Group #19134753 — subgroups

Subgroups — #19134753

Order 5504.

280 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063259	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063258	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582768	C₂	1	2	yes	maximal
5	C₂×#107×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	C₂×Dic₄₃⋊C₄	—	2	4	no	—
9	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
10	#13063259	—	2	2	no	—
11	#13063258	—	2	4	no	—
12	C₈×Dic₄₃	C₄	1	4	yes	complemented
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	#107×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	2	no	—
19	C₂²×Dic₄₃	D₄	1	2	yes	—
20	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₄₃	D₄	1	2	yes	—
22	C₂×C₈×C₄₃	Q₈	1	2	yes	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	—	2	2	no	—
27	Dic₄₃⋊C₄	—	4	8	no	—
28	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
29	C₄×Dic₄₃	Q₈	1	2	yes	—
30	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
31	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
32	C₂×C₄₃⋊C₈	Q₈	1	2	yes	—
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	4	2	no	—
35	C₂×C₄×C₄₃	—	4	4	no	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×Dic₄₃	—	4	2	no	—
43	C₂×Dic₄₃	—	4	4	no	—
44	C₂×Dic₄₃	C₄⋊C₄	1	4	yes	—
45	C₂×Dic₄₃	D₈	1	4	yes	—
46	C₂×Dic₄₃	Q₁₆	1	4	yes	—
47	C₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
48	C₄₃⋊C₈	C₄⋊C₄	1	4	yes	complemented
49	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄₃	#127	1	1	yes	characteristic
51	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
52	C₂²×C₄₃	C₂×D₈	1	2	yes	—
53	C₂²×C₄₃	C₂×Q₁₆	1	2	yes	—
54	C₄×C₄₃	—	8	2	no	—
55	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
58	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
59	Dic₄₃	—	8	2	no	—
60	Dic₄₃	#107	1	8	yes	complemented
61	#1845	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	#384	1	1	yes	characteristic
63	C₂×C₄₃	C₂×#107	1	2	yes	—
64	C₂×C₄₃	#493	1	1	yes	characteristic
65	C₂×C₄₃	#494	1	1	yes	characteristic
66	C₂×C₄₃	#500	1	2	yes	—
67	C₂×#107	—	43	1	no	—
68	C₂×#107	—	43	2	no	—
69	C₂×#107	D₄₃	1	1	yes	characteristic
70	C₂×C₄×C₈	—	43	1	no	—
71	#384	—	43	2	no	—
72	C₄₃	#1845	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	—	43	1	no	—
74	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	43	2	no	—
76	C₂×C₄⋊C₄	—	86	4	no	—
77	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
78	C₂×C₄²	—	43	1	no	—
79	#107	—	2	2	no	—
80	#107	—	86	4	no	—
81	#107	—	86	2	no	—
82	C₄×C₈	—	43	4	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	43	2	no	—
85	C₂²×C₄	—	86	2	no	—
86	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
87	C₂×C₈	—	43	2	no	—
88	C₂×C₈	—	43	2	no	—
89	C₂×C₈	—	43	2	no	—
90	C₂×C₈	Dic₈₆	1	2	yes	—
91	C₂×C₈	C₄×D₄₃	1	2	yes	—
92	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	86	2	no	—
96	C₄⋊C₄	—	86	2	no	—
97	C₄⋊C₄	—	172	8	no	—
98	C₄²	—	43	2	no	—
99	C₄²	—	43	2	no	—
100	C₂³	D₄×D₄₃	1	1	yes	characteristic
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	4	4	no	—
103	C₂×C₄	—	43	4	no	—
104	C₂×C₄	—	43	4	no	—
105	C₂×C₄	—	43	4	no	—
106	C₂×C₄	—	172	2	no	—
107	C₂×C₄	—	172	4	no	—
108	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
109	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
110	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
111	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
112	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
113	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
114	C₈	—	43	4	no	—
115	C₈	Dic₄₃⋊C₄	1	4	yes	complemented
116	C₂²	C₄⋊C₄×D₄₃	1	1	yes	characteristic
117	C₂²	#13063321	1	1	yes	characteristic
118	C₂²	#13063324	1	1	yes	characteristic
119	C₂²	D₈×D₄₃	1	2	yes	—
120	C₂²	Q₁₆×D₄₃	1	2	yes	—
121	C₄	—	8	2	no	—
122	C₄	—	43	8	no	—
123	C₄	—	344	2	no	—
124	C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
125	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
126	C₄	#13063323	1	1	yes	characteristic
127	C₄	#13063324	1	1	yes	characteristic
128	C₂	#14582768	1	1	yes	characteristic
129	C₂	#107×D₄₃	1	2	yes	—
130	C₂	#14583274	1	1	yes	characteristic
131	C₂	#14583277	1	1	yes	characteristic
132	C₂	#14583303	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal, characteristic

