	—
48	C₂×D₄₇	—	4	2	no	—
49	C₂×D₄₇	—	4	6	no	—
50	C₄×C₄₇	—	2	6	no	—
51	C₄×C₄₇	—	4	1	no	—
52	C₄×C₄₇	—	4	3	no	—
53	Dic₄₇	—	4	6	no	—
54	#2823	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	#537	1	3	yes	—
56	C₂×C₄₇	#560	1	1	yes	characteristic
57	C₂×C₄₇	#563	1	3	yes	—
58	D₄₇	—	8	2	no	—
59	C₂×#126	—	47	2	no	—
60	#398	—	47	3	no	—
61	#396	—	47	6	no	—
62	#394	—	47	3	no	—
63	#384	D₄₇	1	1	yes	characteristic, complemented
64	C₄₇	#2823	1	1	yes	characteristic, complemented, Sylow
65	C₂²×D₄	—	47	1	no	—
66	#126	—	94	8	no	—
67	C₂×C₄⋊C₄	—	47	6	no	—
68	C₂×C₄⋊C₄	—	47	3	no	—
69	C₂×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
70	C₂×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
71	C₂×C₂²⋊C₄	—	47	6	no	—
72	C₂×C₂²⋊C₄	—	47	6	no	—
73	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
74	#95	—	47	3	no	—
75	#95	—	47	3	no	—
76	C₂⁴	—	47	2	no	—
77	C₂×D₄	—	188	3	no	—
78	C₂²×C₄	—	47	6	no	—
79	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
80	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
81	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
82	C₄⋊C₄	—	4	3	no	—
83	C₄⋊C₄	—	4	3	no	—
84	C₄⋊C₄	—	94	12	no	—
85	C₄⋊C₄	—	188	3	no	—
86	C₂²⋊C₄	—	94	12	no	—
87	C₂²⋊C₄	—	188	6	no	—
88	C₄²	D₁₈₈	1	4	yes	complemented
89	C₂³	—	94	2	no	—
90	C₂³	—	94	6	no	—
91	C₂³	—	94	6	no	—
92	C₂³	C₂³×D₄₇	1	1	yes	characteristic
93	D₄	—	188	4	no	—
94	C₂×C₄	—	2	3	no	—
95	C₂×C₄	—	2	3	no	—
96	C₂×C₄	—	2	6	no	—
97	C₂×C₄	—	2	3	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	94	6	no	—
100	C₂×C₄	—	94	6	no	—
101	C₂×C₄	—	94	6	no	—
102	C₂×C₄	C₂×D₁₈₈	1	6	yes	—
103	C₂²	—	188	2	no	—
104	C₂²	—	188	6	no	—
105	C₂²	—	188	6	no	—
106	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
107	C₂²	#13094069	1	3	yes	—
108	C₂²	#13094072	1	3	yes	—
109	C₄	—	2	6	no	—
110	C₄	—	4	1	no	—
111	C₄	—	4	3	no	—
112	C₄	—	188	6	no	—
113	C₂	—	376	2	no	—
114	C₂	#15689704	1	3	yes	—
115	C₂	#15689860	1	1	yes	characteristic
116	C₂	#15689872	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094018

C₂

yes

maximal, complemented

#15689053

C₂

yes

maximal, complemented

#15689045

C₂

yes

maximal, complemented

#15689040

C₂

yes

maximal

C₄₇×#384

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

characteristic

#13094018

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×D₁₈₈

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

complemented

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#2823

—

maximal, Sylow

C₂×C₄₇

#537

yes

—

C₂×C₄₇

#560

yes

characteristic

C₂×C₄₇

#563

yes

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2823

yes

characteristic, complemented, Sylow

C₂²×D₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#95

—

#95

—

C₂⁴

—

C₂×D₄

—

188

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

D₁₈₈

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₇

yes

characteristic

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂×D₁₈₈

yes

—

103

C₂²

—

188

—

104

C₂²

—

188

—

105

C₂²

—

188

—

106

C₂²

C₂²×D₁₈₈

yes

characteristic

107

C₂²

#13094069

yes

—

108

C₂²

#13094072

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

188

—

113

C₂

—

376

—

114

C₂

#15689704

yes

—

115

C₂

#15689860

yes

characteristic

116

C₂

#15689872

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#384	C₂
hypercenter	#384	D₄₇
hypocenter	C₄₇	#2823
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#384

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
1. C₂×#13094018	C₂	semidirect
2. #15689053	C₂	semidirect
3. #15689045	C₂	semidirect
5. C₄₇×#384	C₂	semidirect
25. C₄²×C₄₇	D₄	semidirect
63. #384	D₄₇	semidirect
64. C₄₇	#2823	semidirect
88. C₄²	D₁₈₈	semidirect

H ≅ G/N

type

1. C₂×#13094018

C₂

semidirect

2. #15689053

C₂

semidirect

3. #15689045

C₂

semidirect

5. C₄₇×#384

C₂

semidirect

25. C₄²×C₄₇

D₄

semidirect

63. #384

D₄₇

semidirect

64. C₄₇

#2823

semidirect

88. C₄²

D₁₈₈

semidirect

Subgroups — #20251462

Conjugacy classes of subgroups

Complements