Group #20242285 — subgroups

Subgroups — #20242285

Order 6016.

152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 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	#15689254	C₂	1	2	yes	maximal
2	#15688876	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
4	C₈×C₄₇⋊C₈	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	#13093935	—	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	—	2	2	no	—
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	1	no	—
25	C₂×C₄₇⋊C₈	—	2	2	no	—
26	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
27	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
28	Q₈×C₄₇	—	2	2	no	—
29	Q₈×C₄₇	—	2	2	no	—
30	C₂×C₄×C₄₇	—	2	2	no	—
31	C₂×C₄×C₄₇	—	2	2	no	—
32	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
35	C₈×C₄₇	—	2	1	no	—
36	C₈×C₄₇	M₁₆	1	2	yes	—
37	C₄₇⋊C₈	—	2	2	no	—
38	C₄₇⋊C₈	—	2	1	no	—
39	C₄₇⋊C₈	—	4	2	no	—
40	C₄₇⋊C₈	Q₁₆	1	2	yes	complemented
41	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	—	4	2	no	—
44	C₄×C₄₇	—	4	2	no	—
45	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
46	C₄×C₄₇	#131	1	1	yes	characteristic
47	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
48	C₄×C₄₇	#135	1	1	yes	characteristic
49	#1591	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	#436	1	1	yes	characteristic
51	C₂×C₄₇	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₄₇	#443	1	1	yes	characteristic
53	#446	—	47	2	no	—
54	C₄×Q₁₆	D₄₇	1	1	yes	characteristic
55	#335	—	47	1	no	—
56	Q₈⋊C₈	—	47	2	no	—
57	C₈²	—	47	1	no	—
58	C₄₇	#1591	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	Dic₄₇	1	1	yes	characteristic
60	C₄×Q₈	C₂×D₄₇	1	2	yes	—
61	#107	Dic₄₇	1	1	yes	characteristic
62	C₄⋊C₈	—	47	2	no	—
63	C₄⋊C₈	—	94	2	no	—
64	#103	Dic₄₇	1	2	yes	—
65	#97	—	94	2	no	—
66	C₄×C₈	—	47	1	no	—
67	C₄×C₈	—	47	1	no	—
68	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
69	C₂×Q₈	C₂×Dic₄₇	1	2	yes	—
70	Q₁₆	—	2	2	no	—
71	C₂×C₈	—	47	1	no	—
72	C₂×C₈	—	47	1	no	—
73	C₂×C₈	—	94	1	no	—
74	C₂×C₈	—	94	2	no	—
75	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
79	C₄²	—	2	2	no	—
80	C₄²	C₂²×D₄₇	1	1	yes	characteristic
81	Q₈	—	2	2	no	—
82	Q₈	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
86	C₂×C₄	#10625352	1	1	yes	characteristic
87	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	47	2	no	—
90	C₈	—	94	2	no	—
91	C₈	—	94	1	no	—
92	C₈	—	188	2	no	—
93	C₈	#10625329	1	2	yes	—
94	C₂²	D₄×Dic₄₇	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	C₂×#10625329	1	1	yes	characteristic
99	C₄	#13094031	1	1	yes	characteristic
100	C₄	Q₁₆×D₄₇	1	1	yes	characteristic
101	C₄	#13094047	1	1	yes	characteristic
102	C₂	#15689201	1	1	yes	characteristic
103	C₂	Q₁₆×Dic₄₇	1	1	yes	characteristic
104	C₂	#15689240	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689254

C₂

yes

maximal

#15688876

C₂

yes

maximal, characteristic

Q₈⋊(C₄₇⋊C₈)

C₂

yes

maximal

C₈×C₄₇⋊C₈

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₄₇

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093935

—

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

—

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

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

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

M₁₆

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

Q₁₆

yes

complemented

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

#131

yes

characteristic

C₄×C₄₇

C₂×Q₁₆

yes

C₄×C₄₇

yes

—

C₂×C₄₇

yes

C₂×C₄₇

C₄×Q₁₆

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

D₄₇

yes

characteristic

#335

—

Q₈⋊C₈

—

C₈²

—

C₄₇

#1591

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

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

C₂×Dic₄₇

yes

—

Q₁₆

—

C₂×C₈

—

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×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625352

yes

characteristic

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

188

—

C₈

#10625329

yes

—

C₂²

D₄×Dic₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

100

C₄

Q₁₆×D₄₇

yes

characteristic

101

C₄

#13094047

yes

characteristic

102

C₂

#15689201

yes

characteristic

103

C₂

Q₁₆×Dic₄₇

yes

characteristic

104

C₂

#15689240

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#1591
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄×Q₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₄×D₄

hypercenter

C₄×Q₁₆

D₄₇

hypocenter

C₄₇

#1591

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

N	H ≅ G/N	type
40. C₄₇⋊C₈	Q₁₆	semidirect
58. C₄₇	#1591	semidirect

H ≅ G/N

type

40. C₄₇⋊C₈

Q₁₆

semidirect

58. C₄₇

#1591

semidirect

Subgroups — #20242285

Conjugacy classes of subgroups

Complements