Group #19133350 — subgroups

Subgroups — #19133350

Order 5504.

184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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	1	yes	maximal, characteristic
2	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#14582649	C₂	1	4	yes	maximal, complemented
4	C₄₃×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	—	2	1	no	—
6	C₂²×C₄₃⋊C₈	C₄	1	2	yes	—
7	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
9	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
10	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
11	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
12	C₂×M₁₆×C₄₃	—	2	1	no	—
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	—	2	1	no	—
15	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
19	M₁₆×C₄₃	—	4	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₄²×C₄₃	Q₈	1	1	yes	characteristic
24	C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	#10621877	—	4	2	no	—
26	C₂×C₄₃⋊C₈	—	2	4	no	—
27	C₂×C₄₃⋊C₈	—	2	2	no	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
29	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
30	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	—	2	2	no	—
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
37	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
38	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₄₃	—	4	2	no	—
42	C₄₃⋊C₈	—	2	2	no	—
43	C₄₃⋊C₈	—	4	2	no	—
44	C₄₃⋊C₈	M₁₆	1	4	yes	complemented
45	C₂²×C₄₃	—	2	1	no	—
46	C₂²×C₄₃	—	2	1	no	—
47	C₂²×C₄₃	#106	1	2	yes	—
48	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	#106	1	2	yes	—
52	C₄×C₄₃	#108	1	2	yes	—
53	C₄×C₄₃	C₂×M₁₆	1	2	yes	—
54	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
55	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
56	#1566	—	43	1	no	maximal, Sylow
57	C₂×C₄₃	—	2	2	no	—
58	C₂×C₄₃	#423	1	1	yes	characteristic
59	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
60	C₂×C₄₃	C₂×#108	1	1	yes	characteristic
61	#423	—	43	1	no	—
62	#423	D₄₃	1	1	yes	characteristic
63	C₂×C₄×C₈	—	43	1	no	—
64	#334	—	43	4	no	—
65	C₄₃	#1566	1	1	yes	characteristic, complemented, Sylow
66	C₂×M₁₆	—	2	1	no	—
67	C₂×M₁₆	—	86	1	no	—
68	C₂²×C₈	—	43	2	no	—
69	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
70	C₄⋊C₈	—	2	1	no	—
71	C₄⋊C₈	—	43	2	no	—
72	C₄⋊C₈	—	86	1	no	—
73	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
74	C₄×C₈	—	43	2	no	—
75	C₄×C₈	—	43	1	no	—
76	C₄×C₈	—	43	1	no	—
77	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
78	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
79	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
80	M₁₆	—	4	2	no	—
81	M₁₆	—	172	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	43	2	no	—
84	C₂×C₈	—	43	2	no	—
85	C₂×C₈	—	86	4	no	—
86	C₂×C₈	—	86	2	no	—
87	C₄²	Dic₈₆	1	1	yes	characteristic
88	C₄²	C₄×D₄₃	1	1	yes	characteristic
89	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
90	C₄²	C₂²×D₄₃	1	1	yes	characteristic
91	C₂³	Dic₄₃⋊C₄	1	1	yes	characteristic
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
95	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
96	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
97	C₂×C₄	#10621883	1	2	yes	—
98	C₂×C₄	#10621884	1	2	yes	—
99	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
100	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
101	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
102	C₈	—	4	2	no	—
103	C₈	—	43	4	no	—
104	C₈	—	86	2	no	—
105	C₈	—	172	2	no	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	#13063256	1	2	yes	—
109	C₂²	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	#13063256	1	2	yes	—
113	C₄	#13063260	1	2	yes	—
114	C₄	M₁₆×D₄₃	1	2	yes	—
115	C₄	C₂×#10621884	1	1	yes	characteristic
116	C₄	C₂×#10621883	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#14582922	1	1	yes	characteristic
119	C₂	C₂×#13063256	1	1	yes	characteristic
120	C₂	C₂×#13063260	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582923

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

#14582649

C₂

yes

maximal, complemented

C₄₃×#423

C₂

yes

maximal, characteristic

C₂×#10621877

—

C₂²×C₄₃⋊C₈

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄×C₄₃⋊C₈

C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×M₁₆×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

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

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

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

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

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

M₁₆

yes

complemented

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

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

#1566

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₂×C₄×C₈

—

#334

—

C₄₃

#1566

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₈₆

yes

characteristic

C₄²

C₄×D₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

#10621883

yes

—

C₂×C₄

#10621884

yes

—

C₂×C₄

C₂×Dic₈₆

yes

characteristic

100

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

101

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

172

—

106

C₂²

—

107

C₂²

—

108

C₂²

#13063256

yes

—

109

C₂²

C₂×Dic₄₃⋊C₄

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

#13063256

yes

—

113

C₄

#13063260

yes

—

114

C₄

M₁₆×D₄₃

yes

—

115

C₄

C₂×#10621884

yes

characteristic

116

C₄

C₂×#10621883

yes

characteristic

117

C₂

—

118

C₂

#14582922

yes

characteristic

119

C₂

C₂×#13063256

yes

characteristic

120

C₂

C₂×#13063260

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	#423	D₄₃
hypocenter	C₄₃	#1566
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#423

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
3. #14582649	C₂	semidirect
44. C₄₃⋊C₈	M₁₆	semidirect
65. C₄₃	#1566	semidirect

H ≅ G/N

type

3. #14582649

C₂

semidirect

44. C₄₃⋊C₈

M₁₆

semidirect

65. C₄₃

#1566

semidirect

Subgroups — #19133350

Conjugacy classes of subgroups

Complements