Group #19135331 — subgroups

Subgroups — #19135331

Order 5504.

240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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	1	yes	maximal, characteristic
2	C₂×#13063235	C₂	1	1	yes	maximal, characteristic
3	#14582795	C₂	1	2	yes	maximal
4	#14582661	C₂	1	2	yes	maximal
5	C₂×#106×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	C₂×Dic₄₃⋊C₄	—	2	2	no	—
9	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
10	#13063259	C₄	1	4	yes	complemented
11	#13063235	—	2	2	no	—
12	C₄₃⋊#95	—	2	2	no	—
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	#106×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	—	2	2	no	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	2	no	—
19	C₂²×Dic₄₃	D₄	1	2	yes	—
20	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₄₃	D₄	1	2	yes	—
22	C₂×C₈×C₄₃	Q₈	1	2	yes	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
27	Dic₄₃⋊C₄	—	4	4	no	—
28	C₄×Dic₄₃	—	2	1	no	—
29	C₄×Dic₄₃	—	2	1	no	—
30	C₂×C₄₃⋊C₈	—	2	1	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	C₂×C₄₃⋊C₈	Q₈	1	2	yes	—
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	4	2	no	—
35	C₂×C₄×C₄₃	—	4	2	no	—
36	C₂×C₄×C₄₃	—	4	2	no	—
37	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
42	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
43	C₂×Dic₄₃	—	2	4	no	—
44	C₂×Dic₄₃	—	2	2	no	—
45	C₂×Dic₄₃	—	2	2	no	—
46	C₂×Dic₄₃	—	2	2	no	—
47	C₂×Dic₄₃	—	4	2	no	—
48	C₂×Dic₄₃	—	4	2	no	—
49	C₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
50	C₄₃⋊C₈	—	2	2	no	—
51	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
52	C₂²×C₄₃	#121	1	1	yes	characteristic
53	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
54	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
55	C₂²×C₄₃	#137	1	2	yes	—
56	C₄×C₄₃	—	8	2	no	—
57	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
59	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
60	C₄×C₄₃	#125	1	1	yes	characteristic
61	Dic₄₃	—	4	4	no	—
62	Dic₄₃	—	4	2	no	—
63	#1943	—	43	1	no	maximal, Sylow
64	C₂×C₄₃	#389	1	1	yes	characteristic
65	C₂×C₄₃	#441	1	1	yes	characteristic
66	C₂×C₄₃	#442	1	1	yes	characteristic
67	C₂×C₄₃	#468	1	2	yes	—
68	C₂×C₄₃	#501	1	2	yes	—
69	C₂×#107	—	43	1	no	—
70	C₂×#106	D₄₃	1	1	yes	characteristic
71	C₂×#97	—	43	1	no	—
72	#389	—	43	2	no	—
73	#340	—	43	2	no	—
74	C₄₃	#1943	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₈	—	43	1	no	—
76	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
77	C₂×C₄⋊C₄	—	43	2	no	—
78	C₂×C₄⋊C₄	—	86	2	no	—
79	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
80	C₂×C₄²	—	43	1	no	—
81	#107	—	43	4	no	—
82	#106	—	2	2	no	—
83	#97	—	86	2	no	—
84	#95	—	86	2	no	—
85	C₂²×C₄	—	2	2	no	—
86	C₂²×C₄	—	43	2	no	—
87	C₂²×C₄	—	86	2	no	—
88	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
89	C₂×C₈	—	43	2	no	—
90	C₂×C₈	—	86	1	no	—
91	C₂×C₈	—	86	1	no	—
92	C₂×C₈	Dic₈₆	1	2	yes	—
93	C₂×C₈	C₄×D₄₃	1	2	yes	—
94	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	43	4	no	—
98	C₄⋊C₄	—	86	2	no	—
99	C₄⋊C₄	—	172	4	no	—
100	C₄²	—	86	1	no	—
101	C₄²	—	86	1	no	—
102	C₂³	D₄×D₄₃	1	1	yes	characteristic
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	86	4	no	—
107	C₂×C₄	—	86	2	no	—
108	C₂×C₄	—	86	2	no	—
109	C₂×C₄	—	86	2	no	—
110	C₂×C₄	—	172	2	no	—
111	C₂×C₄	—	172	2	no	—
112	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
113	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
114	C₂×C₄	#10621900	1	1	yes	characteristic
115	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
116	C₂×C₄	#10621902	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
118	C₈	—	86	2	no	—
119	C₈	Dic₄₃⋊C₄	1	4	yes	complemented
120	C₂²	#13063287	1	1	yes	characteristic
121	C₂²	#13063296	1	1	yes	characteristic
122	C₂²	#13063324	1	1	yes	characteristic
123	C₂²	#13063352	1	2	yes	—
124	C₂²	#13063354	1	2	yes	—
125	C₄	—	8	2	no	—
126	C₄	—	172	2	no	—
127	C₄	—	172	4	no	—
128	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
129	C₄	#13063290	1	1	yes	characteristic
130	C₄	#13063301	1	1	yes	characteristic
131	C₄	#13063316	1	1	yes	characteristic
132	C₂	#14582795	1	1	yes	characteristic
133	C₂	#14583005	1	1	yes	characteristic
134	C₂	#14583010	1	1	yes	characteristic
135	C₂	#14583142	1	2	yes	—
136	C₂	#14583306	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal, characteristic

C₂×#13063235

C₂

yes

maximal, characteristic

#14582795

C₂

yes

maximal

#14582661

C₂

yes

maximal

C₂×#106×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063259

C₄

yes

complemented

#13063235

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

#106×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

C₄⋊C₄

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₂²×C₄₃

#121

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₂²×C₄₃

#137

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₄×Q₈

yes

characteristic

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

#125

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#501

yes

—

C₂×#107

—

C₂×#106

D₄₃

yes

characteristic

C₂×#97

—

#389

—

#340

—

C₄₃

#1943

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

100

C₄²

—

101

C₄²

—

102

C₂³

D₄×D₄₃

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

172

—

111

C₂×C₄

—

172

—

112

C₂×C₄

C₂×Dic₈₆

yes

characteristic

113

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

114

C₂×C₄

#10621900

yes

characteristic

115

C₂×C₄

Q₈×D₄₃

yes

characteristic

116

C₂×C₄

#10621902

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

118

C₈

—

119

C₈

Dic₄₃⋊C₄

yes

complemented

120

C₂²

#13063287

yes

characteristic

121

C₂²

#13063296

yes

characteristic

122

C₂²

#13063324

yes

characteristic

123

C₂²

#13063352

yes

—

124

C₂²

#13063354

yes

—

125

C₄

—

126

C₄

—

172

—

127

C₄

—

172

—

128

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

129

C₄

#13063290

yes

characteristic

130

C₄

#13063301

yes

characteristic

131

C₄

#13063316

yes

characteristic

132

C₂

#14582795

yes

characteristic

133

C₂

#14583005

yes

characteristic

134

C₂

#14583010

yes

characteristic

135

C₂

#14583142

yes

—

136

C₂

#14583306

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#106×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#106	D₄₃
hypocenter	C₄₃	#1943
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#106×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
10. #13063259	C₄	semidirect
49. C₈×C₄₃	C₄⋊C₄	semidirect
74. C₄₃	#1943	semidirect
119. C₈	Dic₄₃⋊C₄	semidirect

H ≅ G/N

type

10. #13063259

C₄

semidirect

49. C₈×C₄₃

C₄⋊C₄

semidirect

74. C₄₃

#1943

semidirect

119. C₈

Dic₄₃⋊C₄

semidirect

Subgroups — #19135331

Conjugacy classes of subgroups

Complements