Group #19133349 — subgroups

Subgroups — #19133349

Order 5504.

184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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	#14582921	C₂	1	2	yes	maximal
2	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582650	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582649	C₂	1	2	yes	maximal, complemented
5	C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621872	—	2	2	no	—
7	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
9	C₄²×D₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
11	Dic₄₃⋊C₈	—	2	2	no	—
12	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×Dic₄₃	C₄	1	1	yes	characteristic
14	C₈×Dic₄₃	C₄	1	1	yes	characteristic
15	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×D₄₃	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₄₃	D₄	1	1	yes	characteristic
26	C₄×Dic₄₃	Q₈	1	1	yes	characteristic
27	C₂×C₄₃⋊C₈	—	2	2	no	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
30	#10621872	—	4	4	no	—
31	C₈×D₄₃	—	2	2	no	—
32	C₈×D₄₃	—	2	2	no	—
33	C₂²×D₄₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₄₃	—	2	1	no	—
41	C₄×D₄₃	—	2	1	no	—
42	C₄×D₄₃	—	2	2	no	—
43	C₄×D₄₃	SD₁₆	1	4	yes	—
44	C₈×C₄₃	—	2	1	no	—
45	C₈×C₄₃	—	4	2	no	—
46	C₈×C₄₃	M₁₆	1	2	yes	complemented
47	C₄₃⋊C₈	—	2	1	no	—
48	C₄₃⋊C₈	—	4	2	no	—
49	C₄₃⋊C₈	M₁₆	1	2	yes	complemented
50	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×D₄₃	—	2	1	no	—
52	C₂×D₄₃	—	2	1	no	—
53	C₂×D₄₃	#106	1	2	yes	—
54	C₄×C₄₃	—	2	1	no	—
55	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
56	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
57	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
58	Dic₄₃	—	2	1	no	—
59	Dic₄₃	#106	1	2	yes	—
60	Dic₄₃	#108	1	2	yes	—
61	#1566	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	#423	1	1	yes	characteristic
63	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
64	C₂×C₄₃	C₂×#108	1	1	yes	characteristic
65	D₄₃	—	2	2	no	—
66	#423	—	43	2	no	—
67	C₂×C₄×C₈	—	43	1	no	—
68	#334	—	43	2	no	—
69	#334	—	43	1	no	—
70	#334	D₄₃	1	1	yes	characteristic, complemented
71	C₄₃	#1566	1	1	yes	characteristic, complemented, Sylow
72	C₂×M₁₆	—	86	2	no	—
73	C₂²×C₈	—	43	1	no	—
74	C₂²×C₈	—	43	1	no	—
75	C₂×C₄²	—	43	1	no	—
76	C₄⋊C₈	—	43	2	no	—
77	C₄⋊C₈	—	86	2	no	—
78	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
79	C₄×C₈	—	43	1	no	—
80	C₄×C₈	—	43	1	no	—
81	C₄×C₈	—	43	1	no	—
82	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
83	C₂²×C₄	—	43	1	no	—
84	C₂²×C₄	—	43	1	no	—
85	C₂²×C₄	—	43	1	no	—
86	M₁₆	—	172	4	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	43	1	no	—
89	C₂×C₈	—	43	1	no	—
90	C₂×C₈	—	86	2	no	—
91	C₂×C₈	—	86	2	no	—
92	C₂×C₈	—	86	2	no	—
93	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
94	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
95	C₄²	—	43	1	no	—
96	C₄²	—	43	1	no	—
97	C₄²	—	43	1	no	—
98	C₄²	C₂²×D₄₃	1	1	yes	characteristic
99	C₂³	—	43	1	no	—
100	C₂×C₄	—	43	1	no	—
101	C₂×C₄	—	43	1	no	—
102	C₂×C₄	—	43	4	no	—
103	C₂×C₄	—	43	1	no	—
104	C₂×C₄	—	86	2	no	—
105	C₂×C₄	—	86	1	no	—
106	C₂×C₄	—	86	1	no	—
107	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
108	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
109	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	4	2	no	—
112	C₈	—	43	2	no	—
113	C₈	—	86	1	no	—
114	C₈	—	172	2	no	—
115	C₈	#10621872	1	2	yes	complemented
116	C₂²	—	43	2	no	—
117	C₂²	—	86	1	no	—
118	C₂²	—	86	1	no	—
119	C₂²	C₄⋊C₄×D₄₃	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	43	2	no	—
122	C₄	—	43	2	no	—
123	C₄	—	86	1	no	—
124	C₄	M₁₆×D₄₃	1	1	yes	characteristic
125	C₄	C₂×#10621872	1	1	yes	characteristic
126	C₄	SD₁₆×D₄₃	1	2	yes	—
127	C₂	—	86	2	no	—
128	C₂	#14582921	1	1	yes	characteristic
129	C₂	#106×D₄₃	1	1	yes	characteristic
130	C₂	#108×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582921

C₂

yes

maximal

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic

#14582650

C₂

yes

maximal, characteristic, complemented

#14582649

C₂

yes

maximal, complemented

C₄₃×#334

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

—

C₂×C₈×D₄₃

C₄

yes

characteristic

C₂×C₈×D₄₃

C₄

yes

characteristic

C₄²×D₄₃

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

Dic₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

C₄

yes

characteristic

C₈×Dic₄₃

C₄

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

Q₈

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₈×D₄₃

—

C₂²×D₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×Dic₄₃

C₄⋊C₄

yes

characteristic

C₂×Dic₄₃

C₄⋊C₄

yes

characteristic

C₂×Dic₄₃

C₄⋊C₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

SD₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

M₁₆

yes

complemented

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

M₁₆

yes

complemented

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

#106

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

—

Dic₄₃

—

Dic₄₃

#106

yes

—

Dic₄₃

#108

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#423

—

C₂×C₄×C₈

—

#334

—

#334

—

#334

D₄₃

yes

characteristic, complemented

C₄₃

#1566

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

108

C₂×C₄

D₄×D₄₃

yes

characteristic

109

C₂×C₄

Q₈×D₄₃

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

172

—

115

C₈

#10621872

yes

complemented

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

C₄⋊C₄×D₄₃

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

M₁₆×D₄₃

yes

characteristic

125

C₄

C₂×#10621872

yes

characteristic

126

C₄

SD₁₆×D₄₃

yes

—

127

C₂

—

128

C₂

#14582921

yes

characteristic

129

C₂

#106×D₄₃

yes

characteristic

130

C₂

#108×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1566
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
3. #14582650	C₂	semidirect
4. #14582649	C₂	semidirect
5. C₄₃×#334	C₂	semidirect
46. C₈×C₄₃	M₁₆	semidirect
49. C₄₃⋊C₈	M₁₆	semidirect
70. #334	D₄₃	semidirect
71. C₄₃	#1566	semidirect
115. C₈	#10621872	semidirect

H ≅ G/N

type

3. #14582650

C₂

semidirect

4. #14582649

C₂

semidirect

5. C₄₃×#334

C₂

semidirect

46. C₈×C₄₃

M₁₆

semidirect

49. C₄₃⋊C₈

M₁₆

semidirect

70. #334

D₄₃

semidirect

71. C₄₃

#1566

semidirect

115. C₈

#10621872

semidirect

Subgroups — #19133349

Conjugacy classes of subgroups

Complements