Group #19134109 — subgroups

Subgroups — #19134109

Order 5504.

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

normal subgroups only

This group has 166 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	#14583304	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583105	C₂	1	2	yes	maximal
3	#14582978	C₂	1	1	yes	maximal, characteristic
4	#14582646	C₂	1	2	yes	maximal, complemented
5	C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621873	—	2	2	no	—
7	C₂×#10621872	—	2	1	no	—
8	#13063325	C₂²	1	2	yes	—
9	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
10	#13063259	—	2	1	no	—
11	#13063259	—	2	1	no	—
12	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	#13063250	—	2	2	no	—
14	(C₂×D₄₃)⋊C₈	—	2	1	no	—
15	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₁₇₂	D₄	1	1	yes	characteristic
18	C₂×C₄×D₄₃	—	2	1	no	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	(C₂×D₄₃)⋊C₄	—	2	1	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
28	C₂×C₄₃⋊C₈	—	2	1	no	—
29	#10621873	—	4	4	no	—
30	#10621872	—	4	2	no	—
31	C₂²×D₄₃	—	2	1	no	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
35	C₂×Dic₄₃	—	2	1	no	—
36	C₂×Dic₄₃	—	4	2	no	—
37	D₁₇₂	—	2	2	no	—
38	C₄×D₄₃	—	4	1	no	—
39	C₄×D₄₃	—	4	1	no	—
40	Dic₈₆	—	4	2	no	—
41	Dic₈₆	—	4	2	no	—
42	C₈×C₄₃	—	2	1	no	—
43	C₈×C₄₃	—	4	2	no	—
44	C₈×C₄₃	SD₁₆	1	2	yes	complemented
45	C₄₃⋊C₈	—	4	1	no	—
46	C₂²×C₄₃	#121	1	1	yes	characteristic
47	C₂×D₄₃	—	4	1	no	—
48	C₂×D₄₃	—	4	1	no	—
49	C₂×D₄₃	—	4	1	no	—
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
52	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
53	C₄×C₄₃	#137	1	1	yes	characteristic
54	Dic₄₃	—	4	1	no	—
55	Dic₄₃	—	8	2	no	—
56	#1693	—	43	1	no	maximal, Sylow
57	C₂×C₄₃	#461	1	1	yes	characteristic
58	C₂×C₄₃	#469	1	1	yes	characteristic
59	C₂×C₄₃	#473	1	1	yes	characteristic
60	D₄₃	—	8	1	no	—
61	#500	—	43	1	no	—
62	#461	—	43	2	no	—
63	#436	—	43	1	no	—
64	#334	D₄₃	1	1	yes	characteristic, complemented
65	#332	—	43	2	no	—
66	C₄₃	#1693	1	1	yes	characteristic, complemented, Sylow
67	C₂×SD₁₆	—	86	2	no	—
68	C₂×M₁₆	—	86	1	no	—
69	C₄⋊Q₈	—	43	2	no	—
70	C₄×D₄	—	43	1	no	—
71	#107	—	86	1	no	—
72	#107	—	86	1	no	—
73	C₄⋊C₈	—	43	1	no	—
74	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
75	#103	—	86	2	no	—
76	C₂²⋊C₈	—	86	1	no	—
77	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₂×Q₈	—	86	2	no	—
79	C₂×D₄	—	43	1	no	—
80	C₂²×C₄	—	86	1	no	—
81	SD₁₆	—	172	4	no	—
82	M₁₆	—	172	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	86	1	no	—
85	C₂×C₈	D₁₇₂	1	1	yes	characteristic
86	C₂×C₈	D₁₇₂	1	1	yes	characteristic
87	C₄⋊C₄	—	43	1	no	—
88	C₄⋊C₄	—	86	2	no	—
89	C₄⋊C₄	—	86	2	no	—
90	C₂²⋊C₄	—	86	1	no	—
91	C₄²	C₂²×D₄₃	1	1	yes	characteristic
92	C₂³	—	86	1	no	—
93	Q₈	—	172	2	no	—
94	Q₈	—	172	2	no	—
95	D₄	—	86	2	no	—
96	C₂×C₄	—	86	1	no	—
97	C₂×C₄	—	172	2	no	—
98	C₂×C₄	—	172	1	no	—
99	C₂×C₄	—	172	1	no	—
100	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
101	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
102	C₂×C₄	#10621902	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	4	2	no	—
105	C₈	—	172	1	no	—
106	C₈	#10621873	1	2	yes	complemented
107	C₂²	—	172	1	no	—
108	C₂²	—	172	1	no	—
109	C₂²	—	172	1	no	—
110	C₂²	#13063300	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	344	2	no	—
113	C₄	—	172	1	no	—
114	C₄	C₂×#10621873	1	1	yes	characteristic
115	C₄	#13063352	1	2	yes	—
116	C₄	#13063358	1	1	yes	characteristic
117	C₂	—	344	1	no	—
118	C₂	#14583105	1	1	yes	characteristic
119	C₂	#14583153	1	1	yes	characteristic
120	C₂	#14583175	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583304

C₂

yes

maximal, characteristic, complemented

#14583105

C₂

yes

maximal

#14582978

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal, complemented

C₄₃×#334

C₂

yes

maximal, characteristic, complemented

C₂×#10621873

—

C₂×#10621872

—

#13063325

C₂²

yes

—

C₄×D₁₇₂

C₂²

yes

characteristic

#13063259

—

#13063259

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063250

—

(C₂×D₄₃)⋊C₈

—

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

#10621873

—

#10621872

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

SD₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#332

—

C₄₃

#1693

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

172

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

100

C₂×C₄

C₂×D₁₇₂

yes

characteristic

101

C₂×C₄

D₄×D₄₃

yes

characteristic

102

C₂×C₄

#10621902

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

172

—

106

C₈

#10621873

yes

complemented

107

C₂²

—

172

—

108

C₂²

—

172

—

109

C₂²

—

172

—

110

C₂²

#13063300

yes

characteristic

111

C₄

—

112

C₄

—

344

—

113

C₄

—

172

—

114

C₄

C₂×#10621873

yes

characteristic

115

C₄

#13063352

yes

—

116

C₄

#13063358

yes

characteristic

117

C₂

—

344

—

118

C₂

#14583105

yes

characteristic

119

C₂

#14583153

yes

characteristic

120

C₂

#14583175

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#121
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1693
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #14583304	C₂	semidirect
4. #14582646	C₂	semidirect
5. C₄₃×#334	C₂	semidirect
44. C₈×C₄₃	SD₁₆	semidirect
64. #334	D₄₃	semidirect
66. C₄₃	#1693	semidirect
106. C₈	#10621873	semidirect

H ≅ G/N

type

1. #14583304

C₂

semidirect

4. #14582646

C₂

semidirect

5. C₄₃×#334

C₂

semidirect

44. C₈×C₄₃

SD₁₆

semidirect

64. #334

D₄₃

semidirect

66. C₄₃

#1693

semidirect

106. C₈

#10621873

semidirect

Subgroups — #19134109

Conjugacy classes of subgroups

Complements