Group #19134620 — subgroups

Subgroups — #19134620

Order 5504.

336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063257	C₂	1	2	yes	maximal, complemented
2	#14582759	C₂	1	2	yes	maximal
3	#14582662	C₂	1	2	yes	maximal, complemented
4	C₂³×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
6	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
7	#13063257	—	2	4	no	—
8	C₄₃⋊#95	—	2	2	no	—
9	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₃	—	2	4	no	—
11	C₂²×C₈×C₄₃	C₄	1	4	yes	complemented
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₃	—	2	4	no	—
22	C₂×C₈×C₄₃	—	2	2	no	—
23	C₂×C₈×C₄₃	—	2	8	no	—
24	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₄₃	D₄	1	4	yes	—
27	C₂²⋊Dic₄₃	—	4	4	no	—
28	C₄⋊Dic₄₃	—	2	4	no	—
29	C₄⋊Dic₄₃	—	2	4	no	—
30	C₂³×C₄₃	—	2	2	no	—
31	C₂³×C₄₃	—	2	2	no	—
32	C₂³×C₄₃	C₄⋊C₄	1	2	yes	—
33	C₂³×C₄₃	SD₁₆	1	4	yes	—
34	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	2	2	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	2	yes	—
44	C₂×Dic₄₃	—	4	4	no	—
45	C₂×Dic₄₃	—	4	4	no	—
46	C₂×Dic₄₃	—	4	4	no	—
47	C₈×C₄₃	—	2	2	no	—
48	C₈×C₄₃	C₂²⋊C₄	1	4	yes	complemented
49	C₂²×C₄₃	—	2	2	no	—
50	C₂²×C₄₃	—	2	2	no	—
51	C₂²×C₄₃	—	2	8	no	—
52	C₂²×C₄₃	#106	1	4	yes	complemented
53	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄₃	#121	1	2	yes	—
55	C₂²×C₄₃	C₂×SD₁₆	1	2	yes	—
56	C₂²×C₄₃	#135	1	2	yes	—
57	C₄×C₄₃	—	2	2	no	—
58	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₄×C₄₃	#117	1	1	yes	characteristic
60	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
61	Dic₄₃	—	8	4	no	—
62	#1807	—	43	1	no	maximal, Sylow
63	C₂×C₄₃	—	2	4	no	—
64	C₂×C₄₃	#380	1	1	yes	characteristic
65	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
66	C₂×C₄₃	#427	1	1	yes	characteristic
67	C₂×C₄₃	#465	1	4	yes	—
68	C₂³×C₈	D₄₃	1	1	yes	characteristic
69	C₂×#106	—	43	2	no	—
70	#380	—	43	2	no	—
71	#340	—	43	2	no	—
72	C₄₃	#1807	1	1	yes	characteristic, complemented, Sylow
73	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
74	C₂²×C₈	—	2	4	no	—
75	C₂²×C₈	Dic₄₃	1	4	yes	complemented
76	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
77	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₂×C₄⋊C₄	—	43	4	no	—
79	C₂×C₂²⋊C₄	—	86	2	no	—
80	#106	—	86	4	no	—
81	#95	—	86	2	no	—
82	C₂⁴	D₁₇₂	1	1	yes	characteristic
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	86	4	no	—
86	C₂²×C₄	Dic₈₆	1	2	yes	—
87	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
88	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
89	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	8	no	—
92	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
93	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
94	C₂×C₈	C₂²⋊D₄₃	1	4	yes	—
95	C₄⋊C₄	—	86	4	no	—
96	C₄⋊C₄	—	86	4	no	—
97	C₂²⋊C₄	—	172	4	no	—
98	C₂³	—	2	2	no	—
99	C₂³	—	2	2	no	—
100	C₂³	#10621873	1	4	yes	—
101	C₂³	C₄⋊Dic₄₃	1	2	yes	—
102	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	172	4	no	—
108	C₂×C₄	—	172	4	no	—
109	C₂×C₄	—	172	4	no	—
110	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
111	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
112	C₂×C₄	#10621898	1	2	yes	—
113	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
114	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
115	C₈	—	2	2	no	—
116	C₈	C₂²⋊Dic₄₃	1	4	yes	complemented
117	C₂²	—	2	8	no	—
118	C₂²	—	2	2	no	—
119	C₂²	—	2	2	no	—
120	C₂²	#13063257	1	4	yes	complemented
121	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
122	C₂²	#13063299	1	2	yes	—
123	C₂²	C₂×#10621873	1	2	yes	—
124	C₂²	#13063347	1	2	yes	—
125	C₄	—	2	2	no	—
126	C₄	—	344	4	no	—
127	C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
128	C₄	#13063284	1	1	yes	characteristic
129	C₄	#13063304	1	2	yes	—
130	C₂	—	2	4	no	—
131	C₂	#14582759	1	1	yes	characteristic
132	C₂	C₂×#13063257	1	1	yes	characteristic
133	C₂	#14582937	1	1	yes	characteristic
134	C₂	#14583128	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063257

