Group #19132691 — subgroups

Subgroups — #19132691

Order 5504.

132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13063261	C₂	1	1	yes	maximal, characteristic
2	#14582937	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	—	2	1	no	—
5	#13063284	—	2	1	no	—
6	#13063261	—	2	1	no	—
7	#13063261	C₄	1	2	yes	complemented
8	#13063259	C₄	1	2	yes	—
9	#13063257	—	2	1	no	—
10	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₄₃	—	2	1	no	—
12	C₂×C₁₆×C₄₃	—	2	1	no	—
13	C₂×C₁₆×C₄₃	C₄	1	2	yes	complemented
14	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
21	C₂²⋊Dic₄₃	—	4	1	no	—
22	C₄⋊Dic₄₃	—	2	2	no	—
23	C₄×Dic₄₃	—	4	1	no	—
24	#10621877	—	2	2	no	—
25	#10621877	—	4	1	no	—
26	C₂×C₄₃⋊C₈	—	4	1	no	—
27	C₁₆×C₄₃	—	2	2	no	—
28	C₂³×C₄₃	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₄₃	—	4	2	no	—
36	C₈×C₄₃	C₄²	1	1	yes	characteristic
37	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄₃⋊C₈	—	4	2	no	—
41	C₂²×C₄₃	—	2	2	no	—
42	C₂²×C₄₃	#102	1	1	yes	characteristic
43	C₂²×C₄₃	#103	1	1	yes	characteristic
44	C₂²×C₄₃	#106	1	1	yes	characteristic
45	C₄×C₄₃	#95	1	1	yes	characteristic
46	C₄×C₄₃	#102	1	1	yes	characteristic
47	C₄×C₄₃	#103	1	1	yes	characteristic
48	C₄×C₄₃	#107	1	1	yes	characteristic
49	Dic₄₃	—	8	2	no	—
50	#1382	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	—	2	1	no	—
52	C₂×C₄₃	—	2	1	no	—
53	C₂×C₄₃	#340	1	1	yes	characteristic
54	C₂×C₄₃	#359	1	2	yes	—
55	C₂²×C₁₆	D₄₃	1	1	yes	characteristic
56	C₂×#108	—	43	1	no	—
57	#427	—	43	1	no	—
58	C₄₃	#1382	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	86	1	no	—
60	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
61	#117	—	86	1	no	—
62	C₂×C₁₆	—	2	1	no	—
63	C₂×C₁₆	—	2	1	no	—
64	C₂×C₁₆	Dic₄₃	1	2	yes	complemented
65	#108	—	43	2	no	—
66	#108	—	86	1	no	—
67	#107	—	43	2	no	—
68	#106	—	86	1	no	—
69	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
70	M₁₆	—	86	2	no	—
71	M₁₆	—	172	1	no	—
72	C₂×C₈	—	172	1	no	—
73	C₂×C₈	Dic₈₆	1	1	yes	characteristic
74	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
75	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
77	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
79	C₄⋊C₄	—	86	2	no	—
80	C₂²⋊C₄	—	172	1	no	—
81	C₄²	—	172	1	no	—
82	C₁₆	—	2	2	no	—
83	C₂³	#10621873	1	1	yes	characteristic
84	C₂×C₄	—	172	2	no	—
85	C₂×C₄	#10621873	1	1	yes	characteristic
86	C₂×C₄	D₃₄₄	1	1	yes	characteristic
87	C₂×C₄	Dic₁₇₂	1	1	yes	characteristic
88	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
89	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
90	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
91	C₈	—	172	2	no	—
92	C₈	C₄×Dic₄₃	1	1	yes	characteristic
93	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
94	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
95	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
96	C₂²	—	2	2	no	—
97	C₂²	#13063247	1	1	yes	characteristic
98	C₂²	#13063250	1	1	yes	characteristic
99	C₂²	#13063257	1	1	yes	characteristic
100	C₄	—	344	2	no	—
101	C₄	C₄₃⋊#95	1	1	yes	characteristic
102	C₄	#13063247	1	1	yes	characteristic
103	C₄	#13063250	1	1	yes	characteristic
104	C₄	#13063259	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	#14582662	1	1	yes	characteristic
108	C₂	#14582707	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063261

C₂

yes

maximal, characteristic

#14582937

C₂

yes

maximal, characteristic

C₂²×C₁₆×C₄₃

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

#13063259

C₄

yes

—

#13063257

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₄

yes

complemented

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

Q₁₆

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

C₄²

yes

characteristic

C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1382

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#340

yes

characteristic

C₂×C₄₃

#359

yes

—

C₂²×C₁₆

D₄₃

yes

characteristic

C₂×#108

—

#427

—

C₄₃

#1382

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

Dic₄₃

yes

—

—

—

—

C₂²×C₄

D₁₇₂

yes

characteristic

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

Dic₈₆

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

—

172

—

C₁₆

—

C₂³

#10621873

yes

characteristic

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

characteristic

C₂×C₄

D₃₄₄

yes

characteristic

C₂×C₄

Dic₁₇₂

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

172

—

C₈

C₄×Dic₄₃

yes

characteristic

C₈

Dic₄₃⋊C₄

yes

characteristic

C₈

Dic₄₃⋊C₄

yes

characteristic

C₈

C₂²⋊Dic₄₃

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

100

C₄

—

344

—

101

C₄

C₄₃⋊#95

yes

characteristic

102

C₄

#13063247

yes

characteristic

103

C₄

#13063250

yes

characteristic

104

C₄

#13063259

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

#14582662

yes

characteristic

108

C₂

#14582707

yes

—

	subgroup	G/H
center	C₂×C₄	D₃₄₄
commutator	C₈×C₄₃	C₄²
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₂²×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	#102
hypercenter	C₂²×C₁₆	D₄₃
hypocenter	C₄₃	#1382
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂×C₄

D₃₄₄

commutator

C₈×C₄₃

C₄²

Frattini

C₂²×C₈

C₂×D₄₃

Fitting

C₂²×C₁₆×C₄₃

C₂

socle

C₂²×C₄₃

#102

hypercenter

C₂²×C₁₆

D₄₃

hypocenter

C₄₃

#1382

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
7. #13063261	C₄	semidirect
13. C₂×C₁₆×C₄₃	C₄	semidirect
58. C₄₃	#1382	semidirect
64. C₂×C₁₆	Dic₄₃	semidirect

H ≅ G/N

type

7. #13063261

C₄

semidirect

13. C₂×C₁₆×C₄₃

C₄

semidirect

58. C₄₃

#1382

semidirect

64. C₂×C₁₆

Dic₄₃

semidirect

Subgroups — #19132691

Conjugacy classes of subgroups

Complements