Group #19133351 — subgroups

Subgroups — #19133351

Order 5504.

184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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	#14582923	C₂	1	2	yes	maximal
2	#14582650	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	—	2	2	no	—
5	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
6	C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
7	C₂²×C₈×C₄₃	C₄	1	2	yes	—
8	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
10	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
11	C₄×C₈×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
15	C₂×C₈×C₄₃	—	2	4	no	—
16	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	C₄²×C₄₃	Q₈	1	1	yes	characteristic
21	C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	#10621877	—	4	4	no	—
23	C₂×C₄₃⋊C₈	—	2	4	no	—
24	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	2	2	no	—
26	C₂×C₄×C₄₃	—	2	2	no	—
27	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	SD₁₆	1	4	yes	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
34	C₈×C₄₃	—	2	2	no	—
35	C₈×C₄₃	M₁₆	1	4	yes	complemented
36	C₄₃⋊C₈	—	4	4	no	—
37	C₂²×C₄₃	—	2	1	no	—
38	C₂²×C₄₃	—	2	1	no	—
39	C₂²×C₄₃	#106	1	2	yes	—
40	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₄₃	—	2	1	no	—
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	#106	1	2	yes	—
44	C₄×C₄₃	#108	1	2	yes	—
45	C₄×C₄₃	C₂×M₁₆	1	2	yes	—
46	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
47	#1566	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	2	2	no	—
49	C₂×C₄₃	#423	1	1	yes	characteristic
50	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
51	C₂×C₄₃	C₂×#108	1	1	yes	characteristic
52	#423	—	43	2	no	—
53	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
54	#334	—	43	4	no	—
55	C₄₃	#1566	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	86	2	no	—
57	C₂²×C₈	Dic₄₃	1	2	yes	—
58	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
59	C₄⋊C₈	—	43	4	no	—
60	C₄⋊C₈	—	86	2	no	—
61	C₄×C₈	Dic₄₃	1	1	yes	characteristic
62	C₄×C₈	Dic₄₃	1	1	yes	characteristic
63	C₄×C₈	C₂×D₄₃	1	2	yes	—
64	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
65	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
66	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
67	M₁₆	—	172	4	no	—
68	C₂×C₈	—	2	4	no	—
69	C₂×C₈	—	86	4	no	—
70	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
71	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
72	C₄²	Dic₈₆	1	1	yes	characteristic
73	C₄²	D₁₇₂	1	1	yes	characteristic
74	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
75	C₄²	C₂²×D₄₃	1	1	yes	characteristic
76	C₂³	C₄⋊Dic₄₃	1	1	yes	characteristic
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	#10621873	1	4	yes	—
80	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
81	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
82	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
83	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
84	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
85	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	172	4	no	—
88	C₈	#10621877	1	4	yes	complemented
89	C₂²	—	2	1	no	—
90	C₂²	—	2	1	no	—
91	C₂²	#13063257	1	2	yes	—
92	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	1	no	—
95	C₄	#13063257	1	2	yes	—
96	C₄	#13063261	1	2	yes	—
97	C₄	C₂×#10621877	1	2	yes	—
98	C₄	C₂×#10621873	1	2	yes	—
99	C₂	—	2	2	no	—
100	C₂	#14582923	1	1	yes	characteristic
101	C₂	C₂×#13063257	1	1	yes	characteristic
102	C₂	C₂×#13063261	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582923

C₂

yes

maximal

#14582650

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂²×C₈×C₄₃

C₄

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

M₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#106

yes

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#106

yes

—

C₄×C₄₃

#108

yes

—

C₄×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

C₂×SD₁₆

yes

—

#1566

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄×C₈

D₄₃

yes

characteristic

#334

—

C₄₃

#1566

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

Dic₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

Dic₄₃

yes

characteristic

C₄×C₈

Dic₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄²

Dic₈₆

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10621873

yes

—

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

—

C₈

—

172

—

C₈

#10621877

yes

complemented

C₂²

—

C₂²

—

C₂²

#13063257

yes

—

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

C₄

—

C₄

—

C₄

#13063257

yes

—

C₄

#13063261

yes

—

C₄

C₂×#10621877

yes

—

C₄

C₂×#10621873

yes

—

C₂

—

100

C₂

#14582923

yes

characteristic

101

C₂

C₂×#13063257

yes

characteristic

102

C₂

C₂×#13063261

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#1566
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

#1566

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14582650	C₂	semidirect
35. C₈×C₄₃	M₁₆	semidirect
55. C₄₃	#1566	semidirect
88. C₈	#10621877	semidirect

H ≅ G/N

type

2. #14582650

C₂

semidirect

35. C₈×C₄₃

M₁₆

semidirect

55. C₄₃

#1566

semidirect

88. C₈

#10621877

semidirect

Subgroups — #19133351

Conjugacy classes of subgroups

Complements