Group #19132716 — subgroups

Subgroups — #19132716

Order 5504.

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

normal subgroups only

This group has 166 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	#14582873	C₂	1	2	yes	maximal
2	C₄₃×#408	C₂	1	1	yes	maximal, characteristic
3	#13063284	—	2	2	no	—
4	#13063240	—	2	2	no	—
5	#13063240	C₄	1	4	yes	complemented
6	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₈×C₄₃	C₄	1	1	yes	characteristic, complemented
9	C₂²⋊C₈×C₄₃	—	2	2	no	—
10	#41×C₄₃	—	4	1	no	—
11	#41×C₄₃	—	4	1	no	—
12	C₂×Q₈×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×D₄×C₄₃	C₂×C₄	1	2	yes	—
14	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	D₄	1	2	yes	—
17	M₁₆×C₄₃	—	4	1	no	—
18	C₂×C₈×C₄₃	—	2	1	no	—
19	C₂×C₈×C₄₃	—	2	1	no	—
20	C₂×C₈×C₄₃	—	4	1	no	—
21	C₂²⋊Dic₄₃	—	2	4	no	—
22	C₄⋊Dic₄₃	—	4	2	no	—
23	C₄×Dic₄₃	—	4	2	no	—
24	C₂³×C₄₃	C₄²	1	1	yes	characteristic
25	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
26	Q₈×C₄₃	—	4	1	no	—
27	D₄×C₄₃	—	4	2	no	—
28	D₄×C₄₃	—	4	1	no	—
29	C₂×C₄×C₄₃	—	2	2	no	—
30	C₂×C₄×C₄₃	—	2	2	no	—
31	C₂×C₄×C₄₃	—	2	1	no	—
32	C₂×C₄×C₄₃	—	2	1	no	—
33	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×Dic₄₃	—	4	4	no	—
37	C₈×C₄₃	—	4	1	no	—
38	C₈×C₄₃	—	4	1	no	—
39	C₂²×C₄₃	—	2	1	no	—
40	C₂²×C₄₃	—	2	2	no	—
41	C₂²×C₄₃	—	4	1	no	—
42	C₂²×C₄₃	—	4	2	no	—
43	C₂²×C₄₃	#95	1	1	yes	characteristic
44	C₄×C₄₃	—	2	2	no	—
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	#99	1	1	yes	characteristic
47	C₄×C₄₃	#99	1	1	yes	characteristic
48	Dic₄₃	—	8	4	no	—
49	#1391	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	—	4	2	no	—
52	C₂×C₄₃	—	4	1	no	—
53	C₂×C₄₃	#342	1	1	yes	characteristic
54	#410	—	43	2	no	—
55	#408	D₄₃	1	1	yes	characteristic
56	C₄₃	#1391	1	1	yes	characteristic, complemented, Sylow
57	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
58	C₂×M₁₆	Dic₄₃	1	1	yes	characteristic, complemented
59	C₂²×C₈	Dic₄₃	1	1	yes	characteristic, complemented
60	#117	—	86	2	no	—
61	#99	—	43	4	no	—
62	#99	—	86	2	no	—
63	C₂²⋊C₈	—	2	2	no	—
64	#41	—	4	1	no	—
65	#41	—	4	1	no	—
66	C₂×Q₈	Dic₈₆	1	1	yes	characteristic
67	C₂×D₄	C₄×D₄₃	1	2	yes	—
68	C₂×D₄	D₁₇₂	1	1	yes	characteristic
69	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
70	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
71	M₁₆	—	4	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	4	1	no	—
75	C₄⋊C₄	—	172	2	no	—
76	C₂²⋊C₄	—	86	4	no	—
77	C₄²	—	172	2	no	—
78	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
79	C₂³	(C₂×D₄₃)⋊C₄	1	2	yes	—
80	Q₈	—	4	1	no	—
81	D₄	—	4	2	no	—
82	D₄	—	4	1	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	172	4	no	—
88	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
89	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
91	C₈	—	4	1	no	—
92	C₈	—	4	1	no	—
93	C₂²	—	2	2	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	4	2	no	—
97	C₂²	C₄₃⋊#95	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	1	no	—
100	C₄	—	344	4	no	—
101	C₄	#13063240	1	1	yes	characteristic
102	C₄	#13063240	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	4	2	no	—
105	C₂	—	4	1	no	—
106	C₂	#14582666	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582873

C₂

yes

maximal

C₄₃×#408

C₂

yes

maximal, characteristic

#13063284

—

#13063240

—

#13063240

C₄

yes

complemented

C₂×#41×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₄

yes

characteristic, complemented

C₂²×C₈×C₄₃

C₄

yes

characteristic, complemented

C₂²⋊C₈×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

Q₈

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂×D₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₄²

yes

characteristic

C₂³×C₄₃

C₂²⋊C₄

yes

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#95

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1391

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₄₃

#1391

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₃

yes

characteristic

C₂×M₁₆

Dic₄₃

yes

characteristic, complemented

C₂²×C₈

Dic₄₃

yes

characteristic, complemented

#117

—

#99

—

#99

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

Dic₈₆

yes

characteristic

C₂×D₄

C₄×D₄₃

yes

—

C₂×D₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₄²

—

172

—

C₂³

C₄×Dic₄₃

yes

characteristic

C₂³

(C₂×D₄₃)⋊C₄

yes

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

Dic₄₃⋊C₄

yes

—

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄₃⋊#95

yes

characteristic

C₄

—

C₄

—

100

C₄

—

344

—

101

C₄

#13063240

yes

characteristic

102

C₄

#13063240

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

#14582666

yes

characteristic

	subgroup	G/H
center	C₄	#13063240
commutator	C₂³×C₄₃	C₄²
Frattini	C₂×#41	C₂×D₄₃
Fitting	C₄₃×#408	C₂
socle	C₂×C₄₃	#342
hypercenter	#408	D₄₃
hypocenter	C₄₃	#1391
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×#41 ◁ #408

subgroup

G/H

center

C₄

#13063240

commutator

C₂³×C₄₃

C₄²

Frattini

C₂×#41

C₂×D₄₃

Fitting

C₄₃×#408

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×#41 ◁ #408

N	H ≅ G/N	type
5. #13063240	C₄	semidirect
7. C₂×M₁₆×C₄₃	C₄	semidirect
8. C₂²×C₈×C₄₃	C₄	semidirect
56. C₄₃	#1391	semidirect
58. C₂×M₁₆	Dic₄₃	semidirect
59. C₂²×C₈	Dic₄₃	semidirect

H ≅ G/N

type

5. #13063240

C₄

semidirect

7. C₂×M₁₆×C₄₃

C₄

semidirect

8. C₂²×C₈×C₄₃

C₄

semidirect

56. C₄₃

#1391

semidirect

58. C₂×M₁₆

Dic₄₃

semidirect

59. C₂²×C₈

Dic₄₃

semidirect

Subgroups — #19132716

Conjugacy classes of subgroups

Complements