Group #19134339 — subgroups

Subgroups — #19134339

Order 5504.

296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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×C₈×Dic₄₃	C₂	1	2	yes	maximal
2	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582654	C₂	1	1	yes	maximal, characteristic
4	#14582653	C₂	1	2	yes	maximal
5	C₄₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
8	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
9	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₈×Dic₄₃	C₄	1	8	yes	complemented
12	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
17	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
22	C₄²×C₄₃	—	2	2	no	—
23	C₄×Dic₄₃	—	2	1	no	—
24	C₄×Dic₄₃	—	2	1	no	—
25	C₄×Dic₄₃	—	2	4	no	—
26	C₄×Dic₄₃	C₈	1	8	yes	complemented
27	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
28	C₂×C₄₃⋊C₈	—	2	2	no	—
29	C₂×C₄₃⋊C₈	—	2	2	no	—
30	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
31	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	C₂×C₈	1	4	yes	—
35	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₄₃	#41	1	2	yes	—
37	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
39	C₂×Dic₄₃	—	2	2	no	—
40	C₂×Dic₄₃	—	2	2	no	—
41	C₂×Dic₄₃	C₄²	1	2	yes	—
42	C₂×Dic₄₃	C₄²	1	2	yes	—
43	C₂×Dic₄₃	C₂×C₈	1	4	yes	—
44	C₂×Dic₄₃	C₂×C₈	1	4	yes	—
45	C₂×Dic₄₃	M₁₆	1	4	yes	—
46	C₈×C₄₃	—	2	4	no	—
47	C₄₃⋊C₈	—	2	4	no	—
48	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
49	C₂²×C₄₃	#117	1	1	yes	characteristic
50	C₂²×C₄₃	#117	1	1	yes	characteristic
51	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
52	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
53	C₄×C₄₃	—	2	4	no	—
54	C₄×C₄₃	#117	1	2	yes	—
55	C₄×C₄₃	#117	1	2	yes	—
56	Dic₄₃	—	2	4	no	—
57	Dic₄₃	C₄×C₈	1	4	yes	—
58	Dic₄₃	#97	1	4	yes	—
59	#1744	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	#376	1	1	yes	characteristic
61	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
62	C₂×C₄₃	C₂×#97	1	1	yes	characteristic
63	C₂×C₄₃	#431	1	2	yes	—
64	C₂×C₄₃	#431	1	2	yes	—
65	C₂×C₄×C₈	—	43	2	no	—
66	C₄³	—	43	1	no	—
67	#336	—	43	2	no	—
68	#336	—	43	1	no	—
69	#336	D₄₃	1	1	yes	characteristic
70	C₄₃	#1744	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	—	43	2	no	—
72	C₂²×C₈	C₂×D₄₃	1	2	yes	—
73	C₂×C₄²	—	43	1	no	—
74	C₂×C₄²	—	43	2	no	—
75	C₂×C₄²	—	43	1	no	—
76	C₂×C₄²	—	43	2	no	—
77	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
78	C₄×C₈	—	43	8	no	—
79	C₂²×C₄	—	43	1	no	—
80	C₂²×C₄	—	43	1	no	—
81	C₂²×C₄	—	43	2	no	—
82	C₂²×C₄	C₄×D₄₃	1	2	yes	—
83	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	43	4	no	—
87	C₂×C₈	—	86	2	no	—
88	C₂×C₈	—	86	2	no	—
89	C₂×C₈	C₄×D₄₃	1	4	yes	—
90	C₄²	—	2	2	no	—
91	C₄²	—	43	8	no	—
92	C₄²	—	43	4	no	—
93	C₄²	—	86	4	no	—
94	C₄²	—	86	1	no	—
95	C₄²	—	86	1	no	—
96	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	43	2	no	—
100	C₂×C₄	—	43	2	no	—
101	C₂×C₄	—	43	4	no	—
102	C₂×C₄	—	43	4	no	—
103	C₂×C₄	—	43	4	no	—
104	C₂×C₄	—	86	2	no	—
105	C₂×C₄	—	86	2	no	—
106	C₂×C₄	C₈×D₄₃	1	4	yes	—
107	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
108	C₂×C₄	#10621900	1	1	yes	characteristic
109	C₂×C₄	#10621900	1	2	yes	—
110	C₂×C₄	#10621902	1	1	yes	characteristic
111	C₈	—	2	4	no	—
112	C₈	—	86	4	no	—
113	C₂²	C₄²×D₄₃	1	1	yes	characteristic
114	C₂²	#13063281	1	1	yes	characteristic
115	C₂²	#13063283	1	1	yes	characteristic
116	C₂²	C₂×C₈×D₄₃	1	2	yes	—
117	C₂²	M₁₆×D₄₃	1	2	yes	—
118	C₄	—	2	4	no	—
119	C₄	—	43	4	no	—
120	C₄	—	43	4	no	—
121	C₄	—	86	4	no	—
122	C₄	#13063281	1	2	yes	—
123	C₄	#13063283	1	2	yes	—
124	C₂	#14582744	1	1	yes	characteristic
125	C₂	C₄×C₈×D₄₃	1	1	yes	characteristic
126	C₂	#97×D₄₃	1	1	yes	characteristic
127	C₂	#14582949	1	2	yes	—
128	C₂	#14582951	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₄₃

