Group #19132890 — subgroups

Subgroups — #19132890

Order 5504.

190 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 105 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	#14582952	C₂	1	1	yes	maximal, characteristic
2	C₄×#10621877	C₂	1	1	yes	maximal, characteristic
3	#14582621	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582621	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582620	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621877	C₄	1	2	yes	—
9	C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
10	C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
11	#13063236	C₄	1	2	yes	—
12	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₈×C₄₃	C₄	1	2	yes	—
18	C₂²⋊C₈×C₄₃	C₄	1	2	yes	—
19	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
26	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₄₃	C₂³	1	1	yes	characteristic
30	#10621877	—	2	4	no	—
31	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
33	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
34	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
35	C₂³×C₄₃	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	2	2	no	—
38	C₂×C₄×C₄₃	—	2	2	no	—
39	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₈×C₄₃	—	2	2	no	—
46	C₈×C₄₃	—	2	2	no	—
47	C₄₃⋊C₈	—	2	2	no	—
48	C₄₃⋊C₈	—	2	2	no	—
49	C₄₃⋊C₈	—	2	2	no	—
50	C₄₃⋊C₈	M₁₆	1	4	yes	—
51	C₂²×C₄₃	—	2	1	no	—
52	C₂²×C₄₃	—	2	1	no	—
53	C₂²×C₄₃	—	2	1	no	—
54	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	—	2	1	no	—
57	C₄×C₄₃	—	2	1	no	—
58	C₄×C₄₃	C₂×M₁₆	1	2	yes	—
59	C₄×C₄₃	#131	1	2	yes	—
60	C₄×C₄₃	#131	1	2	yes	—
61	#1453	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	4	1	no	—
63	C₂×C₄₃	C₄×M₁₆	1	1	yes	characteristic
64	C₂×C₄₃	#405	1	1	yes	characteristic
65	C₂×C₄₃	#405	1	1	yes	characteristic
66	#431	—	43	1	no	—
67	#431	D₄₃	1	1	yes	characteristic
68	C₄×M₁₆	—	43	1	no	—
69	#322	—	43	1	no	—
70	#322	—	43	1	no	—
71	#322	—	43	1	no	—
72	C₈²	—	43	1	no	—
73	C₄₃	#1453	1	1	yes	characteristic, complemented, Sylow
74	C₂×M₁₆	—	43	2	no	—
75	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
76	C₄⋊C₈	—	43	2	no	—
77	C₄⋊C₈	Dic₄₃	1	2	yes	—
78	C₂²⋊C₈	—	43	2	no	—
79	C₂²⋊C₈	Dic₄₃	1	2	yes	—
80	#97	—	43	2	no	—
81	C₄×C₈	—	43	1	no	—
82	C₄×C₈	—	43	1	no	—
83	C₄×C₈	—	43	1	no	—
84	C₄×C₈	—	43	1	no	—
85	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
86	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
88	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
89	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
90	M₁₆	—	86	4	no	—
91	C₂×C₈	—	43	2	no	—
92	C₂×C₈	—	43	2	no	—
93	C₂×C₈	—	43	2	no	—
94	C₂×C₈	—	43	2	no	—
95	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
96	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
97	C₄²	C₄×D₄₃	1	1	yes	characteristic
98	C₄²	C₄×D₄₃	1	1	yes	characteristic
99	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
100	C₄²	C₂²×D₄₃	1	1	yes	characteristic
101	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
106	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
107	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
108	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
109	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
110	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	2	2	no	—
113	C₈	—	43	4	no	—
114	C₈	—	86	2	no	—
115	C₈	—	86	2	no	—
116	C₈	—	86	2	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	2	1	no	—
123	C₄	—	2	1	no	—
124	C₄	M₁₆×D₄₃	1	2	yes	—
125	C₄	#13063331	1	2	yes	—
126	C₄	#13063332	1	2	yes	—
127	C₂	—	4	1	no	—
128	C₂	M₁₆×Dic₄₃	1	1	yes	characteristic
129	C₂	#14582854	1	1	yes	characteristic
130	C₂	#14582855	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582952

C₂

yes

maximal, characteristic

C₄×#10621877

C₂

yes

maximal, characteristic

#14582621

C₂

yes

maximal, characteristic, complemented

#14582621

C₂

yes

maximal, characteristic, complemented

#14582620

C₂

yes

maximal, characteristic, complemented

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄₃×#431

C₂

yes

maximal, characteristic

C₂×#10621877

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

C₄

yes

—

C₂²⋊(C₄₃⋊C₈)

C₄

yes

—

#13063236

C₄

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₄

yes

—

C₂²⋊C₈×C₄₃

C₄

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

M₁₆

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

#131

yes

—

#1453

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×M₁₆

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₄×M₁₆

—

#322

—

#322

—

#322

—

C₈²

—

C₄₃

#1453

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

Dic₄₃

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₄₃

yes

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄²

C₄×D₄₃

yes

characteristic

C₄²

C₄×D₄₃

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

100

C₄²

C₂²×D₄₃

yes

characteristic

101

C₂³

C₄×Dic₄₃

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₄×Dic₄₃

yes

characteristic

106

C₂×C₄

C₄×Dic₄₃

yes

characteristic

107

C₂×C₄

C₄×Dic₄₃

yes

characteristic

108

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

109

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

110

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

M₁₆×D₄₃

yes

—

125

C₄

#13063331

yes

—

126

C₄

#13063332

yes

—

127

C₂

—

128

C₂

M₁₆×Dic₄₃

yes

characteristic

129

C₂

#14582854

yes

characteristic

130

C₂

#14582855

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂×C₄²
Fitting	C₄₃×#431	C₂
hypercenter	#431	D₄₃
hypocenter	C₄₃	#1453
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ #431

subgroup

G/H

center, Frattini

C₄²

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂×C₄²

Fitting

C₄₃×#431

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₄² ◁ #431

N	H ≅ G/N	type
3. #14582621	C₂	semidirect
4. #14582621	C₂	semidirect
5. #14582620	C₂	semidirect
6. C₈×C₄₃⋊C₈	C₂	semidirect
73. C₄₃	#1453	semidirect

H ≅ G/N

type

3. #14582621

C₂

semidirect

4. #14582621

C₂

semidirect

5. #14582620

C₂

semidirect

6. C₈×C₄₃⋊C₈

C₂

semidirect

73. C₄₃

#1453

semidirect

Subgroups — #19132890

Conjugacy classes of subgroups

Complements