Group #20245143 — subgroups

Subgroups — #20245143

Order 6016.

172 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 97 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	Dic₄₇⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
7	#13093964	—	2	2	no	—
8	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
9	C₈×Dic₄₇	C₄	1	2	yes	—
10	C₈×Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	M₃₂×C₄₇	—	2	2	no	—
13	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₄₇	C₈	1	2	yes	—
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	D₄	1	2	yes	—
18	C₂×C₈×C₄₇	Q₈	1	2	yes	—
19	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
20	C₄×Dic₄₇	C₈	1	1	yes	characteristic
21	C₄×Dic₄₇	C₈	1	1	yes	characteristic
22	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
23	C₂×C₄₇⋊C₈	—	2	2	no	—
24	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
25	C₁₆×C₄₇	—	2	2	no	—
26	C₄₇⋊C₁₆	—	2	2	no	—
27	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	M₁₆	1	2	yes	—
31	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₄₇	—	2	4	no	—
33	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
34	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
35	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
36	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
38	C₄₇⋊C₈	—	2	2	no	—
39	C₂²×C₄₇	—	2	2	no	—
40	C₂²×C₄₇	C₄⋊C₈	1	2	yes	—
41	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₄₇	C₄⋊C₈	1	2	yes	—
43	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
45	Dic₄₇	—	2	2	no	—
46	Dic₄₇	M₃₂	1	4	yes	complemented
47	#2150	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	2	no	—
49	C₂×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
50	C₂×C₄₇	C₂×M₃₂	1	2	yes	—
51	C₂×M₃₂	—	47	1	no	—
52	C₂×M₃₂	D₄₇	1	1	yes	characteristic
53	C₂×C₄×C₈	—	47	1	no	—
54	C₄⋊C₁₆	—	47	4	no	—
55	C₄₇	#2150	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	47	1	no	—
57	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
58	C₂×C₄²	—	47	1	no	—
59	M₃₂	—	2	2	no	—
60	M₃₂	—	94	2	no	—
61	C₂×C₁₆	—	47	2	no	—
62	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
63	C₄×C₈	—	47	2	no	—
64	C₄×C₈	—	47	2	no	—
65	C₂²×C₄	—	47	2	no	—
66	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
67	C₂×C₈	—	47	2	no	—
68	C₂×C₈	—	94	2	no	—
69	C₂×C₈	Dic₉₄	1	2	yes	—
70	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
71	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
72	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
73	C₄²	—	47	1	no	—
74	C₄²	—	47	1	no	—
75	C₄²	—	47	2	no	—
76	C₁₆	—	2	2	no	—
77	C₁₆	—	94	2	no	—
78	C₂³	C₈×D₄₇	1	1	yes	characteristic
79	C₂×C₄	—	47	2	no	—
80	C₂×C₄	—	47	2	no	—
81	C₂×C₄	—	94	4	no	—
82	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
83	C₂×C₄	#10625324	1	2	yes	—
84	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
86	C₈	—	94	2	no	—
87	C₈	Dic₄₇⋊C₄	1	2	yes	—
88	C₈	C₂×Dic₉₄	1	1	yes	characteristic
89	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	Dic₄₇⋊C₈	1	2	yes	—
92	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
93	C₄	—	47	4	no	—
94	C₄	—	94	2	no	—
95	C₄	Dic₄₇⋊C₈	1	2	yes	—
96	C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
97	C₄	C₂×#10625324	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
100	C₂	M₃₂×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

Dic₄₇⋊C₁₆

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

#13093964

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₈×Dic₄₇

C₄

yes

—

C₈×Dic₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₈

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

Q₈

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄×Dic₄₇

C₈

yes

characteristic

C₄×Dic₄₇

C₈

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄⋊C₈

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

C₄⋊C₈

yes

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

M₃₂

yes

complemented

#2150

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

—

C₂×M₃₂

—

C₂×M₃₂

D₄₇

yes

characteristic

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄₇

#2150

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

C₈×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

#10625324

yes

—

C₂×C₄

Dic₄₇⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₈

—

C₈

Dic₄₇⋊C₄

yes

—

C₈

C₂×Dic₉₄

yes

characteristic

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

C₂²

—

C₂²

Dic₄₇⋊C₈

yes

—

C₂²

C₂×C₈×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

Dic₄₇⋊C₈

yes

—

C₄

C₂×Dic₄₇⋊C₄

yes

characteristic

C₄

C₂×#10625324

yes

characteristic

C₂

—

C₂

C₂×Dic₄₇⋊C₈

yes

characteristic

100

C₂

M₃₂×D₄₇

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₂×M₃₂×C₄₇	C₂
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	#2150
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₈

Fitting

C₂×M₃₂×C₄₇

C₂

hypercenter

C₂×M₃₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. Dic₄₇⋊C₁₆	C₂	semidirect
46. Dic₄₇	M₃₂	semidirect
55. C₄₇	#2150	semidirect

H ≅ G/N

type

3. Dic₄₇⋊C₁₆

C₂

semidirect

46. Dic₄₇

M₃₂

semidirect

55. C₄₇

#2150

semidirect

Subgroups — #20245143

Conjugacy classes of subgroups

Complements