Group #19145338 — subgroups

Subgroups — #19145338

Order 5504.

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

normal subgroups only

This group has 358 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	#14583454	C₂	1	2	yes	maximal
2	#14583297	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583249	C₂	1	2	yes	maximal, complemented
4	#14583154	C₂	1	4	yes	maximal
5	#14583006	C₂	1	4	yes	maximal, complemented
6	C₄×#10621872	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621872	C₂²	1	2	yes	—
9	#13063325	C₂²	1	2	yes	—
10	#13063316	—	2	2	no	—
11	#13063305	—	2	2	no	—
12	#13063301	C₂²	1	4	yes	—
13	Q₈×Dic₄₃	C₂²	1	4	yes	—
14	#13063290	—	2	2	no	—
15	#13063283	—	2	2	no	—
16	C₄²×D₄₃	C₂²	1	1	yes	characteristic
17	#13063257	C₂²	1	4	yes	—
18	#13063249	C₂²	1	8	yes	—
19	#13063235	C₂²	1	2	yes	—
20	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₁₆×C₄₃	C₂²	1	4	yes	—
22	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
23	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
25	C₂×C₄×D₄₃	D₄	1	2	yes	—
26	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
27	C₂×Dic₈₆	—	2	2	no	—
28	Q₁₆×C₄₃	—	2	8	no	—
29	C₂×C₈×C₄₃	C₂³	1	2	yes	—
30	C₄⋊C₄×C₄₃	—	2	2	no	—
31	C₄⋊C₄×C₄₃	—	2	2	no	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	(C₂×D₄₃)⋊C₄	—	2	4	no	—
34	C₄⋊Dic₄₃	—	2	2	no	—
35	C₄⋊Dic₄₃	—	2	4	no	—
36	C₄⋊Dic₄₃	C₂³	1	4	yes	—
37	Dic₄₃⋊C₄	—	2	4	no	—
38	C₄×Dic₄₃	—	2	4	no	—
39	C₄×Dic₄₃	D₄	1	2	yes	—
40	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
41	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
42	#10621872	—	2	4	no	—
43	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₄₃	—	2	8	no	—
45	C₂×C₄×C₄₃	—	2	4	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₄₃	—	2	4	no	—
49	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
50	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
51	C₄×D₄₃	—	2	4	no	—
52	C₄×D₄₃	—	2	2	no	—
53	Dic₈₆	—	4	4	no	—
54	C₈×C₄₃	#41	1	4	yes	—
55	C₄₃⋊C₈	—	2	2	no	—
56	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
57	C₂×D₄₃	—	2	1	no	—
58	C₂×D₄₃	—	2	2	no	—
59	C₄×C₄₃	—	4	4	no	—
60	C₄×C₄₃	#137	1	4	yes	—
61	C₄×C₄₃	C₂×#41	1	2	yes	—
62	Dic₄₃	—	2	1	no	—
63	Dic₄₃	—	2	2	no	—
64	Dic₄₃	—	4	4	no	—
65	#3185	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	#532	1	1	yes	characteristic
67	C₂×C₄₃	C₂×#137	1	2	yes	—
68	D₄₃	—	4	1	no	—
69	#533	—	43	2	no	—
70	#498	—	43	1	no	—
71	#494	D₄₃	1	1	yes	characteristic, complemented
72	#487	—	43	2	no	—
73	#470	—	43	4	no	—
74	#441	—	43	4	no	—
75	C₄×M₁₆	—	43	1	no	—
76	C₄₃	#3185	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₁₆	C₂×D₄₃	1	4	yes	—
78	C₂×M₁₆	—	43	2	no	—
79	C₄⋊Q₈	—	43	2	no	—
80	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
81	#125	—	86	2	no	—
82	C₂²⋊Q₈	—	43	4	no	—
83	C₂²⋊Q₈	—	86	2	no	—
84	C₄×Q₈	—	43	4	no	—
85	C₄×Q₈	—	86	2	no	—
86	#117	—	86	2	no	—
87	C₂×C₄²	—	43	1	no	—
88	#106	—	43	4	no	—
89	#103	—	43	8	no	—
90	#97	—	43	2	no	—
91	C₄×C₈	—	43	1	no	—
92	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
93	C₂×Q₈	—	86	2	no	—
94	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
95	C₂²×C₄	—	43	2	no	—
96	C₂²×C₄	—	43	1	no	—
97	Q₁₆	—	2	8	no	—
98	M₁₆	—	86	4	no	—
99	C₂×C₈	—	43	2	no	—
100	C₂×C₈	C₂²×D₄₃	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	43	4	no	—
104	C₄⋊C₄	—	86	4	no	—
105	C₄⋊C₄	—	86	4	no	—
106	C₄⋊C₄	—	86	2	no	—
107	C₂²⋊C₄	—	86	4	no	—
108	C₄²	—	43	2	no	—
109	C₄²	—	43	1	no	—
110	C₄²	—	86	4	no	—
111	C₄²	C₂²×D₄₃	1	1	yes	characteristic
112	C₂³	—	43	1	no	—
113	Q₈	—	2	8	no	—
114	Q₈	—	172	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	43	2	no	—
117	C₂×C₄	—	43	1	no	—
118	C₂×C₄	—	86	4	no	—
119	C₂×C₄	—	86	2	no	—
120	C₂×C₄	—	86	4	no	—
121	C₂×C₄	D₄×D₄₃	1	2	yes	—
122	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
123	C₈	—	86	2	no	—
124	C₈	#10621900	1	4	yes	—
125	C₂²	—	86	2	no	—
126	C₂²	—	86	1	no	—
127	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
128	C₄	—	4	4	no	—
129	C₄	—	86	2	no	—
130	C₄	—	86	1	no	—
131	C₄	—	172	4	no	—
132	C₄	#13063357	1	4	yes	—
133	C₄	C₂×#10621900	1	2	yes	—
134	C₂	—	172	1	no	—
135	C₂	#14583447	1	1	yes	characteristic
136	C₂	C₂×#13063357	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583454

