Group #20245569 — subgroups

Subgroups — #20245569

Order 6016.

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689359	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688949	C₂	1	2	yes	maximal, complemented
4	#15688925	C₂	1	2	yes	maximal, complemented
5	C₄₇×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
7	#13093998	—	2	1	no	—
8	C₂×C₄⋊Dic₄₇	—	2	1	no	—
9	#13093958	—	2	1	no	—
10	#13093958	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	2	yes	—
12	#13093946	—	2	1	no	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂×C₂²⋊D₄₇	—	4	1	no	—
17	C₂²×Dic₄₇	—	4	1	no	—
18	C₂×D₁₈₈	—	2	1	no	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	(C₂×D₄₇)⋊C₄	—	4	1	no	—
23	C₄⋊Dic₄₇	—	2	1	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	—	4	1	no	—
26	D₃₇₆	—	2	2	no	—
27	C₁₆×C₄₇	—	2	2	no	—
28	C₂³×C₄₇	D₈	1	1	yes	characteristic
29	C₂²×D₄₇	—	4	1	no	—
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	—	2	1	no	—
32	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₄₇	—	8	2	no	—
35	C₂×Dic₄₇	—	4	2	no	—
36	C₂×Dic₄₇	—	4	1	no	—
37	C₂×Dic₄₇	—	8	2	no	—
38	D₁₈₈	—	4	1	no	—
39	D₁₈₈	—	4	1	no	—
40	C₈×C₄₇	—	2	1	no	—
41	C₈×C₄₇	#41	1	2	yes	—
42	C₂²×C₄₇	—	2	1	no	—
43	C₂²×C₄₇	—	2	1	no	—
44	C₂²×C₄₇	D₁₆	1	2	yes	—
45	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
46	C₂×D₄₇	—	8	1	no	—
47	C₂×D₄₇	—	8	1	no	—
48	C₂×D₄₇	—	8	1	no	—
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	#123	1	1	yes	characteristic
51	C₄×C₄₇	#137	1	1	yes	characteristic
52	Dic₄₇	—	8	2	no	—
53	Dic₄₇	—	8	1	no	—
54	#2232	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	—	2	2	no	—
56	C₂×C₄₇	#480	1	1	yes	characteristic
57	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
58	C₂×C₄₇	#510	1	1	yes	characteristic
59	D₄₇	—	16	1	no	—
60	#466	—	47	1	no	—
61	C₂×#107	—	47	1	no	—
62	#366	—	47	2	no	—
63	#357	—	47	2	no	—
64	C₂²⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
65	C₄₇	#2232	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₈	—	47	1	no	—
67	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
68	#121	—	94	1	no	—
69	C₂×C₄⋊C₄	—	94	1	no	—
70	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
71	#107	—	47	2	no	—
72	#107	—	47	1	no	—
73	#107	—	94	1	no	—
74	#102	—	94	1	no	—
75	C₂×D₄	—	94	1	no	—
76	C₂×D₄	—	188	1	no	—
77	C₂²×C₄	—	188	1	no	—
78	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
79	D₈	—	94	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	D₁₈₈	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
83	C₄⋊C₄	—	94	1	no	—
84	C₄⋊C₄	—	94	2	no	—
85	C₄⋊C₄	—	188	1	no	—
86	C₂²⋊C₄	—	188	1	no	—
87	C₁₆	—	2	2	no	—
88	C₂³	—	188	1	no	—
89	C₂³	D₃₇₆	1	1	yes	characteristic
90	D₄	—	376	2	no	—
91	D₄	—	188	1	no	—
92	D₄	—	188	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	376	2	no	—
96	C₂×C₄	—	188	1	no	—
97	C₂×C₄	—	188	2	no	—
98	C₂×C₄	D₃₇₆	1	1	yes	characteristic
99	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
100	C₈	—	2	1	no	—
101	C₈	#10625352	1	2	yes	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	—	376	1	no	—
105	C₂²	—	376	1	no	—
106	C₂²	—	376	1	no	—
107	C₂²	D₇₅₂	1	2	yes	—
108	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	376	2	no	—
111	C₄	—	376	1	no	—
112	C₄	#13094008	1	1	yes	characteristic
113	C₄	#13094057	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	—	752	1	no	—
116	C₂	#15689437	1	1	yes	characteristic
117	C₂	C₂×D₇₅₂	1	1	yes	characteristic
118	C₂	#15689566	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689359

C₂

yes

maximal, characteristic

C₂×#13093958

C₂

yes

maximal, characteristic, complemented

#15688949

C₂

yes

maximal, complemented

#15688925

C₂

yes

maximal, complemented

C₄₇×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₂²

yes

characteristic

#13093998

—

C₂×C₄⋊Dic₄₇

—

#13093958

—

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

—

#13093946

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

D₃₇₆

—

C₁₆×C₄₇

—

C₂³×C₄₇

D₈

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

D₁₆

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

#2232

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#480

yes

characteristic

C₂×C₄₇

C₂×D₁₆

yes

characteristic

C₂×C₄₇

#510

yes

characteristic

D₄₇

—

—

—

—

—

C₂²⋊C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

#2232

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#121

—

C₂×C₄⋊C₄

—

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

—

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

—

188

—

C₂²×C₄

D₁₈₈

yes

characteristic

D₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₁₆

—

C₂³

—

188

—

C₂³

D₃₇₆

yes

characteristic

D₄

—

376

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

characteristic

100

C₈

—

101

C₈

#10625352

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

376

—

105

C₂²

—

376

—

106

C₂²

—

376

—

107

C₂²

D₇₅₂

yes

—

108

C₂²

C₂×D₃₇₆

yes

characteristic

109

C₄

—

110

C₄

—

376

—

111

C₄

—

376

—

112

C₄

#13094008

yes

characteristic

113

C₄

#13094057

yes

characteristic

114

C₂

—

115

C₂

—

752

—

116

C₂

#15689437

yes

characteristic

117

C₂

C₂×D₇₅₂

yes

characteristic

118

C₂

#15689566

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×C₂²⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂²⋊C₁₆	D₄₇
hypocenter	C₄₇	#2232
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×C₂²⋊C₁₆

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂²⋊C₁₆

D₄₇

hypocenter

C₄₇

#2232

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. C₂×#13093958	C₂	semidirect
3. #15688949	C₂	semidirect
4. #15688925	C₂	semidirect
5. C₄₇×C₂²⋊C₁₆	C₂	semidirect
64. C₂²⋊C₁₆	D₄₇	semidirect
65. C₄₇	#2232	semidirect

H ≅ G/N

type

2. C₂×#13093958

C₂

semidirect

3. #15688949

C₂

semidirect

4. #15688925

C₂

semidirect

5. C₄₇×C₂²⋊C₁₆

C₂

semidirect

64. C₂²⋊C₁₆

D₄₇

semidirect

65. C₄₇

#2232

semidirect

Subgroups — #20245569

Conjugacy classes of subgroups

Complements