Group #20243054 — subgroups

Subgroups — #20243054

Order 6016.

242 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 69 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	#15689500	C₂	1	2	yes	maximal, complemented
2	#15689500	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689496	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689470	C₂	1	2	yes	maximal, complemented
5	C₄₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625325	—	2	2	no	—
7	C₂×D₃₇₆	—	2	4	no	—
8	C₂×D₃₇₆	—	2	2	no	—
9	#13094024	C₂²	1	1	yes	characteristic
10	#13094021	C₂²	1	1	yes	characteristic
11	#13094021	C₂²	1	2	yes	—
12	#13093946	—	2	4	no	—
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₇	C₂²	1	2	yes	—
15	C₂×D₁₈₈	—	2	2	no	—
16	C₂×D₁₈₈	—	2	2	no	—
17	C₂×D₁₈₈	—	2	2	no	—
18	C₂×D₁₈₈	—	2	2	no	—
19	C₂×D₁₈₈	—	2	1	no	—
20	C₂×Dic₉₄	—	2	1	no	—
21	C₂×C₈×C₄₇	D₄	1	4	yes	—
22	C₂×C₈×C₄₇	D₄	1	2	yes	—
23	C₄²×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊Dic₄₇	—	2	2	no	—
25	D₃₇₆	—	4	8	no	—
26	D₃₇₆	—	4	4	no	—
27	#10625325	—	4	4	no	—
28	C₂²×D₄₇	—	4	2	no	—
29	C₂²×D₄₇	—	4	1	no	—
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
32	C₂×Dic₄₇	—	4	1	no	—
33	D₁₈₈	—	4	2	no	—
34	D₁₈₈	—	4	4	no	—
35	D₁₈₈	—	4	4	no	—
36	D₁₈₈	—	4	4	no	—
37	D₁₈₈	—	4	4	no	—
38	Dic₉₄	—	4	2	no	—
39	C₈×C₄₇	—	2	4	no	—
40	C₈×C₄₇	D₈	1	4	yes	complemented
41	C₂²×C₄₇	#127	1	1	yes	characteristic
42	C₂×D₄₇	—	8	1	no	—
43	C₂×D₄₇	—	8	2	no	—
44	C₂×D₄₇	—	8	2	no	—
45	C₂×D₄₇	—	8	2	no	—
46	C₂×D₄₇	—	8	2	no	—
47	C₄×C₄₇	C₂×D₈	1	2	yes	—
48	C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
49	Dic₄₇	—	8	1	no	—
50	#1721	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	#493	1	1	yes	characteristic
52	C₂×C₄₇	#496	1	2	yes	—
53	D₄₇	—	16	1	no	—
54	D₄₇	—	16	2	no	—
55	#493	—	47	2	no	—
56	#493	—	47	1	no	—
57	#492	—	47	1	no	—
58	#486	—	47	2	no	—
59	#322	D₄₇	1	1	yes	characteristic, complemented
60	C₄₇	#1721	1	1	yes	characteristic, complemented, Sylow
61	C₂×SD₁₆	—	94	2	no	—
62	C₂×D₈	—	94	4	no	—
63	C₂×D₈	—	94	2	no	—
64	C₄⋊Q₈	—	47	1	no	—
65	#127	—	47	2	no	—
66	#127	—	47	1	no	—
67	#102	—	94	4	no	—
68	C₄×C₈	C₂×D₄₇	1	2	yes	—
69	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
70	C₂×Q₈	—	94	1	no	—
71	C₂×D₄	—	94	2	no	—
72	C₂×D₄	—	94	2	no	—
73	C₂×D₄	—	94	2	no	—
74	C₂×D₄	—	94	2	no	—
75	C₂×D₄	—	94	1	no	—
76	SD₁₆	—	188	4	no	—
77	D₈	—	188	8	no	—
78	D₈	—	188	4	no	—
79	C₂×C₈	D₁₈₈	1	4	yes	—
80	C₂×C₈	D₁₈₈	1	2	yes	—
81	C₄⋊C₄	—	94	2	no	—
82	C₄²	C₂²×D₄₇	1	1	yes	characteristic
83	C₂³	—	188	2	no	—
84	C₂³	—	188	1	no	—
85	Q₈	—	188	2	no	—
86	D₄	—	188	4	no	—
87	D₄	—	188	2	no	—
88	D₄	—	188	4	no	—
89	D₄	—	188	4	no	—
90	D₄	—	188	4	no	—
91	C₂×C₄	—	188	1	no	—
92	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
93	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
94	C₈	—	2	4	no	—
95	C₈	D₃₇₆	1	4	yes	complemented
96	C₂²	—	376	2	no	—
97	C₂²	—	376	1	no	—
98	C₂²	—	376	2	no	—
99	C₂²	—	376	2	no	—
100	C₂²	—	376	2	no	—
101	C₂²	#13094021	1	1	yes	characteristic
102	C₄	—	376	1	no	—
103	C₄	C₂×D₃₇₆	1	2	yes	—
104	C₄	#13094052	1	4	yes	—
105	C₂	—	752	2	no	—
106	C₂	—	752	1	no	—
107	C₂	#15689500	1	1	yes	characteristic
108	C₂	#15689512	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689500

