Group #19147695 — subgroups

Subgroups — C₂×#14583317 #19147695

Order 5504.

368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 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×#13063331	C₂	1	1	yes	maximal, characteristic
2	#14583317	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13063264	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
6	C₂×M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10621898	C₄	1	1	yes	characteristic
8	#13063331	C₄	1	4	yes	—
9	#13063331	C₂²	1	4	yes	—
10	C₂×#10621877	C₄	1	1	yes	characteristic
11	C₂×#10621872	C₄	1	2	yes	—
12	C₂×C₈×D₄₃	C₂²	1	2	yes	—
13	#13063264	C₂²	1	8	yes	complemented
14	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄₃⋊C₁₆	C₂²	1	4	yes	complemented
17	C₁₆×D₄₃	C₂²	1	8	yes	complemented
18	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	M₃₂×C₄₃	C₂²	1	4	yes	complemented
20	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₂²⋊D₄₃	C₈	1	2	yes	—
23	#10621898	C₈	1	4	yes	—
24	#10621898	C₂×C₄	1	4	yes	—
25	C₂×D₁₇₂	C₈	1	1	yes	characteristic
26	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
27	C₂×Dic₈₆	C₈	1	1	yes	characteristic
28	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₄₃	C₂³	1	2	yes	—
31	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
32	#10621877	C₂×C₄	1	4	yes	—
33	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
34	#10621872	C₂×C₄	1	8	yes	—
35	C₈×D₄₃	C₂×C₄	1	4	yes	—
36	C₈×D₄₃	C₂³	1	4	yes	—
37	C₁₆×C₄₃	C₂³	1	4	yes	—
38	C₄₃⋊C₁₆	C₂³	1	2	yes	—
39	C₄₃⋊C₁₆	C₂³	1	2	yes	—
40	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
41	C₂²×D₄₃	C₂×C₈	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
44	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
46	C₂²⋊D₄₃	C₂×C₈	1	8	yes	—
47	C₂×Dic₄₃	C₂×C₈	1	2	yes	—
48	D₁₇₂	C₂×C₈	1	4	yes	—
49	C₄×D₄₃	C₂×C₈	1	4	yes	—
50	C₄×D₄₃	C₂²×C₄	1	4	yes	—
51	Dic₈₆	C₂×C₈	1	4	yes	—
52	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₈×C₄₃	C₂²×C₄	1	2	yes	—
54	C₈×C₄₃	C₂⁴	1	1	yes	characteristic
55	C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
56	C₂²×C₄₃	—	2	2	no	—
57	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
58	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
59	C₂×D₄₃	—	2	4	no	—
60	C₂×D₄₃	C₂²×C₈	1	4	yes	—
61	C₄×C₄₃	C₂²×C₈	1	2	yes	—
62	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
63	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
