Group #20245202 — subgroups

Subgroups — #20245202

Order 6016.

122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689080	C₂	1	1	yes	maximal, characteristic
2	#15688943	C₂	1	2	yes	maximal, complemented
3	#15688904	C₂	1	2	yes	maximal
4	#15688901	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625324	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₄₇	C₄	1	1	yes	characteristic
8	#13093981	C₄	1	1	yes	characteristic
9	#13093964	C₂²	1	2	yes	—
10	#13093934	C₄	1	1	yes	characteristic
11	C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
12	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
13	M₃₂×C₄₇	C₂²	1	2	yes	—
14	#97×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
19	(C₂×D₄₇)⋊C₄	—	2	1	no	—
20	Dic₄₇⋊C₄	—	2	1	no	—
21	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#10625324	—	2	2	no	—
25	C₈×D₄₇	—	2	2	no	—
26	C₁₆×C₄₇	—	2	2	no	—
27	C₄₇⋊C₁₆	—	2	2	no	—
28	C₂²×D₄₇	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₄₇	—	2	1	no	—
32	C₂×Dic₄₇	M₁₆	1	1	yes	characteristic
33	C₄×D₄₇	—	2	1	no	—
34	C₄×D₄₇	—	2	1	no	—
35	C₈×C₄₇	—	2	1	no	—
36	C₈×C₄₇	#41	1	2	yes	—
37	C₄₇⋊C₈	—	2	1	no	—
38	C₄₇⋊C₈	M₁₆	1	2	yes	—
39	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
40	C₂×D₄₇	—	2	1	no	—
41	C₂×D₄₇	—	4	1	no	—
42	C₄×C₄₇	—	4	1	no	—
43	C₄×C₄₇	#117	1	1	yes	characteristic
44	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
45	Dic₄₇	—	2	1	no	—
46	Dic₄₇	—	4	1	no	—
47	#2166	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	1	no	—
49	C₂×C₄₇	#432	1	1	yes	characteristic
50	D₄₇	—	4	1	no	—
51	#405	—	47	1	no	—
52	#364	—	47	2	no	—
53	#349	—	47	2	no	—
54	#347	—	47	1	no	—
55	#347	D₄₇	1	1	yes	characteristic, complemented
56	C₄₇	#2166	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	47	1	no	—
58	C₂²×C₈	—	47	1	no	—
59	#117	—	47	1	no	—
60	M₃₂	—	47	2	no	—
61	M₃₂	C₂×D₄₇	1	2	yes	—
62	#97	—	47	1	no	—
63	#97	C₂×D₄₇	1	1	yes	characteristic
64	C₄×C₈	—	47	1	no	—
65	C₄×C₈	—	47	1	no	—
66	C₂²×C₄	—	47	1	no	—
67	M₁₆	—	94	2	no	—
68	C₂×C₈	—	47	1	no	—
69	C₂×C₈	—	47	1	no	—
70	C₂×C₈	—	94	2	no	—
71	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	—	94	1	no	—
74	C₂²⋊C₄	—	94	1	no	—
75	C₄²	—	47	1	no	—
76	C₄²	C₄×D₄₇	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	94	2	no	—
79	C₂³	—	47	1	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	47	1	no	—
82	C₂×C₄	—	94	1	no	—
83	C₂×C₄	—	94	1	no	—
84	C₂×C₄	—	94	1	no	—
85	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	47	2	no	—
88	C₈	—	94	1	no	—
89	C₈	#10625350	1	2	yes	—
90	C₂²	—	94	1	no	—
91	C₂²	—	188	1	no	—
92	C₂²	M₁₆×D₄₇	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	94	1	no	—
95	C₄	—	188	1	no	—
96	C₄	#13093981	1	1	yes	characteristic
97	C₄	M₁₆×D₄₇	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	188	1	no	—
100	C₂	#15689178	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689080

C₂

yes

maximal, characteristic

#15688943

C₂

yes

maximal, complemented

#15688904

C₂

yes

maximal

#15688901

C₂

yes

maximal, characteristic, complemented

C₄₇×#347

C₂

yes

maximal, characteristic, complemented

C₂×#10625324

C₂²

yes

characteristic

C₂×C₈×D₄₇

C₄

yes

characteristic

#13093981

C₄

yes

characteristic

#13093964

C₂²

yes

—

#13093934

C₄

yes

characteristic

C₄×C₄₇⋊C₈

C₄

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

—

#97×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

M₁₆

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

#41

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

M₁₆

yes

—

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2166

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#432

yes

characteristic

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2166

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

—

#97

—

#97

C₂×D₄₇

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#10625350

yes

—

C₂²

—

C₂²

—

188

—

C₂²

M₁₆×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

188

—

C₄

#13093981

yes

characteristic

C₄

M₁₆×D₄₇

yes

characteristic

C₂

—

C₂

—

188

—

100

C₂

#15689178

yes

characteristic

	subgroup	G/H
center	C₄	#13093981
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#347	C₂
socle	C₂×C₄₇	#432
hypercenter	#347	D₄₇
hypocenter	C₄₇	#2166
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₄

#13093981

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#347

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #15688943	C₂	semidirect
4. #15688901	C₂	semidirect
5. C₄₇×#347	C₂	semidirect
55. #347	D₄₇	semidirect
56. C₄₇	#2166	semidirect

H ≅ G/N

type

2. #15688943

C₂

semidirect

4. #15688901

C₂

semidirect

5. C₄₇×#347

C₂

semidirect

55. #347

D₄₇

semidirect

56. C₄₇

#2166

semidirect

Subgroups — #20245202

Conjugacy classes of subgroups

Complements