Group #20241313 — subgroups

Subgroups — #20241313

Order 6016.

116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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	#15689089	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625350	C₄	1	1	yes	characteristic
5	C₂×#10625329	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₁₆	—	2	1	no	—
7	(C₂×D₄₇)⋊C₈	—	2	1	no	—
8	(C₂×D₄₇)⋊C₈	—	2	1	no	—
9	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₄₇	—	2	1	no	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₇	—	2	1	no	—
13	#10625350	—	4	1	no	—
14	#10625350	—	4	1	no	—
15	C₂×D₁₈₈	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₇	—	2	1	no	—
17	C₂×Dic₉₄	C₈	1	1	yes	characteristic
18	C₂×C₈×C₄₇	—	4	1	no	—
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	#10625329	—	4	1	no	—
22	C₂×C₄₇⋊C₈	—	2	1	no	—
23	C₁₆×C₄₇	—	4	1	no	—
24	C₄₇⋊C₁₆	—	4	1	no	—
25	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
26	C₂²×D₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	2	1	no	—
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
31	C₂²⋊D₄₇	—	4	2	no	—
32	C₂×Dic₄₇	—	2	1	no	—
33	D₁₈₈	—	4	1	no	—
34	C₄×D₄₇	—	4	1	no	—
35	C₄×D₄₇	—	4	1	no	—
36	Dic₉₄	—	4	1	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	—	2	1	no	—
39	C₄₇⋊C₈	—	4	1	no	—
40	C₂²×C₄₇	—	2	1	no	—
41	C₂²×C₄₇	—	2	1	no	—
42	C₂²×C₄₇	—	2	1	no	—
43	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
44	C₂×D₄₇	—	4	1	no	—
45	C₂×D₄₇	—	4	1	no	—
46	C₂×D₄₇	—	4	1	no	—
47	C₄×C₄₇	—	2	1	no	—
48	C₄×C₄₇	#99	1	1	yes	characteristic
49	C₄×C₄₇	#100	1	1	yes	characteristic
50	Dic₄₇	—	4	1	no	—
51	#1315	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	—	4	1	no	—
53	C₂×C₄₇	#323	1	1	yes	characteristic
54	C₂×C₄₇	#350	1	1	yes	characteristic
55	C₂×C₄₇	#350	1	1	yes	characteristic
56	D₄₇	—	8	1	no	—
57	#408	—	47	1	no	—
58	C₂²⋊C₁₆	—	47	1	no	—
59	C₂²⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
60	C₄₇	#1315	1	1	yes	characteristic, complemented, Sylow
61	C₂×#41	—	47	1	no	—
62	C₂×M₁₆	—	47	1	no	—
63	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₂×C₁₆	—	2	1	no	—
65	C₂×C₁₆	—	94	1	no	—
66	C₂²⋊C₈	—	94	1	no	—
67	C₂²⋊C₈	—	94	1	no	—
68	#41	—	188	1	no	—
69	#41	—	188	1	no	—
70	C₂×Q₈	—	47	1	no	—
71	C₂×D₄	—	47	1	no	—
72	C₂×D₄	—	94	1	no	—
73	C₂²×C₄	—	94	1	no	—
74	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
75	M₁₆	—	188	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	—	94	1	no	—
78	C₂×C₈	D₁₈₈	1	1	yes	characteristic
79	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
80	C₁₆	—	4	1	no	—
81	C₁₆	—	188	1	no	—
82	C₂³	—	94	1	no	—
83	C₂³	#10625324	1	1	yes	characteristic
84	Q₈	—	188	1	no	—
85	D₄	—	188	1	no	—
86	D₄	—	188	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	94	1	no	—
90	C₂×C₄	—	188	1	no	—
91	C₂×C₄	—	188	1	no	—
92	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
93	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	2	1	no	—
96	C₈	—	188	1	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	188	1	no	—
101	C₂²	—	188	1	no	—
102	C₂²	—	188	1	no	—
103	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	188	1	no	—
106	C₄	#13093938	1	1	yes	characteristic
107	C₄	#13093940	1	1	yes	characteristic
108	C₂	—	4	1	no	—
109	C₂	—	376	1	no	—
110	C₂	#15688846	1	1	yes	characteristic
111	C₂	#15688906	1	1	yes	characteristic
112	C₂	#15688908	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689089

C₂

yes

maximal, characteristic

C₂²⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₄₇×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₄

yes

characteristic

C₂×#10625329

C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

—

(C₂×D₄₇)⋊C₈

—

(C₂×D₄₇)⋊C₈

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₈

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

M₁₆

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1315

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#408

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

#1315

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#41

—

188

—

#41

—

188

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

188

—

C₂³

—

C₂³

#10625324

yes

characteristic

Q₈

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

188

—

101

C₂²

—

188

—

102

C₂²

—

188

—

103

C₂²

(C₂×D₄₇)⋊C₈

yes

characteristic

104

C₄

—

105

C₄

—

188

—

106

C₄

#13093938

yes

characteristic

107

C₄

#13093940

yes

characteristic

108

C₂

—

109

C₂

—

376

—

110

C₂

#15688846

yes

characteristic

111

C₂

#15688906

yes

characteristic

112

C₂

#15688908

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₈
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₄₇×C₂²⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂²⋊C₈
hypercenter	C₂²⋊C₁₆	D₄₇
hypocenter	C₄₇	#1315
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂×C₄

(C₂×D₄₇)⋊C₄

commutator

C₂×C₄×C₄₇

C₂×C₈

Frattini

C₂²×C₈

C₂×D₄₇

Fitting

C₄₇×C₂²⋊C₁₆

C₂

socle

C₂²×C₄₇

C₂²⋊C₈

hypercenter

C₂²⋊C₁₆

D₄₇

hypocenter

C₄₇

#1315

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. C₂²⋊(C₄₇⋊C₁₆)	C₂	semidirect
3. C₄₇×C₂²⋊C₁₆	C₂	semidirect
59. C₂²⋊C₁₆	D₄₇	semidirect
60. C₄₇	#1315	semidirect

H ≅ G/N

type

2. C₂²⋊(C₄₇⋊C₁₆)

C₂

semidirect

3. C₄₇×C₂²⋊C₁₆

C₂

semidirect

59. C₂²⋊C₁₆

D₄₇

semidirect

60. C₄₇

#1315

semidirect

Subgroups — #20241313

Conjugacy classes of subgroups

Complements