C₂×#13063258

C₂

yes

maximal

C₂×C₈×Dic₄₃

C₂

yes

maximal, characteristic

#14582768

C₂

yes

maximal

C₂×#107×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063259

—

#13063258

—

C₈×Dic₄₃

C₄

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

#107×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

Q₈

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₄⋊C₄

yes

—

C₂×Dic₄₃

D₈

yes

—

C₂×Dic₄₃

Q₁₆

yes

—

C₈×C₄₃

C₄⋊C₄

yes

complemented

C₄₃⋊C₈

C₄⋊C₄

yes

complemented

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

#127

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

—

C₂²×C₄₃

C₂×Q₁₆

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

characteristic

Dic₄₃

—

Dic₄₃

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×#107

—

C₂×#107

—

C₂×#107

D₄₃

yes

characteristic

C₂×C₄×C₈

—

#384

—

C₄₃

#1845

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

#107

—

#107

—

#107

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

—

100

C₂³

D₄×D₄₃

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

C₂×Dic₈₆

yes

characteristic

109

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

110

C₂×C₄

D₄×D₄₃

yes

characteristic

111

C₂×C₄

Q₈×D₄₃

yes

characteristic

112

C₂×C₄

Q₈×D₄₃

yes

characteristic

113

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

114

C₈

—

115

C₈

Dic₄₃⋊C₄

yes

complemented

116

C₂²

C₄⋊C₄×D₄₃

yes

characteristic

117

C₂²

#13063321

yes

characteristic

118

C₂²

#13063324

yes

characteristic

119

C₂²

D₈×D₄₃

yes

—

120

C₂²

Q₁₆×D₄₃

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

344

—

124

C₄

C₄⋊C₄×D₄₃

yes

characteristic

125

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

126

C₄

#13063323

yes

characteristic

127

C₄

#13063324

yes

characteristic

128

C₂

#14582768

yes

characteristic

129

C₂

#107×D₄₃

yes

—

130

C₂

#14583274

yes

characteristic

131

C₂

#14583277

yes

characteristic

132

C₂

#14583303

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#107×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#107	D₄₃
hypocenter	C₄₃	#1845
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#107×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
12. C₈×Dic₄₃	C₄	semidirect
47. C₈×C₄₃	C₄⋊C₄	semidirect
48. C₄₃⋊C₈	C₄⋊C₄	semidirect
60. Dic₄₃	#107	semidirect
72. C₄₃	#1845	semidirect
115. C₈	Dic₄₃⋊C₄	semidirect

H ≅ G/N

type

12. C₈×Dic₄₃

C₄

semidirect

47. C₈×C₄₃

C₄⋊C₄

semidirect

48. C₄₃⋊C₈

C₄⋊C₄

semidirect

60. Dic₄₃

#107

semidirect

72. C₄₃

#1845

semidirect

115. C₈

Dic₄₃⋊C₄

semidirect

Subgroups — #19134753

Conjugacy classes of subgroups

Complements