Group #20245471 — subgroups

Subgroups — #20245471

Order 6016.

174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689356	C₂	1	2	yes	maximal, complemented
3	#15688949	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688924	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
7	#13093995	—	2	2	no	—
8	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₁₆×D₄₇	—	2	2	no	—
10	#13093958	C₂²	1	2	yes	—
11	#13093945	—	2	2	no	—
12	C₂×D₈×C₄₇	C₂²	1	2	yes	—
13	D₁₆×C₄₇	—	2	2	no	—
14	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₄₇	—	2	2	no	—
16	C₂×C₂²⋊D₄₇	—	4	2	no	—
17	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
18	D₈×C₄₇	—	2	2	no	—
19	D₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²⋊Dic₄₇	—	4	2	no	—
22	C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
24	C₈×D₄₇	—	2	1	no	—
25	C₈×D₄₇	—	2	1	no	—
26	C₁₆×C₄₇	D₄	1	2	yes	complemented
27	C₄₇⋊C₁₆	—	2	1	no	—
28	C₂³×C₄₇	—	4	2	no	—
29	C₂²×D₄₇	D₈	1	1	yes	characteristic
30	D₄×C₄₇	—	4	2	no	—
31	D₄×C₄₇	—	4	2	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂²⋊D₄₇	—	8	4	no	—
34	C₂×Dic₄₇	—	4	2	no	—
35	C₂×Dic₄₇	D₈	1	1	yes	characteristic
36	C₄×D₄₇	—	2	1	no	—
37	C₄×D₄₇	—	2	1	no	—
38	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₇	#41	1	1	yes	characteristic
40	C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇	—	8	2	no	—
42	C₂²×C₄₇	—	8	2	no	—
43	C₂²×C₄₇	—	8	2	no	—
44	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
45	C₂×D₄₇	—	2	1	no	—
46	C₂×D₄₇	—	2	1	no	—
47	C₂×D₄₇	D₁₆	1	2	yes	complemented
48	C₄×C₄₇	#121	1	1	yes	characteristic
49	C₄×C₄₇	#135	1	1	yes	characteristic
50	Dic₄₇	—	2	1	no	—
51	Dic₄₇	—	8	2	no	—
52	#2215	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	—	16	2	no	—
54	C₂×C₄₇	#466	1	1	yes	characteristic
55	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
56	C₂×C₄₇	#508	1	1	yes	characteristic
57	D₄₇	—	2	2	no	—
58	C₂×D₁₆	D₄₇	1	1	yes	characteristic, complemented
59	C₂²×C₁₆	—	47	1	no	—
60	#466	—	47	2	no	—
61	#366	—	47	1	no	—
62	#357	—	47	2	no	—
63	C₄₇	#2215	1	1	yes	characteristic, complemented, Sylow
64	C₂×D₈	C₂×D₄₇	1	2	yes	—
65	C₂²×C₈	—	47	1	no	—
66	#121	—	94	2	no	—
67	D₁₆	—	2	2	no	—
68	C₂×C₁₆	—	47	1	no	—
69	C₂×C₁₆	—	94	2	no	—
70	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
71	#107	—	47	2	no	—
72	#102	—	94	2	no	—
73	C₂×D₄	—	2	2	no	—
74	C₂×D₄	—	188	2	no	—
75	C₂²×C₄	—	47	1	no	—
76	D₈	—	2	2	no	—
77	D₈	—	2	2	no	—
78	C₂×C₈	—	47	1	no	—
79	C₂×C₈	—	94	1	no	—
80	C₂×C₈	—	94	1	no	—
81	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
82	C₄⋊C₄	—	94	2	no	—
83	C₂²⋊C₄	—	188	2	no	—
84	C₁₆	—	94	1	no	—
85	C₁₆	C₂²⋊D₄₇	1	2	yes	complemented
86	C₂³	—	4	2	no	—
87	C₂³	—	47	1	no	—
88	D₄	—	4	2	no	—
89	D₄	—	4	2	no	—
90	D₄	—	376	4	no	—
91	C₂×C₄	—	47	1	no	—
92	C₂×C₄	—	94	1	no	—
93	C₂×C₄	—	94	1	no	—
94	C₂×C₄	—	188	2	no	—
95	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
96	C₈	—	94	1	no	—
97	C₈	#10625352	1	1	yes	characteristic
98	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
99	C₂²	—	8	2	no	—
100	C₂²	—	8	2	no	—
101	C₂²	—	8	2	no	—
102	C₂²	—	47	2	no	—
103	C₂²	—	94	1	no	—
104	C₂²	—	94	1	no	—
105	C₂²	D₈×D₄₇	1	1	yes	characteristic
106	C₄	—	94	1	no	—
107	C₄	—	376	2	no	—
108	C₄	#13093995	1	1	yes	characteristic
109	C₄	#13094043	1	1	yes	characteristic
110	C₂	—	16	2	no	—
111	C₂	—	94	2	no	—
112	C₂	#15689356	1	1	yes	characteristic
113	C₂	D₁₆×D₄₇	1	1	yes	characteristic
114	C₂	#15689552	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₄₇

