Group #20245637 — subgroups

Subgroups — #20245637

Order 6016.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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	C₂×#13093965	C₂	1	4	yes	maximal, complemented
2	#15689500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₇₆	—	2	1	no	—
6	C₂×D₃₇₆	C₂²	1	2	yes	—
7	#13094021	—	2	1	no	—
8	#13093965	—	2	8	no	—
9	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
10	C₂×D₈×C₄₇	—	2	1	no	—
11	C₂×D₈×C₄₇	C₂²	1	2	yes	—
12	#127×C₄₇	—	2	1	no	—
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₄₇	—	2	2	no	—
15	C₂×D₄×C₄₇	—	4	2	no	—
16	C₂×D₁₈₈	—	2	2	no	—
17	C₂×D₁₈₈	—	4	2	no	—
18	D₈×C₄₇	—	2	4	no	—
19	D₈×C₄₇	—	4	2	no	—
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₄²×C₄₇	D₄	1	1	yes	characteristic
23	D₃₇₆	—	2	4	no	—
24	D₃₇₆	—	4	2	no	—
25	C₄₇⋊C₁₆	D₄	1	4	yes	complemented
26	C₂³×C₄₇	—	4	2	no	—
27	C₂²×D₄₇	—	4	2	no	—
28	D₄×C₄₇	—	4	2	no	—
29	D₄×C₄₇	—	4	2	no	—
30	D₄×C₄₇	—	8	4	no	—
31	C₂×C₄×C₄₇	D₈	1	2	yes	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	D₁₈₈	—	4	2	no	—
34	D₁₈₈	—	4	2	no	—
35	D₁₈₈	—	8	4	no	—
36	C₈×C₄₇	D₈	1	2	yes	—
37	C₈×C₄₇	C₂×D₄	1	2	yes	—
38	C₂²×C₄₇	—	8	2	no	—
39	C₂²×C₄₇	—	8	4	no	—
40	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
41	C₂×D₄₇	—	8	2	no	—
42	C₂×D₄₇	—	8	4	no	—
43	C₄×C₄₇	D₁₆	1	4	yes	complemented
44	C₄×C₄₇	#127	1	1	yes	characteristic
45	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
46	#2246	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	—	16	2	no	—
48	C₂×C₄₇	#493	1	1	yes	characteristic
49	C₂×C₄₇	C₂×D₁₆	1	2	yes	—
50	D₄₇	—	16	2	no	—
51	C₂×D₁₆	—	47	4	no	—
52	#493	—	47	1	no	—
53	#493	D₄₇	1	1	yes	characteristic, complemented
54	C₄×C₁₆	—	47	1	no	—
55	C₄₇	#2246	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	2	1	no	—
57	C₂×D₈	—	47	2	no	—
58	C₂×D₈	—	94	1	no	—
59	C₂×D₈	C₂×D₄₇	1	2	yes	—
60	#127	—	2	1	no	—
61	#127	—	94	1	no	—
62	D₁₆	—	94	8	no	—
63	C₂×C₁₆	—	47	2	no	—
64	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	4	2	no	—
67	C₂×D₄	—	94	2	no	—
68	C₂×D₄	—	188	2	no	—
69	D₈	—	2	4	no	—
70	D₈	—	4	2	no	—
71	D₈	—	94	4	no	—
72	D₈	—	188	2	no	—
73	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
75	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
76	C₁₆	—	47	4	no	—
77	C₂³	—	4	2	no	—
78	C₂³	—	188	2	no	—
79	D₄	—	4	2	no	—
80	D₄	—	4	2	no	—
81	D₄	—	8	4	no	—
82	D₄	—	376	4	no	—
83	D₄	—	188	2	no	—
84	D₄	—	188	2	no	—
85	C₂×C₄	#10625334	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
87	C₈	#10625334	1	2	yes	—
88	C₈	D₄×D₄₇	1	2	yes	—
89	C₂²	—	8	2	no	—
90	C₂²	—	8	4	no	—
91	C₂²	—	376	2	no	—
92	C₂²	—	376	4	no	—
93	C₂²	C₂×#10625334	1	1	yes	characteristic
94	C₄	#13093965	1	4	yes	complemented
95	C₄	#13094020	1	1	yes	characteristic
96	C₄	C₂×#10625334	1	1	yes	characteristic
97	C₂	—	16	2	no	—
98	C₂	—	752	2	no	—
99	C₂	#15689499	1	1	yes	characteristic
100	C₂	C₂×#13093965	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093965

C₂

yes

maximal, complemented

#15689500

C₂

yes

maximal, characteristic, complemented

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₇×#493

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂²

yes

—

#13094021

—

#13093965

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₂×D₈×C₄₇

—

C₂×D₈×C₄₇

C₂²

yes

—

#127×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

D₃₇₆

—

D₃₇₆

—

C₄₇⋊C₁₆

D₄

yes

complemented

C₂³×C₄₇

—

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

D₈

yes

—

C₈×C₄₇

C₂×D₄

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

D₁₆

yes

complemented

C₄×C₄₇

#127

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

#2246

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#493

yes

characteristic

C₂×C₄₇

C₂×D₁₆

yes

—

D₄₇

—

C₂×D₁₆

—

#493

—

#493

D₄₇

yes

characteristic, complemented

C₄×C₁₆

—

C₄₇

#2246

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₇

yes

—

#127

—

#127

—

D₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

188

—

D₈

—

D₈

—

D₈

—

D₈

—

188

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

188

—

D₄

—

D₄

—

D₄

—

D₄

—

376

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

#10625334

yes

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

#10625334

yes

—

C₈

D₄×D₄₇

yes

—

C₂²

—

C₂²

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

—

752

—

C₂

#15689499

yes

characteristic

100

C₂

C₂×#13093965

yes

—

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#493	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#493	D₄₇
hypocenter	C₄₇	#2246
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#493

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. C₂×#13093965	C₂	semidirect
2. #15689500	C₂	semidirect
3. C₄×C₄₇⋊C₁₆	C₂	semidirect
4. C₄₇×#493	C₂	semidirect
25. C₄₇⋊C₁₆	D₄	semidirect
43. C₄×C₄₇	D₁₆	semidirect
53. #493	D₄₇	semidirect
55. C₄₇	#2246	semidirect
94. C₄	#13093965	semidirect

H ≅ G/N

type

1. C₂×#13093965

C₂

semidirect

2. #15689500

C₂

semidirect

3. C₄×C₄₇⋊C₁₆

C₂

semidirect

4. C₄₇×#493

C₂

semidirect

25. C₄₇⋊C₁₆

D₄

semidirect

43. C₄×C₄₇

D₁₆

semidirect

53. #493

D₄₇

semidirect

55. C₄₇

#2246

semidirect

94. C₄

#13093965

semidirect

Subgroups — #20245637

Conjugacy classes of subgroups

Complements