Group #20241379 — subgroups

Subgroups — #20241379

Order 6016.

110 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 33 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	#15688905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#469	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625329	—	2	1	no	—
5	#13093964	—	2	1	no	—
6	C₂×D₈×C₄₇	C₄	1	1	yes	characteristic
7	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
8	#121×C₄₇	—	2	1	no	—
9	#106×C₄₇	C₄	1	1	yes	characteristic
10	#102×C₄₇	—	2	1	no	—
11	C₂×D₄×C₄₇	—	2	1	no	—
12	C₂×D₄×C₄₇	—	4	1	no	—
13	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
14	D₈×C₄₇	—	4	1	no	—
15	M₁₆×C₄₇	—	4	1	no	—
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₄₇	—	2	1	no	—
19	C₂²⋊C₄×C₄₇	—	4	1	no	—
20	#10625329	—	4	1	no	—
21	#10625329	—	4	1	no	—
22	C₂×C₄₇⋊C₈	—	2	2	no	—
23	C₄₇⋊C₁₆	—	4	1	no	—
24	C₂³×C₄₇	—	4	1	no	—
25	C₂³×C₄₇	SD₁₆	1	1	yes	characteristic
26	D₄×C₄₇	—	4	1	no	—
27	D₄×C₄₇	—	4	1	no	—
28	D₄×C₄₇	—	8	2	no	—
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	—	4	1	no	—
32	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
34	C₈×C₄₇	—	2	1	no	—
35	C₈×C₄₇	—	2	1	no	—
36	C₄₇⋊C₈	—	4	2	no	—
37	C₂²×C₄₇	—	2	1	no	—
38	C₂²×C₄₇	—	4	1	no	—
39	C₂²×C₄₇	—	8	1	no	—
40	C₂²×C₄₇	—	8	1	no	—
41	C₂²×C₄₇	—	8	1	no	—
42	C₂²×C₄₇	#102	1	1	yes	characteristic
43	C₄×C₄₇	—	2	1	no	—
44	C₄×C₄₇	—	8	1	no	—
45	C₄×C₄₇	#99	1	1	yes	characteristic
46	C₄×C₄₇	#104	1	1	yes	characteristic
47	#1341	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	1	no	—
49	C₂×C₄₇	—	4	1	no	—
50	C₂×C₄₇	—	16	1	no	—
51	C₂×C₄₇	#327	1	1	yes	characteristic
52	#469	D₄₇	1	1	yes	characteristic
53	#349	—	47	1	no	—
54	#338	—	47	1	no	—
55	C₄₇	#1341	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	Dic₄₇	1	1	yes	characteristic
57	C₂×M₁₆	—	94	1	no	—
58	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
59	#121	—	2	1	no	—
60	M₃₂	—	94	1	no	—
61	#106	Dic₄₇	1	1	yes	characteristic
62	#102	—	2	1	no	—
63	C₂×D₄	—	2	1	no	—
64	C₂×D₄	—	4	1	no	—
65	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
66	D₈	—	4	1	no	—
67	M₁₆	—	4	1	no	—
68	M₁₆	—	188	1	no	—
69	M₁₆	—	188	1	no	—
70	C₂×C₈	—	94	2	no	—
71	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
72	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₁₆	—	188	1	no	—
76	C₂³	—	4	1	no	—
77	C₂³	#10625335	1	1	yes	characteristic
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	8	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	#10625334	1	1	yes	characteristic
85	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	—	188	2	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	4	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	1	no	—
94	C₂²	#13093945	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	#13093939	1	1	yes	characteristic
98	C₄	#13093951	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	16	1	no	—
102	C₂	#15688857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15688905

C₂

yes

maximal, characteristic, complemented

C₄₇⋊#338

C₂

yes

maximal, characteristic, complemented

C₄₇×#469

C₂

yes

maximal, characteristic

C₂×#10625329

—

#13093964

—

C₂×D₈×C₄₇

C₄

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#121×C₄₇

—

#106×C₄₇

C₄

yes

characteristic

#102×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

D₈×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

SD₁₆

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#102

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#327

yes

characteristic

#469

D₄₇

yes

characteristic

#349

—

#338

—

C₄₇

#1341

yes

characteristic, complemented, Sylow

C₂×D₈

Dic₄₇

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

#121

—

M₃₂

—

#106

Dic₄₇

yes

characteristic

#102

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

188

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

188

—

C₂³

—

C₂³

#10625335

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10625334

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#13093945

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

102

C₂

#15688857

yes

characteristic

	subgroup	G/H
center	C₂	#15688857
commutator	C₂×C₈×C₄₇	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#469	C₂
socle	C₂×C₄₇	#327
hypercenter	#469	D₄₇
hypocenter	C₄₇	#1341
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#15688857

commutator

C₂×C₈×C₄₇

C₂×C₄

Frattini

C₂×M₁₆

C₂×D₄₇

Fitting

C₄₇×#469

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #15688905	C₂	semidirect
2. C₄₇⋊#338	C₂	semidirect
55. C₄₇	#1341	semidirect

H ≅ G/N

type

1. #15688905

C₂

semidirect

2. C₄₇⋊#338

C₂

semidirect

55. C₄₇

#1341

semidirect

Subgroups — #20241379

Conjugacy classes of subgroups

Complements