Group #20245224 — subgroups

Subgroups — #20245224

Order 6016.

146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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	#15689541	C₂	1	2	yes	maximal, complemented
2	#15689241	C₂	1	1	yes	maximal, characteristic
3	#15688908	C₂	1	2	yes	maximal, complemented
4	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094046	C₄	1	1	yes	characteristic
7	#13094030	C₂²	1	2	yes	—
8	#13093963	—	2	2	no	—
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₁₆×D₄₇	—	2	2	no	—
12	#13093960	C₄	1	1	yes	characteristic
13	#13093952	C₄	1	2	yes	—
14	M₃₂×C₄₇	C₂²	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	#10625350	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
20	#10625329	C₂×C₄	1	2	yes	—
21	Dic₁₈₈	C₈	1	1	yes	characteristic
22	D₃₇₆	C₈	1	1	yes	characteristic
23	#10625325	C₈	1	2	yes	—
24	#10625324	—	2	2	no	—
25	C₈×D₄₇	—	2	2	no	—
26	C₁₆×C₄₇	—	2	2	no	—
27	C₄₇⋊C₁₆	—	2	1	no	—
28	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
29	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂²⋊D₄₇	—	2	2	no	—
33	D₁₈₈	C₂×C₈	1	2	yes	—
34	C₄×D₄₇	—	2	2	no	—
35	Dic₉₄	C₂×C₈	1	2	yes	—
36	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
37	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
38	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₇	#41	1	1	yes	characteristic
40	C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇	#131	1	1	yes	characteristic
42	C₂×D₄₇	—	2	2	no	—
43	C₄×C₄₇	—	2	2	no	—
44	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
45	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
46	Dic₄₇	—	2	2	no	—
47	#2170	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	1	no	—
49	C₂×C₄₇	C₈×D₄	1	1	yes	characteristic
50	D₄₇	—	4	2	no	—
51	#504	—	47	2	no	—
52	#443	—	47	1	no	—
53	#364	D₄₇	1	1	yes	characteristic, complemented
54	#350	—	47	2	no	—
55	C₄×C₁₆	—	47	1	no	—
56	C₄₇	#2170	1	1	yes	characteristic, complemented, Sylow
57	#135	—	47	1	no	—
58	#131	—	47	2	no	—
59	M₃₂	—	94	2	no	—
60	M₃₂	C₂×D₄₇	1	2	yes	—
61	C₂×C₁₆	—	47	1	no	—
62	C₂×C₁₆	—	47	1	no	—
63	C₂×C₁₆	—	94	2	no	—
64	#108	—	47	1	no	—
65	#104	—	47	2	no	—
66	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
67	#41	—	47	2	no	—
68	Q₁₆	—	47	1	no	—
69	SD₁₆	—	47	2	no	—
70	D₈	—	47	1	no	—
71	M₁₆	—	47	2	no	—
72	M₁₆	—	94	2	no	—
73	C₂×C₈	—	94	2	no	—
74	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
76	C₄²	C₄×D₄₇	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	47	1	no	—
79	C₁₆	—	47	1	no	—
80	C₁₆	—	94	1	no	—
81	Q₈	—	47	2	no	—
82	D₄	—	47	2	no	—
83	D₄	—	94	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	94	2	no	—
86	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
87	C₈	—	94	2	no	—
88	C₈	C₈×D₄₇	1	1	yes	characteristic
89	C₈	C₈×D₄₇	1	1	yes	characteristic
90	C₈	D₄×D₄₇	1	1	yes	characteristic
91	C₈	#10625354	1	1	yes	characteristic
92	C₂²	—	94	2	no	—
93	C₂²	#13094032	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	94	2	no	—
96	C₄	#13093986	1	1	yes	characteristic
97	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	188	2	no	—
100	C₂	#15689188	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689541

C₂

yes

maximal, complemented

#15689241

C₂

yes

maximal, characteristic

#15688908

C₂

yes

maximal, complemented

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₇×#364

C₂

yes

maximal, characteristic, complemented

#13094046

C₄

yes

characteristic

#13094030

C₂²

yes

—

#13093963

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₇

—

#13093960

C₄

yes

characteristic

#13093952

C₄

yes

—

M₃₂×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

#10625350

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

#10625329

C₂×C₄

yes

—

Dic₁₈₈

C₈

yes

characteristic

D₃₇₆

C₈

yes

characteristic

#10625325

C₈

yes

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

D₄

yes

characteristic

C₄₇⋊C₁₆

D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²⋊D₄₇

—

D₁₈₈

C₂×C₈

yes

—

C₄×D₄₇

—

Dic₉₄

C₂×C₈

yes

—

C₈×C₄₇

C₂×C₈

yes

characteristic

C₈×C₄₇

C₂×C₈

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

#131

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

C₂²×C₈

yes

characteristic

Dic₄₇

—

#2170

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₈×D₄

yes

characteristic

D₄₇

—

#504

—

#443

—

#364

D₄₇

yes

characteristic, complemented

#350

—

C₄×C₁₆

—

C₄₇

#2170

yes

characteristic, complemented, Sylow

#135

—

#131

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#104

—

C₄×C₈

C₂×D₄₇

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₈

—

C₈

C₈×D₄₇

yes

characteristic

C₈

C₈×D₄₇

yes

characteristic

C₈

D₄×D₄₇

yes

characteristic

C₈

#10625354

yes

characteristic

C₂²

—

C₂²

#13094032

yes

characteristic

C₄

—

C₄

—

C₄

#13093986

yes

characteristic

C₄

C₂×C₈×D₄₇

yes

characteristic

C₂

—

C₂

—

188

—

100

C₂

#15689188

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#364	C₂
socle	C₂×C₄₇	C₈×D₄
hypercenter	#364	D₄₇
hypocenter	C₄₇	#2170
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₄₇

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#364

C₂

socle

C₂×C₄₇

C₈×D₄

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
1. #15689541	C₂	semidirect
3. #15688908	C₂	semidirect
4. C₄×C₄₇⋊C₁₆	C₂	semidirect
5. C₄₇×#364	C₂	semidirect
53. #364	D₄₇	semidirect
56. C₄₇	#2170	semidirect

H ≅ G/N

type

1. #15689541

C₂

semidirect

3. #15688908

C₂

semidirect

4. C₄×C₄₇⋊C₁₆

C₂

semidirect

5. C₄₇×#364

C₂

semidirect

53. #364

D₄₇

semidirect

56. C₄₇

#2170

semidirect

Subgroups — #20245224

Conjugacy classes of subgroups

Complements