Group #19132874 — subgroups

Subgroups — #19132874

Order 5504.

224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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	#14582950	C₂	1	1	yes	maximal, characteristic
2	C₄×#10621872	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582621	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621872	C₄	1	2	yes	—
9	C₂×C₈×D₄₃	C₄	1	2	yes	—
10	C₄²×D₄₃	C₂²	1	1	yes	characteristic
11	Dic₄₃⋊C₈	C₄	1	2	yes	—
12	(C₂×D₄₃)⋊C₈	C₄	1	2	yes	—
13	#13063235	C₄	1	2	yes	—
14	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₈×Dic₄₃	C₄	1	2	yes	—
18	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₄₃	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	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
27	C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
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	#10621872	C₈	1	8	yes	complemented
35	C₈×D₄₃	—	2	4	no	—
36	C₂²×D₄₃	C₄²	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₄₃	C₄²	1	1	yes	characteristic
41	C₂×Dic₄₃	C₄²	1	1	yes	characteristic
42	C₂×Dic₄₃	C₄²	1	1	yes	characteristic
43	C₄×D₄₃	—	2	2	no	—
44	C₄×D₄₃	—	2	2	no	—
45	C₄×D₄₃	C₂×C₈	1	4	yes	—
46	C₈×C₄₃	—	2	2	no	—
47	C₈×C₄₃	—	2	2	no	—
48	C₈×C₄₃	C₂×C₈	1	4	yes	complemented
49	C₄₃⋊C₈	—	2	2	no	—
50	C₄₃⋊C₈	C₂×C₈	1	4	yes	complemented
51	C₄₃⋊C₈	M₁₆	1	4	yes	complemented
52	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
53	C₂×D₄₃	—	2	1	no	—
54	C₂×D₄₃	—	2	1	no	—
55	C₂×D₄₃	C₄×C₈	1	2	yes	—
56	C₄×C₄₃	C₂²×C₈	1	2	yes	—
57	C₄×C₄₃	C₂×M₁₆	1	2	yes	—
58	C₄×C₄₃	#131	1	2	yes	—
59	Dic₄₃	—	2	1	no	—
60	Dic₄₃	—	2	1	no	—
61	Dic₄₃	C₄×C₈	1	2	yes	—
62	C₈×M₁₆	—	43	1	no	maximal, Sylow
63	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
64	C₂×C₄₃	C₄×M₁₆	1	1	yes	characteristic
65	C₂×C₄₃	#405	1	1	yes	characteristic
66	D₄₃	—	2	2	no	—
67	#431	—	43	1	no	—
68	C₄×M₁₆	—	43	1	no	—
69	C₂×C₄×C₈	—	43	1	no	—
70	#322	—	43	1	no	—
71	#322	D₄₃	1	1	yes	characteristic, complemented
72	C₈²	—	43	1	no	—
73	C₈²	—	43	1	no	—
74	C₄₃	C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
75	C₂×M₁₆	—	43	2	no	—
76	C₂²×C₈	—	43	2	no	—
77	C₂×C₄²	—	43	1	no	—
78	C₄⋊C₈	—	43	2	no	—
79	C₂²⋊C₈	—	43	2	no	—
80	#97	—	43	2	no	—
81	C₄×C₈	—	43	2	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	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
88	C₂²×C₄	—	43	1	no	—
89	C₂²×C₄	—	43	1	no	—
90	C₂²×C₄	—	43	1	no	—
91	M₁₆	—	43	8	no	—
92	C₂×C₈	—	43	2	no	—
93	C₂×C₈	—	43	2	no	—
94	C₂×C₈	—	43	2	no	—
95	C₂×C₈	—	86	4	no	—
96	C₂×C₈	C₄×D₄₃	1	2	yes	—
97	C₂×C₈	C₄×D₄₃	1	2	yes	—
98	C₂×C₈	C₄×D₄₃	1	2	yes	—
99	C₄²	—	43	1	no	—
100	C₄²	—	43	1	no	—
101	C₄²	—	43	1	no	—
102	C₄²	C₂²×D₄₃	1	1	yes	characteristic
103	C₂³	—	43	1	no	—
104	C₂×C₄	—	43	1	no	—
105	C₂×C₄	—	43	4	no	—
106	C₂×C₄	—	43	1	no	—
107	C₂×C₄	—	43	1	no	—
108	C₂×C₄	—	86	2	no	—
109	C₂×C₄	—	86	2	no	—
110	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
111	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	2	2	no	—
115	C₈	—	43	4	no	—
116	C₈	—	43	4	no	—
117	C₈	—	86	2	no	—
118	C₈	C₈×D₄₃	1	4	yes	complemented
119	C₂²	—	43	2	no	—
120	C₂²	—	86	1	no	—
121	C₂²	—	86	1	no	—
122	C₂²	C₄²×D₄₃	1	1	yes	characteristic
123	C₄	—	43	2	no	—
124	C₄	—	86	1	no	—
125	C₄	—	86	1	no	—
126	C₄	C₂×C₈×D₄₃	1	2	yes	—
127	C₄	M₁₆×D₄₃	1	2	yes	—
128	C₄	#13063333	1	2	yes	—
129	C₂	—	86	2	no	—
130	C₂	C₄×C₈×D₄₃	1	1	yes	characteristic
131	C₂	#14582851	1	1	yes	characteristic
132	C₂	#14582856	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582950

