Group #20245540 — subgroups

Subgroups — #20245540

Order 6016.

130 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689528	C₂	1	1	yes	maximal, characteristic
2	#15688948	C₂	1	2	yes	maximal
3	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#15688927	C₂	1	2	yes	maximal
5	C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#13094024	—	2	1	no	—
7	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
8	#13093958	—	2	1	no	—
9	#13093958	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	C₄×Q₈×C₄₇	—	2	1	no	—
12	#107×C₄₇	C₂²	1	1	yes	characteristic
13	#103×C₄₇	—	2	1	no	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₇	—	2	1	no	—
16	C₂×Dic₉₄	—	4	1	no	—
17	Q₁₆×C₄₇	—	2	1	no	—
18	Q₁₆×C₄₇	Q₈	1	2	yes	complemented
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₄₇	—	2	1	no	—
22	C₄⋊C₄×C₄₇	—	4	1	no	—
23	C₄²×C₄₇	—	4	1	no	—
24	C₄²×C₄₇	D₄	1	1	yes	characteristic
25	C₄⋊Dic₄₇	—	2	2	no	—
26	C₄⋊Dic₄₇	—	4	1	no	—
27	C₄₇⋊C₁₆	—	2	2	no	—
28	Q₈×C₄₇	—	2	2	no	—
29	Q₈×C₄₇	—	4	1	no	—
30	C₂×C₄×C₄₇	—	4	1	no	—
31	C₂×C₄×C₄₇	—	4	1	no	—
32	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₄₇	—	4	2	no	—
36	Dic₉₄	—	8	2	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₄₇	#41	1	1	yes	characteristic
40	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
41	C₄×C₄₇	—	2	1	no	—
42	C₄×C₄₇	—	4	2	no	—
43	C₄×C₄₇	—	8	1	no	—
44	C₄×C₄₇	Q₃₂	1	2	yes	—
45	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
46	C₄×C₄₇	#137	1	1	yes	characteristic
47	Dic₄₇	—	8	2	no	—
48	#2227	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	#474	1	1	yes	characteristic
50	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
51	C₂×C₄₇	#509	1	1	yes	characteristic
52	#500	—	47	1	no	—
53	C₄×Q₁₆	D₄₇	1	1	yes	characteristic
54	#366	—	47	2	no	—
55	C₄⋊C₁₆	—	47	1	no	—
56	#358	—	47	2	no	—
57	C₄₇	#2227	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
59	C₄⋊Q₈	—	94	1	no	—
60	C₄×Q₈	—	2	1	no	—
61	C₂×C₁₆	—	47	2	no	—
62	#107	—	47	2	no	—
63	#107	—	94	1	no	—
64	#107	C₂×D₄₇	1	1	yes	characteristic
65	#103	—	2	1	no	—
66	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
67	C₂×Q₈	—	2	1	no	—
68	C₂×Q₈	—	188	1	no	—
69	Q₁₆	—	2	1	no	—
70	Q₁₆	Dic₉₄	1	2	yes	complemented
71	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄⋊C₄	—	94	2	no	—
76	C₄⋊C₄	—	188	1	no	—
77	C₄²	—	4	1	no	—
78	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
79	C₁₆	—	94	2	no	—
80	Q₈	—	2	2	no	—
81	Q₈	—	4	1	no	—
82	Q₈	—	376	2	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	—	188	2	no	—
86	C₂×C₄	#10625334	1	1	yes	characteristic
87	C₂×C₄	#10625334	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	C₂×Dic₉₄	1	1	yes	characteristic
91	C₈	#10625350	1	1	yes	characteristic
92	C₂²	C₂×#10625334	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	4	2	no	—
95	C₄	—	8	1	no	—
96	C₄	—	376	2	no	—
97	C₄	#13093970	1	2	yes	—
98	C₄	#13094003	1	1	yes	characteristic
99	C₄	#13094054	1	1	yes	characteristic
100	C₂	#15689403	1	1	yes	characteristic
101	C₂	C₂×#13093970	1	1	yes	characteristic
102	C₂	#15689558	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic

#15688948

C₂

yes

maximal

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic

#15688927

C₂

yes

maximal

C₄×Q₁₆×C₄₇

C₂

yes

maximal, characteristic

#13094024

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

#13093958

—

#13093958

C₂²

yes

—

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

#107×C₄₇

C₂²

yes

characteristic

#103×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

Q₈

yes

complemented

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

Q₃₂

yes

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×Q₃₂

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

D₄₇

yes

characteristic

#366

—

C₄⋊C₁₆

—

#358

—

C₄₇

#2227

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₄₇

yes

characteristic

#103

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

188

—

Q₁₆

—

Q₁₆

Dic₉₄

yes

complemented

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄²

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

376

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

—

C₈

C₂×Dic₉₄

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

376

—

C₄

#13093970

yes

—

C₄

yes

C₄

yes

100

C₂

#15689403

yes

characteristic

101

C₂

C₂×#13093970

yes

characteristic

102

C₂

#15689558

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#2227
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄×Q₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄×Q₁₆

D₄₇

hypocenter

C₄₇

#2227

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
18. Q₁₆×C₄₇	Q₈	semidirect
57. C₄₇	#2227	semidirect
70. Q₁₆	Dic₉₄	semidirect

H ≅ G/N

type

18. Q₁₆×C₄₇

Q₈

semidirect

57. C₄₇

#2227

semidirect

70. Q₁₆

Dic₉₄

semidirect

Subgroups — #20245540

Conjugacy classes of subgroups

Complements