64	Dic₄₃	C₂²×C₈	1	4	yes	—
65	C₂×#504	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	—	2	2	no	—
67	C₂×C₄₃	#504	1	2	yes	complemented
68	C₂×C₄₃	C₂³×C₈	1	1	yes	characteristic
69	D₄₃	—	2	4	no	—
70	C₂×#131	—	43	1	no	—
71	#504	—	43	8	no	—
72	C₂×M₃₂	—	43	2	no	—
73	C₂×M₃₂	D₄₃	1	1	yes	characteristic, complemented
74	C₂²×C₁₆	—	43	1	no	—
75	C₂²×C₁₆	—	43	2	no	—
76	C₄₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
77	C₂×#41	—	43	1	no	—
78	#131	—	43	4	no	—
79	#131	—	43	4	no	—
80	C₂×M₁₆	—	43	1	no	—
81	C₂×M₁₆	—	43	2	no	—
82	C₂²×C₈	—	43	2	no	—
83	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
84	M₃₂	—	43	8	no	—
85	M₃₂	C₂×D₄₃	1	4	yes	complemented
86	C₂×C₁₆	—	43	4	no	—
87	C₂×C₁₆	—	43	1	no	—
88	C₂×C₁₆	—	43	1	no	—
89	C₂×C₁₆	—	43	8	no	—
90	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
91	#41	—	43	4	no	—
92	#41	—	43	4	no	—
93	C₂×Q₈	—	43	1	no	—
94	C₂×D₄	—	43	2	no	—
95	C₂×D₄	—	43	1	no	—
96	C₂²×C₄	—	43	2	no	—
97	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
98	M₁₆	—	43	4	no	—
99	M₁₆	—	43	8	no	—
100	C₂×C₈	—	43	2	no	—
101	C₂×C₈	—	43	4	no	—
102	C₂×C₈	—	43	4	no	—
103	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
104	C₂×C₈	C₄×D₄₃	1	2	yes	—
105	C₂×C₈	C₂²×D₄₃	1	2	yes	—
106	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
107	C₁₆	—	43	2	no	—
108	C₁₆	—	43	2	no	—
109	C₁₆	C₂²×D₄₃	1	4	yes	—
110	C₂³	—	43	2	no	—
111	C₂³	C₈×D₄₃	1	1	yes	characteristic
112	Q₈	—	43	4	no	—
113	D₄	—	43	8	no	—
114	D₄	—	43	4	no	—
115	C₂×C₄	—	43	2	no	—
116	C₂×C₄	—	43	4	no	—
117	C₂×C₄	—	43	4	no	—
118	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
119	C₂×C₄	C₈×D₄₃	1	2	yes	—
120	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
121	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
122	C₈	—	43	4	no	—
123	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
124	C₈	C₂×C₄×D₄₃	1	2	yes	—
125	C₈	C₂³×D₄₃	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	—	43	4	no	—
128	C₂²	—	86	4	no	—
129	C₂²	C₂×C₈×D₄₃	1	2	yes	—
130	C₂²	C₂×C₈×D₄₃	1	1	yes	characteristic
131	C₄	—	43	4	no	—
132	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
133	C₄	C₂×C₈×D₄₃	1	2	yes	—
134	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
135	C₂	—	2	2	no	—
136	C₂	—	86	4	no	—
137	C₂	#14583317	1	2	yes	direct product factor
138	C₂	C₂²×C₈×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063331

