Group #19134086 — subgroups

Subgroups — #19134086

Order 5504.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14583181	C₂	1	2	yes	maximal
2	#14583029	C₂	1	1	yes	maximal, characteristic
3	#14582650	C₂	1	1	yes	maximal, characteristic
4	#14582645	C₂	1	2	yes	maximal
5	C₄₃×#494	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
7	#13063256	—	2	2	no	—
8	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	Dic₄₃⋊C₈	—	2	1	no	—
11	#13063248	—	2	2	no	—
12	#13063235	—	2	1	no	—
13	C₂×Q₁₆×C₄₃	—	2	1	no	—
14	C₂×Q₁₆×C₄₃	—	2	1	no	—
15	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	—	2	2	no	—
18	C₂×Dic₈₆	D₄	1	1	yes	characteristic
19	Q₁₆×C₄₃	—	4	2	no	—
20	Q₁₆×C₄₃	—	4	2	no	—
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	—	2	2	no	—
25	C₄²×C₄₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
27	Dic₄₃⋊C₄	—	2	1	no	—
28	C₄×Dic₄₃	—	2	1	no	—
29	C₂×C₄₃⋊C₈	—	2	1	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	Q₈×C₄₃	—	4	2	no	—
32	Q₈×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
37	C₂×Dic₄₃	—	2	1	no	—
38	C₂×Dic₄₃	—	2	1	no	—
39	Dic₈₆	—	2	2	no	—
40	C₈×C₄₃	—	2	1	no	—
41	C₈×C₄₃	SD₁₆	1	2	yes	—
42	C₄₃⋊C₈	—	4	1	no	—
43	C₄₃⋊C₈	—	4	2	no	—
44	C₂²×C₄₃	#121	1	1	yes	characteristic
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	8	2	no	—
47	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
48	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
49	C₄×C₄₃	#137	1	2	yes	—
50	Dic₄₃	—	4	1	no	—
51	Dic₄₃	—	4	1	no	—
52	#1690	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	#460	1	1	yes	characteristic
54	C₂×C₄₃	#470	1	1	yes	characteristic
55	C₂×C₄₃	#473	1	1	yes	characteristic
56	#494	D₄₃	1	1	yes	characteristic
57	#475	—	43	2	no	—
58	#446	—	43	1	no	—
59	#334	—	43	1	no	—
60	#332	—	43	2	no	—
61	C₄₃	#1690	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₁₆	—	2	1	no	—
63	C₂×Q₁₆	—	2	1	no	—
64	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
65	C₄×Q₈	—	43	1	no	—
66	#106	—	86	2	no	—
67	C₄⋊C₈	—	43	1	no	—
68	C₄⋊C₈	—	43	2	no	—
69	C₄⋊C₈	—	86	1	no	—
70	#103	—	86	2	no	—
71	#97	—	86	1	no	—
72	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	43	1	no	—
75	Q₁₆	—	4	2	no	—
76	Q₁₆	—	4	2	no	—
77	C₂×C₈	—	86	2	no	—
78	C₂×C₈	—	86	1	no	—
79	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	43	1	no	—
84	C₄⋊C₄	—	86	1	no	—
85	C₄²	—	86	1	no	—
86	C₄²	C₂²×D₄₃	1	1	yes	characteristic
87	Q₈	—	4	2	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	86	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	86	1	no	—
92	C₂×C₄	—	86	1	no	—
93	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
94	C₂×C₄	#10621900	1	1	yes	characteristic
95	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	172	1	no	—
98	C₈	—	172	2	no	—
99	C₈	#10621883	1	2	yes	—
100	C₂²	#13063296	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	8	2	no	—
103	C₄	—	172	1	no	—
104	C₄	—	172	1	no	—
105	C₄	C₂×#10621883	1	1	yes	characteristic
106	C₄	#13063351	1	1	yes	characteristic
107	C₄	#13063357	1	2	yes	—
108	C₂	#14583096	1	1	yes	characteristic
109	C₂	#14583154	1	1	yes	characteristic
110	C₂	#14583171	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583181

C₂

yes

maximal

#14583029

C₂

yes

maximal, characteristic

#14582650

C₂

yes

maximal, characteristic

#14582645

C₂

yes

maximal

C₄₃×#494

C₂

yes

maximal, characteristic

C₄×Dic₈₆

C₂²

yes

characteristic

#13063256

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

Dic₄₃⋊C₈

—

#13063248

—

#13063235

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

SD₁₆

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

—

—

—

—

C₄₃

#1690

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₄₃

yes

—

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621900

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

C₈

—

172

—

C₈

—

172

—

C₈

#10621883

yes

—

100

C₂²

#13063296

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

172

—

104

C₄

—

172

—

105

C₄

C₂×#10621883

yes

characteristic

106

C₄

#13063351

yes

characteristic

107

C₄

#13063357

yes

—

108

C₂

#14583096

yes

characteristic

109

C₂

#14583154

yes

characteristic

110

C₂

#14583171

yes

characteristic

	subgroup	G/H
center	C₂²	#13063296
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	#121
hypercenter	#494	D₄₃
hypocenter	C₄₃	#1690
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#13063296

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#494

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
61. C₄₃	#1690	semidirect

H ≅ G/N

type

61. C₄₃

#1690

semidirect

Subgroups — #19134086

Conjugacy classes of subgroups

Complements