Group #19143529 — subgroups

Subgroups — #19143529

Order 5504.

364 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 197 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	#14583456	C₂	1	1	yes	maximal, characteristic
2	#14583029	C₂	1	4	yes	maximal, complemented
3	C₈×Dic₈₆	C₂	1	4	yes	maximal, complemented
4	#14582925	C₂	1	2	yes	maximal
5	#14582923	C₂	1	1	yes	maximal, characteristic
6	#14582854	C₂	1	2	yes	maximal
7	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621877	C₂²	1	2	yes	—
9	#13063325	C₄	1	2	yes	—
10	#13063317	C₄	1	2	yes	—
11	#13063304	C₄	1	4	yes	—
12	C₄×Dic₈₆	C₂²	1	4	yes	—
13	#13063284	C₂²	1	2	yes	—
14	C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
15	Dic₄₃⋊C₈	C₂²	1	8	yes	—
16	#13063235	C₂²	1	4	yes	—
17	C₈×Dic₄₃	C₂²	1	4	yes	—
18	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄×C₈×C₄₃	C₂²	1	2	yes	—
22	C₄×C₈×C₄₃	C₂²	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₈₆	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	Q₈	1	4	yes	complemented
28	C₂×C₈×C₄₃	C₂³	1	2	yes	—
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₄₃	C₂³	1	2	yes	—
34	C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
35	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
36	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
37	Dic₄₃⋊C₄	C₂×C₄	1	8	yes	—
38	C₄×Dic₄₃	C₂³	1	4	yes	—
39	#10621877	—	2	4	no	—
40	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
41	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	—	2	4	no	—
43	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₄₃	#41	1	2	yes	—
48	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
49	C₂×Dic₄₃	C₂²×C₄	1	8	yes	—
50	Dic₈₆	—	2	8	no	—
51	C₈×C₄₃	—	2	2	no	—
52	C₈×C₄₃	C₂×Q₈	1	2	yes	—
53	C₈×C₄₃	C₂×Q₈	1	2	yes	—
54	C₄₃⋊C₈	—	2	4	no	—
55	C₂²×C₄₃	—	2	2	no	—
56	C₂²×C₄₃	C₄×Q₈	1	2	yes	—
57	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
58	C₄×C₄₃	—	2	2	no	—
59	C₄×C₄₃	C₄×Q₈	1	2	yes	—
60	C₄×C₄₃	#131	1	4	yes	—
61	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
62	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
63	Dic₄₃	—	2	8	no	—
64	#2960	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	—	2	2	no	—
66	C₂×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
67	C₂×C₄₃	C₂×#131	1	2	yes	—
68	#533	—	43	1	no	—
69	#446	—	43	4	no	—
70	C₈×Q₈	—	43	4	no	—
71	#424	—	43	2	no	—
72	#423	—	43	1	no	—
73	#405	—	43	2	no	—
74	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
75	C₄₃	#2960	1	1	yes	characteristic, complemented, Sylow
76	C₂×M₁₆	—	43	2	no	—
77	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
79	C₄⋊Q₈	—	43	2	no	—
80	#125	—	43	2	no	—
81	C₂²⋊Q₈	—	43	4	no	—
82	C₄×Q₈	—	43	4	no	—
83	#117	—	43	2	no	—
84	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
85	C₄⋊C₈	—	43	8	no	—
86	C₄⋊C₈	—	43	4	no	—
87	#97	—	43	4	no	—
88	C₄×C₈	—	43	4	no	—
89	C₄×C₈	C₂×D₄₃	1	2	yes	—
90	C₄×C₈	C₂×D₄₃	1	2	yes	—
91	C₂×Q₈	—	43	4	no	—
92	C₂²×C₄	C₄×D₄₃	1	2	yes	—
93	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
94	M₁₆	—	86	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	43	4	no	—
97	C₂×C₈	Dic₈₆	1	4	yes	complemented
98	C₂×C₈	C₂²×D₄₃	1	2	yes	—
99	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
100	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
101	C₄⋊C₄	—	43	4	no	—
102	C₄⋊C₄	—	43	8	no	—
103	C₄⋊C₄	—	43	4	no	—
104	C₂²⋊C₄	—	43	4	no	—
105	C₄²	—	43	4	no	—
106	C₄²	C₄×D₄₃	1	1	yes	characteristic
107	C₄²	C₄×D₄₃	1	1	yes	characteristic
108	C₄²	C₂²×D₄₃	1	2	yes	—
109	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
110	Q₈	—	86	8	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	43	8	no	—
113	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
114	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
115	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
116	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
117	C₂×C₄	#10621898	1	2	yes	—
118	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
119	C₈	—	2	2	no	—
120	C₈	—	86	4	no	—
121	C₈	C₂×Dic₈₆	1	2	yes	—
122	C₈	C₂×Dic₈₆	1	2	yes	—
123	C₂²	—	2	2	no	—
124	C₂²	C₄×Dic₈₆	1	2	yes	—
125	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
126	C₄	—	2	2	no	—
127	C₄	—	86	8	no	—
128	C₄	C₄×Dic₈₆	1	2	yes	—
129	C₄	#13063331	1	4	yes	—
130	C₄	C₂²×Dic₈₆	1	1	yes	characteristic
131	C₄	C₂×#10621898	1	1	yes	characteristic
132	C₂	—	2	2	no	—
133	C₂	C₂×C₄×Dic₈₆	1	1	yes	characteristic
134	C₂	C₂×#13063331	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583456

