Group #20241469 — subgroups

Subgroups — #20241469

Order 6016.

148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 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×#13093964	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
6	#13093964	—	2	1	no	—
7	#13093964	C₄	1	2	yes	complemented
8	C₂×C₄₇⋊C₁₆	—	2	1	no	—
9	C₈×Dic₄₇	—	2	1	no	—
10	C₈×Dic₄₇	—	2	1	no	—
11	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	M₃₂×C₄₇	—	2	1	no	—
13	M₃₂×C₄₇	C₄	1	2	yes	complemented
14	C₂×C₁₆×C₄₇	—	2	1	no	—
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₄₇	—	2	1	no	—
17	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
23	C₄×Dic₄₇	—	2	1	no	—
24	C₄×Dic₄₇	C₈	1	2	yes	—
25	C₂×C₄₇⋊C₈	—	2	1	no	—
26	C₂×C₄₇⋊C₈	—	2	1	no	—
27	C₂×C₄₇⋊C₈	C₈	1	2	yes	—
28	C₁₆×C₄₇	—	2	2	no	—
29	C₄₇⋊C₁₆	—	2	2	no	—
30	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
37	C₂×Dic₄₇	—	2	4	no	—
38	C₂×Dic₄₇	—	2	2	no	—
39	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
41	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
43	C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇	—	2	2	no	—
45	C₂²×C₄₇	#97	1	1	yes	characteristic
46	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
47	C₂²×C₄₇	C₄⋊C₈	1	1	yes	characteristic
48	C₄×C₄₇	#95	1	1	yes	characteristic
49	C₄×C₄₇	C₄×C₈	1	1	yes	characteristic
50	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
52	Dic₄₇	—	2	4	no	—
53	#1376	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	—	2	1	no	—
55	C₂×C₄₇	—	2	1	no	—
56	C₂×C₄₇	#336	1	1	yes	characteristic
57	C₂×C₄₇	#364	1	2	yes	—
58	C₂×M₃₂	—	47	1	no	—
59	C₂×M₃₂	D₄₇	1	1	yes	characteristic
60	C₂×C₄×C₈	—	47	1	no	—
61	C₄₇	#1376	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	47	1	no	—
63	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₂×C₄²	—	47	1	no	—
65	M₃₂	—	2	1	no	—
66	M₃₂	—	47	2	no	—
67	M₃₂	—	94	1	no	—
68	M₃₂	Dic₄₇	1	2	yes	complemented
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	94	1	no	—
71	C₄×C₈	—	94	1	no	—
72	C₄×C₈	—	94	1	no	—
73	C₂²×C₄	—	94	1	no	—
74	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
75	C₂×C₈	—	47	2	no	—
76	C₂×C₈	—	94	1	no	—
77	C₂×C₈	—	94	1	no	—
78	C₂×C₈	Dic₉₄	1	1	yes	characteristic
79	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
80	C₂×C₈	D₁₈₈	1	1	yes	characteristic
81	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
84	C₄²	—	47	2	no	—
85	C₄²	—	94	1	no	—
86	C₁₆	—	2	2	no	—
87	C₁₆	—	94	2	no	—
88	C₂³	#10625324	1	1	yes	characteristic
89	C₂×C₄	—	94	4	no	—
90	C₂×C₄	—	94	2	no	—
91	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
92	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
93	C₂×C₄	#10625324	1	1	yes	characteristic
94	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
95	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
96	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
97	C₈	—	94	2	no	—
98	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
99	C₈	C₄⋊Dic₄₇	1	1	yes	characteristic
100	C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
101	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
102	C₂²	—	2	2	no	—
103	C₂²	#13093934	1	1	yes	characteristic
104	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
105	C₂²	Dic₄₇⋊C₈	1	1	yes	characteristic
106	C₄	—	94	4	no	—
107	C₄	C₄₇⋊#95	1	1	yes	characteristic
108	C₄	C₈×Dic₄₇	1	1	yes	characteristic
109	C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
110	C₄	Dic₄₇⋊C₈	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	#15688877	1	1	yes	characteristic
114	C₂	#15688943	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

#13093964

—

#13093964

C₄

yes

complemented

C₂×C₄₇⋊C₁₆

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

C₄

yes

complemented

C₂×C₁₆×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

characteristic

C₄×Dic₄₇

—

C₄×Dic₄₇

C₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₈

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

#97

yes

characteristic

C₂²×C₄₇

C₂²⋊C₈

yes

characteristic

C₂²×C₄₇

C₄⋊C₈

yes

characteristic

C₄×C₄₇

#95

yes

characteristic

C₄×C₄₇

C₄×C₈

yes

characteristic

C₄×C₄₇

C₂²⋊C₈

yes

characteristic

C₄×C₄₇

C₄⋊C₈

yes

characteristic

Dic₄₇

—

#1376

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#336

yes

characteristic

C₂×C₄₇

#364

yes

—

C₂×M₃₂

—

C₂×M₃₂

D₄₇

yes

characteristic

C₂×C₄×C₈

—

C₄₇

#1376

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

Dic₄₇

yes

complemented

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

#10625324

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

#10625324

yes

characteristic

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

Dic₄₇⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

Dic₄₇⋊C₄

yes

characteristic

C₈

C₄⋊Dic₄₇

yes

characteristic

100

C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

101

C₈

C₂²⋊Dic₄₇

yes

characteristic

102

C₂²

—

103

C₂²

#13093934

yes

characteristic

104

C₂²

(C₂×D₄₇)⋊C₈

yes

characteristic

105

C₂²

Dic₄₇⋊C₈

yes

characteristic

106

C₄

—

107

C₄

C₄₇⋊#95

yes

characteristic

108

C₄

C₈×Dic₄₇

yes

characteristic

109

C₄

(C₂×D₄₇)⋊C₈

yes

characteristic

110

C₄

Dic₄₇⋊C₈

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

#15688877

yes

characteristic

114

C₂

#15688943

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₄×C₈
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂×M₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₄⋊C₈
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	#1376
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²⋊D₄₇

commutator

C₄×C₄₇

C₄×C₈

Frattini

C₂²×C₈

C₂×D₄₇

Fitting

C₂×M₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₄⋊C₈

hypercenter

C₂×M₃₂

D₄₇

hypocenter

C₄₇

#1376

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
7. #13093964	C₄	semidirect
13. M₃₂×C₄₇	C₄	semidirect
61. C₄₇	#1376	semidirect
68. M₃₂	Dic₄₇	semidirect

H ≅ G/N

type

7. #13093964

C₄

semidirect

13. M₃₂×C₄₇

C₄

semidirect

61. C₄₇

#1376

semidirect

68. M₃₂

Dic₄₇

semidirect

Subgroups — #20241469

Conjugacy classes of subgroups

Complements