C₂

yes

maximal, complemented

#14582759

C₂

yes

maximal

#14582662

C₂

yes

maximal, complemented

C₂³×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

—

#13063257

—

C₄₃⋊#95

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₄

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₄⋊C₄

yes

—

C₂³×C₄₃

SD₁₆

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂²⋊C₄

yes

complemented

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#106

yes

complemented

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

#121

yes

—

C₂²×C₄₃

C₂×SD₁₆

yes

—

C₂²×C₄₃

#135

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₂²⋊Q₈

yes

—

Dic₄₃

—

#1807

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂³×C₈

D₄₃

yes

—

—

—

C₄₃

#1807

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₄₃

yes

complemented

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#106

—

#95

—

C₂⁴

D₁₇₂

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₂³

—

C₂³

—

100

C₂³

#10621873

yes

—

101

C₂³

C₄⋊Dic₄₃

yes

—

102

C₂³

C₂×D₁₇₂

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

172

—

108

C₂×C₄

—

172

—

109

C₂×C₄

—

172

—

110

C₂×C₄

C₄⋊Dic₄₃

yes

—

111

C₂×C₄

C₂×Dic₈₆

yes

characteristic

112

C₂×C₄

#10621898

yes

—

113

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

114

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

115

C₈

—

116

C₈

C₂²⋊Dic₄₃

yes

complemented

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

#13063257

yes

complemented

121

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

122

C₂²

#13063299

yes

—

123

C₂²

C₂×#10621873

yes

—

124

C₂²

#13063347

yes

—

125

C₄

—

126

C₄

—

344

—

127

C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

128

C₄

#13063284

yes

characteristic

129

C₄

#13063304

yes

—

130

C₂

—

131

C₂

#14582759

yes

characteristic

132

C₂

C₂×#13063257

yes

characteristic

133

C₂

#14582937

yes

characteristic

134

C₂

#14583128

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂³×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂³×C₈	D₄₃
hypocenter	C₄₃	#1807
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂³×C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂³×C₈

D₄₃

hypocenter

C₄₃

#1807

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

N	H ≅ G/N	type
1. C₂×#13063257	C₂	semidirect
3. #14582662	C₂	semidirect
11. C₂²×C₈×C₄₃	C₄	semidirect
48. C₈×C₄₃	C₂²⋊C₄	semidirect
52. C₂²×C₄₃	#106	semidirect
72. C₄₃	#1807	semidirect
75. C₂²×C₈	Dic₄₃	semidirect
116. C₈	C₂²⋊Dic₄₃	semidirect
120. C₂²	#13063257	semidirect

H ≅ G/N

type

1. C₂×#13063257

C₂

semidirect

3. #14582662

C₂

semidirect

11. C₂²×C₈×C₄₃

C₄

semidirect

48. C₈×C₄₃

C₂²⋊C₄

semidirect

52. C₂²×C₄₃

#106

semidirect

72. C₄₃

#1807

semidirect

75. C₂²×C₈

Dic₄₃

semidirect

116. C₈

C₂²⋊Dic₄₃

semidirect

120. C₂²

#13063257

semidirect

Subgroups — #19134620

Conjugacy classes of subgroups

Complements