Group #19136132 — subgroups

Subgroups — #19136132

Order 5504.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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	2	yes	maximal
2	C₂×#13063250	C₂	1	2	yes	maximal
3	#14582805	C₂	1	1	yes	maximal, characteristic
4	#14582769	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₃	—	2	2	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	#13063259	—	2	4	no	—
11	#13063250	—	2	4	no	—
12	C₄₃⋊#95	—	2	2	no	—
13	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	2	yes	—
16	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₃	—	2	1	no	—
18	C₂²×Dic₄₃	—	2	1	no	—
19	C₂²×Dic₄₃	—	2	2	no	—
20	C₂×Dic₈₆	—	2	2	no	—
21	C₂×Dic₈₆	—	2	2	no	—
22	C₂×Dic₈₆	—	2	1	no	—
23	C₂×Dic₈₆	Q₈	1	2	yes	—
24	C₂×C₈×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	—	2	2	no	—
26	C₂×C₈×C₄₃	D₄	1	4	yes	—
27	C₄²×C₄₃	—	2	2	no	—
28	C₄⋊Dic₄₃	—	2	2	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₄⋊Dic₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	—	4	4	no	—
32	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	Q₁₆	1	4	yes	—
36	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#41	1	2	yes	—
39	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
40	C₂×Dic₄₃	—	2	2	no	—
41	C₂×Dic₄₃	—	4	1	no	—
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	2	no	—
44	C₂×Dic₄₃	—	4	1	no	—
45	C₂×Dic₄₃	—	4	4	no	—
46	C₂×Dic₄₃	—	4	2	no	—
47	Dic₈₆	—	2	4	no	—
48	Dic₈₆	—	4	2	no	—
49	C₈×C₄₃	—	2	4	no	—
50	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₄₃	#123	1	1	yes	characteristic
52	C₂²×C₄₃	#127	1	1	yes	characteristic
53	C₂²×C₄₃	C₂×Q₁₆	1	2	yes	—
54	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
55	C₄×C₄₃	—	2	4	no	—
56	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
57	C₄×C₄₃	#123	1	2	yes	—
58	Dic₄₃	—	4	2	no	—
59	Dic₄₃	—	8	2	no	—
60	Dic₄₃	—	8	1	no	—
61	#2095	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	#399	1	1	yes	characteristic
63	C₂×C₄₃	#477	1	2	yes	—
64	C₂×C₄₃	#484	1	2	yes	—
65	C₂×C₄₃	#494	1	1	yes	characteristic
66	C₂×C₄₃	#496	1	1	yes	characteristic
67	C₂×#107	—	43	2	no	—
68	C₂×#103	—	43	2	no	—
69	#391	—	43	1	no	—
70	#384	—	43	1	no	—
71	#336	D₄₃	1	1	yes	characteristic
72	C₄₃	#2095	1	1	yes	characteristic, complemented, Sylow
73	C₂²×Q₈	—	43	1	no	—
74	C₂²×C₈	C₂×D₄₃	1	2	yes	—
75	C₂×C₄⋊C₄	—	43	2	no	—
76	C₂×C₄⋊C₄	—	43	1	no	—
77	C₂×C₄⋊C₄	—	86	2	no	—
78	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
79	#107	—	86	4	no	—
80	#103	—	86	4	no	—
81	#95	—	86	2	no	—
82	C₂×Q₈	—	43	2	no	—
83	C₂×Q₈	—	86	1	no	—
84	C₂×Q₈	—	86	2	no	—
85	C₂×Q₈	—	86	2	no	—
86	C₂²×C₄	—	86	1	no	—
87	C₂²×C₄	—	86	1	no	—
88	C₂²×C₄	—	86	2	no	—
89	C₂²×C₄	D₁₇₂	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	D₁₇₂	1	4	yes	—
94	C₄⋊C₄	—	86	2	no	—
95	C₄⋊C₄	—	86	2	no	—
96	C₄⋊C₄	—	86	2	no	—
97	C₄⋊C₄	—	172	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
100	Q₈	—	86	4	no	—
101	Q₈	—	172	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	86	2	no	—
105	C₂×C₄	—	172	2	no	—
106	C₂×C₄	—	172	1	no	—
107	C₂×C₄	—	172	4	no	—
108	C₂×C₄	—	172	2	no	—
109	C₂×C₄	—	172	1	no	—
110	C₂×C₄	—	172	1	no	—
111	C₂×C₄	Dic₁₇₂	1	4	yes	—
112	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
113	C₂×C₄	#10621900	1	2	yes	—
114	C₂×C₄	#10621900	1	1	yes	characteristic
115	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₂²	#13063305	1	1	yes	characteristic
118	C₂²	#13063309	1	1	yes	characteristic
119	C₂²	#13063322	1	1	yes	characteristic
120	C₂²	C₂×Dic₁₇₂	1	2	yes	—
121	C₂²	#13063353	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	344	2	no	—
124	C₄	—	344	1	no	—
125	C₄	—	172	2	no	—
126	C₄	#13063305	1	2	yes	—
127	C₄	#13063309	1	2	yes	—
128	C₂	#14582836	1	1	yes	characteristic
129	C₂	#14583195	1	2	yes	—
130	C₂	#14583235	1	2	yes	—
131	C₂	#14583279	1	1	yes	characteristic
132	C₂	#14583288	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal

C₂×#13063250

C₂

yes

maximal

#14582805

C₂

yes

maximal, characteristic

#14582769

C₂

yes

maximal, characteristic

C₄₃×#336

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063259

—

#13063250

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

Q₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×Q₁₆

yes

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#484

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2095

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

C₂³

C₂×D₁₇₂

yes

characteristic

100

Q₈

—

101

Q₈

—

172

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

172

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

—

172

—

109

C₂×C₄

—

172

—

110

C₂×C₄

—

172

—

111

C₂×C₄

Dic₁₇₂

yes

—

112

C₂×C₄

C₂×D₁₇₂

yes

—

113

C₂×C₄

#10621900

yes

—

114

C₂×C₄

#10621900

yes

characteristic

115

C₂×C₄

Q₈×D₄₃

yes

characteristic

116

C₈

—

117

C₂²

#13063305

yes

characteristic

118

C₂²

#13063309

yes

characteristic

119

C₂²

#13063322

yes

characteristic

120

C₂²

C₂×Dic₁₇₂

yes

—

121

C₂²

#13063353

yes

—

122

C₄

—

123

C₄

—

344

—

124

C₄

—

344

—

125

C₄

—

172

—

126

C₄

#13063305

yes

—

127

C₄

#13063309

yes

—

128

C₂

#14582836

yes

characteristic

129

C₂

#14583195

yes

—

130

C₂

#14583235

yes

—

131

C₂

#14583279

yes

characteristic

132

C₂

#14583288

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#336	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#336	D₄₃
hypocenter	C₄₃	#2095
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#336

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
72. C₄₃	#2095	semidirect

H ≅ G/N

type

72. C₄₃

#2095

semidirect

Subgroups — #19136132

Conjugacy classes of subgroups

Complements