C₂

yes

maximal, characteristic, complemented

#15689356

C₂

yes

maximal, complemented

#15688949

C₂

yes

maximal, characteristic, complemented

#15688924

C₂

yes

maximal, complemented

C₂×D₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₂²

yes

characteristic

#13093995

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₇

—

#13093958

C₂²

yes

—

#13093945

—

C₂×D₈×C₄₇

C₂²

yes

—

D₁₆×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂×C₂²⋊D₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

D₄

yes

complemented

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂²×D₄₇

D₈

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

D₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

#2215

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#466

yes

characteristic

C₂×C₄₇

C₂×D₁₆

yes

characteristic

C₂×C₄₇

#508

yes

characteristic

D₄₇

—

C₂×D₁₆

D₄₇

yes

characteristic, complemented

C₂²×C₁₆

—

#466

—

#366

—

#357

—

C₄₇

#2215

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₇

yes

—

C₂²×C₈

—

#121

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#102

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₁₆

—

C₁₆

C₂²⋊D₄₇

yes

complemented

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

376

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

#10625352

yes

characteristic

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

D₈×D₄₇

yes

characteristic

106

C₄

—

107

C₄

—

376

—

108

C₄

#13093995

yes

characteristic

109

C₄

#13094043

yes

characteristic

110

C₂

—

111

C₂

—

112

C₂

#15689356

yes

characteristic

113

C₂

D₁₆×D₄₇

yes

characteristic

114

C₂

#15689552

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×D₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×D₁₆	D₄₇
hypocenter	C₄₇	#2215
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×D₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂×D₁₆

D₄₇

hypocenter

C₄₇

#2215

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. C₂×C₁₆×D₄₇	C₂	semidirect
2. #15689356	C₂	semidirect
3. #15688949	C₂	semidirect
4. #15688924	C₂	semidirect
5. C₂×D₁₆×C₄₇	C₂	semidirect
26. C₁₆×C₄₇	D₄	semidirect
47. C₂×D₄₇	D₁₆	semidirect
58. C₂×D₁₆	D₄₇	semidirect
63. C₄₇	#2215	semidirect
85. C₁₆	C₂²⋊D₄₇	semidirect

H ≅ G/N

type

1. C₂×C₁₆×D₄₇

C₂

semidirect

2. #15689356

C₂

semidirect

3. #15688949

C₂

semidirect

4. #15688924

C₂

semidirect

5. C₂×D₁₆×C₄₇

C₂

semidirect

26. C₁₆×C₄₇

D₄

semidirect

47. C₂×D₄₇

D₁₆

semidirect

58. C₂×D₁₆

D₄₇

semidirect

63. C₄₇

#2215

semidirect

85. C₁₆

C₂²⋊D₄₇

semidirect

Subgroups — #20245471

Conjugacy classes of subgroups

Complements