C₂

yes

maximal, characteristic

C₄×#10621872

C₂

yes

maximal, characteristic

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic

#14582621

C₂

yes

maximal, characteristic, complemented

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄₃×#322

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

C₄

yes

—

C₂×C₈×D₄₃

C₄

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

C₄

yes

—

(C₂×D₄₃)⋊C₈

C₄

yes

—

#13063235

C₄

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

C₄

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

#10621872

C₈

yes

complemented

C₈×D₄₃

—

C₂²×D₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

C₄²

yes

characteristic

C₂×Dic₄₃

C₄²

yes

characteristic

C₂×Dic₄₃

C₄²

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

C₂×C₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₈

yes

complemented

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂×C₈

yes

complemented

C₄₃⋊C₈

M₁₆

yes

complemented

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₄×C₈

yes

—

C₄×C₄₃

C₂²×C₈

yes

—

C₄×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

#131

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

C₄×C₈

yes

—

C₈×M₁₆

—

maximal, Sylow

C₂×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×C₄₃

C₄×M₁₆

yes

characteristic

C₂×C₄₃

#405

yes

characteristic

D₄₃

—

#431

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#322

—

#322

D₄₃

yes

characteristic, complemented

C₈²

—

C₈²

—

C₄₃

C₈×M₁₆

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂²×D₄₃

yes

characteristic

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

111

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

112

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

C₈×D₄₃

yes

complemented

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₄²×D₄₃

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

C₂×C₈×D₄₃

yes

—

127

C₄

M₁₆×D₄₃

yes

—

128

C₄

#13063333

yes

—

129

C₂

—

130

C₂

C₄×C₈×D₄₃

yes

characteristic

131

C₂

#14582851

yes

characteristic

132

C₂

#14582856

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Fitting	C₄₃×#322	C₂
socle	C₂²×C₄₃	C₂×C₄²
hypercenter	#322	D₄₃
hypocenter	C₄₃	C₈×M₁₆
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Fitting

C₄₃×#322

C₂

socle

C₂²×C₄₃

C₂×C₄²

hypercenter

#322

D₄₃

hypocenter

C₄₃

C₈×M₁₆

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
4. #14582621	C₂	semidirect
5. C₈×C₄₃⋊C₈	C₂	semidirect
6. C₈×C₄₃⋊C₈	C₂	semidirect
7. C₄₃×#322	C₂	semidirect
34. #10621872	C₈	semidirect
48. C₈×C₄₃	C₂×C₈	semidirect
50. C₄₃⋊C₈	C₂×C₈	semidirect
51. C₄₃⋊C₈	M₁₆	semidirect
71. #322	D₄₃	semidirect
74. C₄₃	C₈×M₁₆	semidirect
118. C₈	C₈×D₄₃	semidirect

H ≅ G/N

type

4. #14582621

C₂

semidirect

5. C₈×C₄₃⋊C₈

C₂

semidirect

6. C₈×C₄₃⋊C₈

C₂

semidirect

7. C₄₃×#322

C₂

semidirect

34. #10621872

C₈

semidirect

48. C₈×C₄₃

C₂×C₈

semidirect

50. C₄₃⋊C₈

C₂×C₈

semidirect

51. C₄₃⋊C₈

M₁₆

semidirect

71. #322

D₄₃

semidirect

74. C₄₃

C₈×M₁₆

semidirect

118. C₈

C₈×D₄₃

semidirect

Subgroups — #19132874

Conjugacy classes of subgroups

Complements