Group #20241344 — subgroups

Subgroups — #20241344

Order 6016.

110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₄₇	—	2	1	no	—
5	C₄×D₁₈₈	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₁₆	—	2	1	no	—
7	C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
8	(C₂×D₄₇)⋊C₈	—	2	1	no	—
9	C₂×C₁₆×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₈₈	C₈	1	1	yes	characteristic
12	C₂×C₄×D₄₇	—	2	1	no	—
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
16	(C₂×D₄₇)⋊C₄	—	2	1	no	—
17	C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	—	2	1	no	—
19	C₈×D₄₇	—	4	1	no	—
20	C₈×D₄₇	—	4	1	no	—
21	C₁₆×C₄₇	—	2	2	no	—
22	C₄₇⋊C₁₆	—	4	1	no	—
23	C₂²×D₄₇	—	2	1	no	—
24	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
27	C₂×Dic₄₇	—	2	1	no	—
28	D₁₈₈	—	2	1	no	—
29	D₁₈₈	C₁₆	1	2	yes	complemented
30	C₄×D₄₇	—	4	1	no	—
31	C₄×D₄₇	—	4	1	no	—
32	C₈×C₄₇	—	2	1	no	—
33	C₈×C₄₇	D₈	1	1	yes	characteristic
34	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
35	C₄₇⋊C₈	—	4	1	no	—
36	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₄₇	—	2	2	no	—
38	C₂×D₄₇	—	4	1	no	—
39	C₂×D₄₇	—	4	1	no	—
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	#102	1	1	yes	characteristic
42	C₄×C₄₇	#104	1	1	yes	characteristic
43	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
44	C₄×C₄₇	M₃₂	1	1	yes	characteristic
45	Dic₄₇	—	4	1	no	—
46	D₄⋊C₁₆	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
48	C₂×C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic
49	C₂×C₄₇	#350	1	1	yes	characteristic
50	D₄₇	—	4	2	no	—
51	C₈×D₄	—	47	1	no	—
52	C₄⋊C₁₆	—	47	1	no	—
53	C₄×C₁₆	D₄₇	1	1	yes	characteristic, complemented
54	C₄₇	D₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	—	94	1	no	—
56	C₄×D₄	—	47	1	no	—
57	C₂×C₁₆	—	2	1	no	—
58	C₂×C₁₆	—	94	1	no	—
59	C₄⋊C₈	—	47	1	no	—
60	C₂²⋊C₈	—	94	1	no	—
61	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
62	C₂×D₄	—	47	1	no	—
63	C₂²×C₄	—	94	1	no	—
64	C₂×C₈	—	94	1	no	—
65	C₂×C₈	—	188	1	no	—
66	C₂×C₈	—	188	1	no	—
67	C₂×C₈	D₁₈₈	1	1	yes	characteristic
68	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
69	C₄⋊C₄	—	47	1	no	—
70	C₂²⋊C₄	—	94	1	no	—
71	C₄²	C₄×D₄₇	1	1	yes	characteristic
72	C₁₆	—	2	2	no	—
73	C₁₆	—	188	1	no	—
74	C₂³	—	94	1	no	—
75	D₄	—	47	2	no	—
76	D₄	—	94	1	no	—
77	C₂×C₄	—	94	1	no	—
78	C₂×C₄	—	188	1	no	—
79	C₂×C₄	—	188	1	no	—
80	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
81	C₂×C₄	#10625324	1	1	yes	characteristic
82	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	188	1	no	—
85	C₈	#10625325	1	1	yes	characteristic
86	C₈	D₃₇₆	1	1	yes	characteristic
87	C₂²	—	94	2	no	—
88	C₂²	—	188	1	no	—
89	C₂²	—	188	1	no	—
90	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	188	1	no	—
93	C₄	#13093946	1	1	yes	characteristic
94	C₄	#13093952	1	1	yes	characteristic
95	C₄	C₁₆×D₄₇	1	1	yes	characteristic
96	C₄	#13093963	1	1	yes	characteristic
97	C₂	—	188	2	no	—
98	C₂	#15688852	1	1	yes	characteristic
99	C₂	(C₂×D₄₇)⋊C₁₆	1	1	yes	characteristic
100	C₂	#15688906	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×D₁₈₈

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

—

C₄×D₁₈₈

C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

—

C₄⋊(C₄₇⋊C₈)

C₄

yes

characteristic

(C₂×D₄₇)⋊C₈

—

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₈

yes

characteristic

C₂×C₄₇⋊C₈

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

C₁₆

yes

complemented

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

D₈

yes

characteristic

C₈×C₄₇

SD₁₆

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

C₂×C₁₆

yes

characteristic

C₄×C₄₇

M₃₂

yes

characteristic

Dic₄₇

—

D₄⋊C₁₆

—

maximal, Sylow

C₂×C₄₇

D₄⋊C₈

yes

characteristic

C₂×C₄₇

C₂²⋊C₁₆

yes

characteristic

C₂×C₄₇

#350

yes

characteristic

D₄₇

—

C₈×D₄

—

C₄⋊C₁₆

—

C₄×C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

D₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

188

—

C₂×C₈

—

188

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

188

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

#10625324

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

—

188

—

C₈

#10625325

yes

characteristic

C₈

D₃₇₆

yes

characteristic

C₂²

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

(C₂×D₄₇)⋊C₈

yes

characteristic

C₄

—

C₄

—

188

—

C₄

yes

C₄

yes

C₄

C₁₆×D₄₇

yes

characteristic

C₄

#13093963

yes

characteristic

C₂

—

188

—

C₂

#15688852

yes

characteristic

C₂

(C₂×D₄₇)⋊C₁₆

yes

characteristic

100

C₂

#15688906

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₁₈₈
commutator	C₄×C₄₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²⋊C₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	D₄⋊C₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₈

D₁₈₈

commutator

C₄×C₄₇

C₂×C₁₆

Frattini

C₄×C₈

C₂×D₄₇

Fitting

C₄×C₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂²⋊C₈

hypercenter

C₄×C₁₆

D₄₇

hypocenter

C₄₇

D₄⋊C₁₆

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
3. C₄×C₁₆×C₄₇	C₂	semidirect
29. D₁₈₈	C₁₆	semidirect
53. C₄×C₁₆	D₄₇	semidirect
54. C₄₇	D₄⋊C₁₆	semidirect

H ≅ G/N

type

2. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

3. C₄×C₁₆×C₄₇

C₂

semidirect

29. D₁₈₈

C₁₆

semidirect

53. C₄×C₁₆

D₄₇

semidirect

54. C₄₇

D₄⋊C₁₆

semidirect

Subgroups — #20241344

Conjugacy classes of subgroups

Complements