C₂

yes

maximal, complemented

#15689500

C₂

yes

maximal, characteristic, complemented

#15689496

C₂

yes

maximal, characteristic, complemented

#15689470

C₂

yes

maximal, complemented

C₄₇×#322

C₂

yes

maximal, characteristic, complemented

C₂×#10625325

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

#13094024

C₂²

yes

characteristic

#13094021

C₂²

yes

characteristic

#13094021

C₂²

yes

—

#13093946

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

—

D₃₇₆

—

D₃₇₆

—

#10625325

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

D₈

yes

complemented

C₂²×C₄₇

#127

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

C₂×D₈

yes

—

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#1721

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

#127

—

#102

—

C₄×C₈

C₂×D₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

188

—

D₈

—

188

—

D₈

—

188

—

C₂×C₈

D₁₈₈

yes

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

188

—

C₂³

—

188

—

Q₈

—

188

—

D₄

—

188

—

D₄

—

188

—

D₄

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

—

C₈

—

C₈

D₃₇₆

yes

complemented

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

376

—

100

C₂²

—

376

—

101

C₂²

#13094021

yes

characteristic

102

C₄

—

376

—

103

C₄

C₂×D₃₇₆

yes

—

104

C₄

#13094052

yes

—

105

C₂

—

752

—

106

C₂

—

752

—

107

C₂

#15689500

yes

characteristic

108

C₂

#15689512

yes

—

	subgroup	G/H
center	C₂²	#13094021
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#322	C₂
socle	C₂²×C₄₇	#127
hypercenter	#322	D₄₇
hypocenter	C₄₇	#1721
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#13094021

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#322

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
1. #15689500	C₂	semidirect
2. #15689500	C₂	semidirect
3. #15689496	C₂	semidirect
4. #15689470	C₂	semidirect
5. C₄₇×#322	C₂	semidirect
40. C₈×C₄₇	D₈	semidirect
59. #322	D₄₇	semidirect
60. C₄₇	#1721	semidirect
95. C₈	D₃₇₆	semidirect

H ≅ G/N

type

1. #15689500

C₂

semidirect

2. #15689500

C₂

semidirect

3. #15689496

C₂

semidirect

4. #15689470

C₂

semidirect

5. C₄₇×#322

C₂

semidirect

40. C₈×C₄₇

D₈

semidirect

59. #322

D₄₇

semidirect

60. C₄₇

#1721

semidirect

95. C₈

D₃₇₆

semidirect

Subgroups — #20243054

Conjugacy classes of subgroups

Complements