Group #20245198 — subgroups

Subgroups — #20245198

Order 6016.

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

normal subgroups only

This group has 128 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	#15689075	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	C₄	1	1	yes	characteristic
7	C₂×#10625324	C₂²	1	1	yes	characteristic
8	C₄²×D₄₇	C₄	1	1	yes	characteristic
9	#13093964	C₂²	1	2	yes	—
10	#13093935	C₄	1	1	yes	characteristic
11	C₈×Dic₄₇	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	—	2	1	no	—
16	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
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	C₄×Dic₄₇	—	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	#10625324	—	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	C₄×D₄₇	—	4	2	no	—
36	C₈×C₄₇	—	2	1	no	—
37	C₈×C₄₇	#41	1	2	yes	—
38	C₄₇⋊C₈	—	2	1	no	—
39	C₄₇⋊C₈	M₁₆	1	2	yes	—
40	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₄₇	—	2	1	no	—
42	C₂×D₄₇	—	4	1	no	—
43	C₄×C₄₇	—	4	1	no	—
44	C₄×C₄₇	#117	1	1	yes	characteristic
45	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
46	Dic₄₇	—	2	2	no	—
47	Dic₄₇	—	2	1	no	—
48	#2165	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	—	2	1	no	—
50	C₂×C₄₇	#432	1	1	yes	characteristic
51	D₄₇	—	4	1	no	—
52	C₄×M₁₆	—	47	1	no	—
53	#364	—	47	2	no	—
54	#349	—	47	2	no	—
55	#347	—	47	1	no	—
56	#347	D₄₇	1	1	yes	characteristic, complemented
57	C₄₇	#2165	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	47	1	no	—
59	C₂×M₁₆	—	47	1	no	—
60	C₂×C₄²	—	47	1	no	—
61	M₃₂	—	47	2	no	—
62	M₃₂	C₂×D₄₇	1	2	yes	—
63	#97	—	47	1	no	—
64	#97	C₂×D₄₇	1	1	yes	characteristic
65	C₄×C₈	—	47	1	no	—
66	C₄×C₈	—	47	1	no	—
67	C₂²×C₄	—	47	1	no	—
68	C₂²×C₄	—	94	1	no	—
69	M₁₆	—	94	2	no	—
70	M₁₆	—	94	2	no	—
71	C₂×C₈	—	47	1	no	—
72	C₂×C₈	—	47	1	no	—
73	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
75	C₄²	—	47	1	no	—
76	C₄²	—	94	1	no	—
77	C₄²	C₄×D₄₇	1	1	yes	characteristic
78	C₁₆	—	2	2	no	—
79	C₁₆	—	94	2	no	—
80	C₂³	—	47	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	47	1	no	—
83	C₂×C₄	—	94	1	no	—
84	C₂×C₄	—	94	1	no	—
85	C₂×C₄	—	94	1	no	—
86	C₂×C₄	—	188	2	no	—
87	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	47	2	no	—
90	C₈	—	94	1	no	—
91	C₈	#10625350	1	2	yes	—
92	C₂²	—	94	1	no	—
93	C₂²	—	188	1	no	—
94	C₂²	M₁₆×D₄₇	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	94	2	no	—
97	C₄	—	94	1	no	—
98	C₄	#13093981	1	1	yes	characteristic
99	C₄	M₁₆×D₄₇	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	188	1	no	—
102	C₂	#15689178	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689075

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

C₄

yes

characteristic

C₂×#10625324

C₂²

yes

characteristic

C₄²×D₄₇

C₄

yes

characteristic

#13093964

C₂²

yes

—

#13093935

C₄

yes

characteristic

C₈×Dic₄₇

C₄

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

—

#97×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄₇

—

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

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

#10625324

—

#10625324

—

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

—

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

—

#2165

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#432

yes

characteristic

D₄₇

—

C₄×M₁₆

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2165

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×C₄²

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

—

#97

—

#97

C₂×D₄₇

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₄²

—

C₄²

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#10625350

yes

—

C₂²

—

C₂²

—

188

—

C₂²

M₁₆×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#13093981

yes

characteristic

C₄

M₁₆×D₄₇

yes

characteristic

100

C₂

—

101

C₂

—

188

—

102

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	#2165
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
56. #347	D₄₇	semidirect
57. C₄₇	#2165	semidirect

H ≅ G/N

type

2. #15688943

C₂

semidirect

4. #15688901

C₂

semidirect

5. C₄₇×#347

C₂

semidirect

56. #347

D₄₇

semidirect

57. C₄₇

#2165

semidirect

Subgroups — #20245198

Conjugacy classes of subgroups

Complements