Group #19145989 — subgroups

Subgroups — #19145989

Order 5504.

342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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	2	yes	maximal
2	#14583185	C₂	1	4	yes	maximal, complemented
3	#14583157	C₂	1	4	yes	maximal
4	#14583110	C₂	1	4	yes	maximal, complemented
5	C₄₃×#423	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	4	yes	—
7	#13063325	C₂²	1	2	yes	—
8	#13063325	C₂²	1	2	yes	—
9	#13063317	—	2	2	no	—
10	#13063304	—	2	2	no	—
11	#13063304	C₂²	1	4	yes	—
12	C₄×Dic₈₆	—	2	2	no	—
13	C₄×Dic₈₆	C₂²	1	4	yes	—
14	#13063284	—	2	2	no	—
15	#13063257	C₂²	1	4	yes	—
16	#13063250	C₂²	1	8	yes	—
17	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₈₆	—	2	2	no	—
23	C₂×Dic₈₆	C₂³	1	4	yes	—
24	M₁₆×C₄₃	—	4	2	no	—
25	C₂×C₈×C₄₃	C₂³	1	4	yes	—
26	C₄²×C₄₃	D₄	1	1	yes	characteristic
27	C₄²×C₄₃	D₄	1	1	yes	characteristic
28	C₄²×C₄₃	C₂³	1	2	yes	—
29	C₂²⋊Dic₄₃	—	2	4	no	—
30	C₄⋊Dic₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	—	2	2	no	—
32	C₄⋊Dic₄₃	—	2	2	no	—
33	C₄⋊Dic₄₃	C₂³	1	4	yes	—
34	Dic₄₃⋊C₄	—	2	4	no	—
35	Dic₄₃⋊C₄	—	2	4	no	—
36	C₄×Dic₄₃	—	2	4	no	—
37	Dic₁₇₂	—	4	4	no	—
38	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₄₃	—	2	4	no	—
47	C₂×Dic₄₃	—	2	4	no	—
48	Dic₈₆	—	2	4	no	—
49	Dic₈₆	—	2	4	no	—
50	Dic₈₆	—	4	4	no	—
51	C₈×C₄₃	—	2	4	no	—
52	C₂²×C₄₃	—	2	1	no	—
53	C₂²×C₄₃	—	2	2	no	—
54	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	—	2	2	no	—
57	C₄×C₄₃	#137	1	4	yes	—
58	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
59	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
60	Dic₄₃	—	4	4	no	—
61	Dic₄₃	—	4	4	no	—
62	#3255	—	43	1	no	maximal, Sylow
63	C₂×C₄₃	—	4	1	no	—
64	C₂×C₄₃	#537	1	1	yes	characteristic
65	C₂×C₄₃	C₂×#137	1	2	yes	—
66	#533	—	43	2	no	—
67	#475	—	43	4	no	—
68	#470	—	43	4	no	—
69	#462	—	43	4	no	—
70	#423	D₄₃	1	1	yes	characteristic
71	C₄₃	#3255	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₁₆	—	43	4	no	—
73	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
74	C₄⋊Q₈	—	43	2	no	—
75	C₄⋊Q₈	—	43	2	no	—
76	#125	—	86	2	no	—
77	C₂²⋊Q₈	—	43	4	no	—
78	C₂²⋊Q₈	—	86	2	no	—
79	C₄×Q₈	—	43	4	no	—
80	C₄×Q₈	—	86	2	no	—
81	#117	—	86	2	no	—
82	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
83	#106	—	43	4	no	—
84	C₄⋊C₈	C₂×D₄₃	1	4	yes	—
85	#103	—	43	8	no	—
86	C₂×Q₈	—	43	4	no	—
87	C₂×Q₈	—	86	2	no	—
88	C₂²×C₄	D₁₇₂	1	2	yes	—
89	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
90	Q₁₆	—	172	4	no	—
91	M₁₆	—	4	2	no	—
92	C₂×C₈	C₂²×D₄₃	1	4	yes	—
93	C₄⋊C₄	—	43	4	no	—
94	C₄⋊C₄	—	86	2	no	—
95	C₄⋊C₄	—	86	2	no	—
96	C₄⋊C₄	—	86	4	no	—
97	C₄⋊C₄	—	86	4	no	—
98	C₄⋊C₄	—	86	2	no	—
99	C₂²⋊C₄	—	86	4	no	—
100	C₄²	—	86	4	no	—
101	C₄²	D₁₇₂	1	1	yes	characteristic
102	C₄²	D₁₇₂	1	1	yes	characteristic
103	C₄²	C₂²×D₄₃	1	2	yes	—
104	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
105	Q₈	—	86	4	no	—
106	Q₈	—	86	4	no	—
107	Q₈	—	172	4	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	86	4	no	—
112	C₂×C₄	—	86	4	no	—
113	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
114	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
115	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
116	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
117	C₈	—	2	4	no	—
118	C₂²	—	2	2	no	—
119	C₂²	—	2	1	no	—
120	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
121	C₄	—	2	2	no	—
122	C₄	—	2	1	no	—
123	C₄	—	172	4	no	—
124	C₄	—	172	4	no	—
125	C₄	#13063358	1	4	yes	—
126	C₄	#13063370	1	1	yes	characteristic
127	C₄	#13063373	1	1	yes	characteristic
128	C₂	—	4	1	no	—
129	C₂	#14583480	1	1	yes	characteristic
130	C₂	C₂×#13063358	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583456

C₂

yes

maximal

#14583185

C₂

yes

maximal, complemented

#14583157

C₂

yes

maximal

#14583110

C₂

yes

maximal, complemented

C₄₃×#423

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

#13063325

C₂²

yes

—

#13063325

C₂²

yes

—

#13063317

—

#13063304

—

#13063304

C₂²

yes

—

C₄×Dic₈₆

—

C₄×Dic₈₆

C₂²

yes

—

#13063284

—

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#137

yes

—

C₄×C₄₃

H(5,𝔽₂)

yes

characteristic

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#3255

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#537

yes

characteristic

C₂×C₄₃

C₂×#137

yes

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#3255

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#106

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

Q₁₆

—

172

—

M₁₆

—

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

D₁₇₂

yes

characteristic

102

C₄²

D₁₇₂

yes

characteristic

103

C₄²

C₂²×D₄₃

yes

—

104

C₂³

C₂×D₁₇₂

yes

characteristic

105

Q₈

—

106

Q₈

—

107

Q₈

—

172

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×D₁₇₂

yes

—

114

C₂×C₄

C₂×D₁₇₂

yes

characteristic

115

C₂×C₄

C₂×D₁₇₂

yes

—

116

C₂×C₄

C₂³×D₄₃

yes

characteristic

117

C₈

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₂²×D₁₇₂

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

172

—

124

C₄

—

172

—

125

C₄

#13063358

yes

—

126

C₄

#13063370

yes

characteristic

127

C₄

#13063373

yes

characteristic

128

C₂

—

129

C₂

#14583480

yes

characteristic

130

C₂

C₂×#13063358

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#423	D₄₃
hypocenter	C₄₃	#3255
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#423

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
2. #14583185	C₂	semidirect
4. #14583110	C₂	semidirect
71. C₄₃	#3255	semidirect

H ≅ G/N

type

2. #14583185

C₂

semidirect

4. #14583110

C₂

semidirect

71. C₄₃

#3255

semidirect

Subgroups — #19145989

Conjugacy classes of subgroups

Complements