C₂

yes

maximal, characteristic

#14583317

C₂

yes

maximal, direct product factor

C₂×#13063264

C₂

yes

maximal, complemented

C₂²×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₄₃

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₄

yes

characteristic

#13063331

C₄

yes

—

#13063331

C₂²

yes

—

C₂×#10621877

C₄

yes

characteristic

C₂×#10621872

C₄

yes

—

C₂×C₈×D₄₃

C₂²

yes

—

#13063264

C₂²

yes

complemented

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

complemented

C₁₆×D₄₃

C₂²

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

complemented

C₂×C₁₆×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

C₈

yes

—

#10621898

C₈

yes

—

#10621898

C₂×C₄

yes

—

C₂×D₁₇₂

C₈

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×Dic₈₆

C₈

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

#10621877

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

#10621872

C₂×C₄

yes

—

C₈×D₄₃

C₂×C₄

yes

—

C₈×D₄₃

C₂³

yes

—

C₁₆×C₄₃

C₂³

yes

—

C₄₃⋊C₁₆

C₂³

yes

—

C₄₃⋊C₁₆

C₂³

yes

—

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂²×D₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂²⋊D₄₃

C₂×C₈

yes

—

C₂×Dic₄₃

C₂×C₈

yes

—

D₁₇₂

C₂×C₈

yes

—

C₄×D₄₃

C₂×C₈

yes

—

C₄×D₄₃

C₂²×C₄

yes

—

Dic₈₆

C₂×C₈

yes

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂²×C₄

yes

—

C₈×C₄₃

C₂⁴

yes

characteristic

C₄₃⋊C₈

C₂²×C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

C₂²×C₈

yes

—

C₄×C₄₃

C₂²×C₈

yes

—

C₄×C₄₃

C₂²×C₈

yes

characteristic

C₄×C₄₃

C₂³×C₄

yes

characteristic

Dic₄₃

C₂²×C₈

yes

—

C₂×#504

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#504

yes

complemented

C₂×C₄₃

C₂³×C₈

yes

characteristic

D₄₃

—

C₂×#131

—

#504

—

C₂×M₃₂

—

C₂×M₃₂

D₄₃

yes

characteristic, complemented

C₂²×C₁₆

—

C₂²×C₁₆

—

C₄₃

C₂×#504

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

M₃₂

—

M₃₂

C₂×D₄₃

yes

complemented

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

C₄×D₄₃

yes

characteristic

104

C₂×C₈

C₄×D₄₃

yes

—

105

C₂×C₈

C₂²×D₄₃

yes

—

106

C₂×C₈

C₂²×D₄₃

yes

characteristic

107

C₁₆

—

108

C₁₆

—

109

C₁₆

C₂²×D₄₃

yes

—

110

C₂³

—

111

C₂³

C₈×D₄₃

yes

characteristic

112

Q₈

—

113

D₄

—

114

D₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₈×D₄₃

yes

characteristic

119

C₂×C₄

C₈×D₄₃

yes

—

120

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

121

C₂×C₄

C₂×C₄×D₄₃

yes

—

122

C₈

—

123

C₈

C₂×C₄×D₄₃

yes

characteristic

124

C₈

C₂×C₄×D₄₃

yes

—

125

C₈

C₂³×D₄₃

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

C₂×C₈×D₄₃

yes

—

130

C₂²

C₂×C₈×D₄₃

yes

characteristic

131

C₄

—

132

C₄

C₂×C₈×D₄₃

yes

characteristic

133

C₄

C₂×C₈×D₄₃

yes

—

134

C₄

C₂²×C₄×D₄₃

yes

characteristic

135

C₂

—

136

C₂

—

137

C₂

#14583317

yes

direct product factor

138

C₂

C₂²×C₈×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₄₃
commutator	C₂×C₄₃	C₂³×C₈
Frattini	C₈	C₂³×D₄₃
Fitting	C₂×M₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×C₈
hypercenter	C₂×M₃₂	D₄₃
hypocenter	C₄₃	C₂×#504
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²×D₄₃

commutator

C₂×C₄₃

C₂³×C₈

Frattini

C₈

C₂³×D₄₃

Fitting

C₂×M₃₂×C₄₃

C₂

socle

C₂²×C₄₃

C₂²×C₈

hypercenter

C₂×M₃₂

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
2. #14583317	C₂	direct (N × H)
3. C₂×#13063264	C₂	semidirect
4. C₂²×C₄₃⋊C₁₆	C₂	semidirect
5. C₂×C₁₆×D₄₃	C₂	semidirect
6. C₂×M₃₂×C₄₃	C₂	semidirect
13. #13063264	C₂²	semidirect
16. C₂×C₄₃⋊C₁₆	C₂²	semidirect
17. C₁₆×D₄₃	C₂²	semidirect
19. M₃₂×C₄₃	C₂²	semidirect
67. C₂×C₄₃	#504	semidirect
73. C₂×M₃₂	D₄₃	semidirect
76. C₄₃	C₂×#504	semidirect
85. M₃₂	C₂×D₄₃	semidirect
137. C₂	#14583317	direct (N × H)

H ≅ G/N

type

2. #14583317

C₂

direct (N × H)

3. C₂×#13063264

C₂

semidirect

4. C₂²×C₄₃⋊C₁₆

C₂

semidirect

5. C₂×C₁₆×D₄₃

C₂

semidirect

6. C₂×M₃₂×C₄₃

C₂

semidirect

13. #13063264

C₂²

semidirect

16. C₂×C₄₃⋊C₁₆

C₂²

semidirect

17. C₁₆×D₄₃

C₂²

semidirect

19. M₃₂×C₄₃

C₂²

semidirect

67. C₂×C₄₃

#504

semidirect

73. C₂×M₃₂

D₄₃

semidirect

76. C₄₃

C₂×#504

semidirect

85. M₃₂

C₂×D₄₃

semidirect

137. C₂

#14583317

direct (N × H)

Subgroups — C₂×#14583317 #19147695

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583317 #19147695

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583317 #19147695