C₂

yes

maximal

#14583297

C₂

yes

maximal, characteristic, complemented

#14583249

C₂

yes

maximal, complemented

#14583154

C₂

yes

maximal

#14583006

C₂

yes

maximal, complemented

C₄×#10621872

C₂

yes

maximal, characteristic

C₄₃×#494

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

C₂²

yes

—

#13063325

C₂²

yes

—

#13063316

—

#13063305

—

#13063301

C₂²

yes

—

Q₈×Dic₄₃

C₂²

yes

—

#13063290

—

#13063283

—

C₄²×D₄₃

C₂²

yes

characteristic

#13063257

C₂²

yes

—

#13063249

C₂²

yes

—

#13063235

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

C₂³

yes

—

C₂×C₄×D₄₃

D₄

yes

—

C₂×C₄×D₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

—

#10621872

—

C₂²×D₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#137

yes

—

C₄×C₄₃

C₂×#41

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

#533

—

#498

—

#494

D₄₃

yes

characteristic, complemented

#487

—

#470

—

#441

—

C₄×M₁₆

—

C₄₃

#3185

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₃

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#106

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₂²×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

Q₁₆

—

M₁₆

—

C₂×C₈

—

100

C₂×C₈

C₂²×D₄₃

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₂²×D₄₃

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

—

172

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

D₄×D₄₃

yes

—

122

C₂×C₄

C₂³×D₄₃

yes

characteristic

123

C₈

—

124

C₈

#10621900

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂×D₄×D₄₃

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

172

—

132

C₄

#13063357

yes

—

133

C₄

C₂×#10621900

yes

—

134

C₂

—

172

—

135

C₂

#14583447

yes

characteristic

136

C₂

C₂×#13063357

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#494	D₄₃
hypocenter	C₄₃	#3185
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#494

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
2. #14583297	C₂	semidirect
3. #14583249	C₂	semidirect
5. #14583006	C₂	semidirect
7. C₄₃×#494	C₂	semidirect
71. #494	D₄₃	semidirect
76. C₄₃	#3185	semidirect

H ≅ G/N

type

2. #14583297

C₂

semidirect

3. #14583249

C₂

semidirect

5. #14583006

C₂

semidirect

7. C₄₃×#494

C₂

semidirect

71. #494

D₄₃

semidirect

76. C₄₃

#3185

semidirect

Subgroups — #19145338

Conjugacy classes of subgroups

Complements