C₂

yes

maximal, characteristic

#14583029

C₂

yes

maximal, complemented

C₈×Dic₈₆

C₂

yes

maximal, complemented

#14582925

C₂

yes

maximal

#14582923

C₂

yes

maximal, characteristic

#14582854

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063325

C₄

yes

—

#13063317

C₄

yes

—

#13063304

C₄

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063284

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

Dic₄₃⋊C₈

C₂²

yes

—

#13063235

C₂²

yes

—

C₈×Dic₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

Q₈

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

C₂²⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

#10621877

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

C₂²×C₄

yes

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×Q₈

yes

—

C₈×C₄₃

C₂×Q₈

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×Q₈

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×Q₈

yes

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

#2960

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄×Q₈

yes

characteristic

C₂×C₄₃

C₂×#131

yes

—

#533

—

#446

—

C₈×Q₈

—

#424

—

#423

—

#405

—

C₂×C₄×C₈

D₄₃

yes

characteristic

C₄₃

#2960

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

complemented

C₂×C₈

C₂²×D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

100

C₂×C₈

C₂²×D₄₃

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₄²

—

106

C₄²

C₄×D₄₃

yes

characteristic

107

C₄²

C₄×D₄₃

yes

characteristic

108

C₄²

C₂²×D₄₃

yes

—

109

C₂³

C₂×C₄×D₄₃

yes

characteristic

110

Q₈

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×Dic₈₆

yes

—

114

C₂×C₄

C₂×C₄×D₄₃

yes

—

115

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

116

C₂×C₄

C₂×C₄×D₄₃

yes

—

117

C₂×C₄

#10621898

yes

—

118

C₂×C₄

C₂³×D₄₃

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

C₂×Dic₈₆

yes

—

122

C₈

C₂×Dic₈₆

yes

—

123

C₂²

—

124

C₂²

C₄×Dic₈₆

yes

—

125

C₂²

C₂²×C₄×D₄₃

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

C₄×Dic₈₆

yes

—

129

C₄

#13063331

yes

—

130

C₄

C₂²×Dic₈₆

yes

characteristic

131

C₄

C₂×#10621898

yes

characteristic

132

C₂

—

133

C₂

C₂×C₄×Dic₈₆

yes

characteristic

134

C₂

C₂×#13063331

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#2960
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

hypercenter

C₂×C₄×C₈

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14583029	C₂	semidirect
3. C₈×Dic₈₆	C₂	semidirect
27. C₂×C₈×C₄₃	Q₈	semidirect
75. C₄₃	#2960	semidirect
97. C₂×C₈	Dic₈₆	semidirect

H ≅ G/N

type

2. #14583029

C₂

semidirect

3. C₈×Dic₈₆

C₂

semidirect

27. C₂×C₈×C₄₃

Q₈

semidirect

75. C₄₃

#2960

semidirect

97. C₂×C₈

Dic₈₆

semidirect

Subgroups — #19143529

Conjugacy classes of subgroups

Complements