C₂

yes

maximal

C₄²×Dic₄₃

C₂

yes

maximal, characteristic

#14582654

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal

C₄₃×#336

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₈×Dic₄₃

C₄

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₈

yes

complemented

C₄×Dic₄₃

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₄²

yes

—

C₂×Dic₄₃

C₄²

yes

—

C₂×Dic₄₃

C₂×C₈

yes

—

C₂×Dic₄₃

C₂×C₈

yes

—

C₂×Dic₄₃

M₁₆

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₄²

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

#117

yes

—

Dic₄₃

—

Dic₄₃

C₄×C₈

yes

—

Dic₄₃

#97

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×C₄₃

C₂×#97

yes

characteristic

C₂×C₄₃

#431

yes

—

C₂×C₄₃

#431

yes

—

C₂×C₄×C₈

—

C₄³

—

#336

—

#336

—

#336

D₄₃

yes

characteristic

C₄₃

#1744

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₄₃

yes

—

107

C₂×C₄

C₂×C₄×D₄₃

yes

—

108

C₂×C₄

#10621900

yes

characteristic

109

C₂×C₄

#10621900

yes

—

110

C₂×C₄

#10621902

yes

characteristic

111

C₈

—

112

C₈

—

113

C₂²

C₄²×D₄₃

yes

characteristic

114

C₂²

#13063281

yes

characteristic

115

C₂²

#13063283

yes

characteristic

116

C₂²

C₂×C₈×D₄₃

yes

—

117

C₂²

M₁₆×D₄₃

yes

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#13063281

yes

—

123

C₄

#13063283

yes

—

124

C₂

#14582744

yes

characteristic

125

C₂

C₄×C₈×D₄₃

yes

characteristic

126

C₂

#97×D₄₃

yes

characteristic

127

C₂

#14582949

yes

—

128

C₂

#14582951

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Fitting	C₄₃×#336	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	#336	D₄₃
hypocenter	C₄₃	#1744
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Fitting

C₄₃×#336

C₂

socle

C₂³×C₄₃

C₂²×C₄

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
11. C₈×Dic₄₃	C₄	semidirect
26. C₄×Dic₄₃	C₈	semidirect
70. C₄₃	#1744	semidirect

H ≅ G/N

type

11. C₈×Dic₄₃

C₄

semidirect

26. C₄×Dic₄₃

C₈

semidirect

70. C₄₃

#1744

semidirect

Subgroups — #19134339

Conjugacy classes of subgroups

Complements