Group #20242207 — subgroups

Subgroups — #20242207

Order 6016.

160 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 87 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	Q₈×C₄₇⋊C₈	C₂	1	2	yes	maximal
2	#15688874	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
4	#15688844	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
7	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₄×C₄₇⋊C₈	—	2	2	no	—
9	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₄₇	C₄	1	1	yes	characteristic
12	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
13	#107×C₄₇	C₄	1	1	yes	characteristic
14	#103×C₄₇	C₄	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₇	C₂×C₄	1	2	yes	—
17	Q₁₆×C₄₇	C₈	1	4	yes	complemented
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₄₇	—	2	2	no	—
21	C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₄²×C₄₇	—	2	2	no	—
23	C₄²×C₄₇	C₂³	1	1	yes	characteristic
24	C₂×C₄₇⋊C₈	—	2	2	no	—
25	C₂×C₄₇⋊C₈	—	2	1	no	—
26	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
27	Q₈×C₄₇	—	2	2	no	—
28	Q₈×C₄₇	C₂×C₈	1	4	yes	—
29	C₂×C₄×C₄₇	—	2	2	no	—
30	C₂×C₄×C₄₇	—	2	2	no	—
31	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
34	C₈×C₄₇	—	2	1	no	—
35	C₈×C₄₇	C₂×C₈	1	2	yes	—
36	C₄₇⋊C₈	—	2	2	no	—
37	C₄₇⋊C₈	—	4	1	no	—
38	C₄₇⋊C₈	—	4	2	no	—
39	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
40	C₄×C₄₇	—	2	4	no	—
41	C₄×C₄₇	—	2	1	no	—
42	C₄×C₄₇	—	4	2	no	—
43	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₄₇	#131	1	1	yes	characteristic
45	C₄×C₄₇	#137	1	2	yes	—
46	#1579	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	C₈×D₄	1	1	yes	characteristic
48	C₂×C₄₇	#441	1	1	yes	characteristic
49	C₂×C₄₇	#444	1	1	yes	characteristic
50	C₈×Q₈	—	47	2	no	—
51	C₄×Q₁₆	D₄₇	1	1	yes	characteristic
52	#334	—	47	1	no	—
53	Q₈⋊C₈	—	47	2	no	—
54	#322	—	47	1	no	—
55	C₄₇	#1579	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	Dic₄₇	1	1	yes	characteristic
57	C₄×Q₈	C₂×D₄₇	1	2	yes	—
58	#107	Dic₄₇	1	1	yes	characteristic
59	C₄⋊C₈	—	47	2	no	—
60	C₄⋊C₈	—	94	2	no	—
61	#103	Dic₄₇	1	2	yes	—
62	C₄×C₈	—	47	1	no	—
63	C₄×C₈	—	47	1	no	—
64	C₄×C₈	—	94	2	no	—
65	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
66	C₂×Q₈	C₂×Dic₄₇	1	2	yes	—
67	Q₁₆	C₄₇⋊C₈	1	4	yes	complemented
68	C₂×C₈	—	47	2	no	—
69	C₂×C₈	—	94	2	no	—
70	C₂×C₈	—	94	1	no	—
71	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
72	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
75	C₄²	—	2	2	no	—
76	C₄²	C₂²×D₄₇	1	1	yes	characteristic
77	Q₈	—	2	2	no	—
78	Q₈	C₂×C₄₇⋊C₈	1	4	yes	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
82	C₂×C₄	#10625352	1	1	yes	characteristic
83	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	94	2	no	—
86	C₈	—	188	1	no	—
87	C₈	—	188	2	no	—
88	C₈	C₂×C₄₇⋊C₈	1	2	yes	—
89	C₂²	D₄×Dic₄₇	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	2	4	no	—
92	C₄	—	4	2	no	—
93	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
94	C₄	#13094031	1	1	yes	characteristic
95	C₄	#13094056	1	2	yes	—
96	C₂	D₄×C₄₇⋊C₈	1	1	yes	characteristic
97	C₂	#15689230	1	1	yes	characteristic
98	C₂	#15689245	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×C₄₇⋊C₈

C₂

yes

maximal

#15688874

C₂

yes

maximal, characteristic

Q₈⋊(C₄₇⋊C₈)

C₂

yes

maximal

#15688844

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₄₇

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₄

yes

characteristic

C₄×Q₈×C₄₇

C₂²

yes

—

#107×C₄₇

C₄

yes

characteristic

#103×C₄₇

C₄

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

C₂×C₄

yes

—

Q₁₆×C₄₇

C₈

yes

complemented

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

Q₈×C₄₇

—

Q₈×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

C₂×C₈

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²×C₈

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

#1579

—

maximal, Sylow

C₂×C₄₇

C₈×D₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₈×Q₈

—

C₄×Q₁₆

D₄₇

yes

characteristic

#334

—

Q₈⋊C₈

—

#322

—

C₄₇

#1579

yes

characteristic, complemented, Sylow

C₂×Q₁₆

Dic₄₇

yes

characteristic

C₄×Q₈

C₂×D₄₇

yes

—

#107

Dic₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#103

Dic₄₇

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

C₂×Dic₄₇

yes

—

Q₁₆

C₄₇⋊C₈

yes

complemented

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₄₇

yes

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

Q₈

—

Q₈

C₂×C₄₇⋊C₈

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625352

yes

characteristic

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₈

—

188

—

C₈

C₂×C₄₇⋊C₈

yes

—

C₂²

D₄×Dic₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂²×C₄₇⋊C₈

yes

C₄

yes

C₄

yes

—

C₂

D₄×C₄₇⋊C₈

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#1579
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄×Q₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₄×D₄

hypercenter

C₄×Q₁₆

D₄₇

hypocenter

C₄₇

#1579

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

N	H ≅ G/N	type
17. Q₁₆×C₄₇	C₈	semidirect
55. C₄₇	#1579	semidirect
67. Q₁₆	C₄₇⋊C₈	semidirect

H ≅ G/N

type

17. Q₁₆×C₄₇

C₈

semidirect

55. C₄₇

#1579

semidirect

67. Q₁₆

C₄₇⋊C₈

semidirect

Subgroups — #20242207

Conjugacy classes of subgroups

Complements