Group #19136752 — subgroups

Subgroups — #19136752

Order 5504.

136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583301	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582726	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582724	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582700	C₂	1	1	yes	maximal, characteristic
6	#14582700	C₂	1	1	yes	maximal, characteristic
7	C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
8	#13063317	—	2	1	no	—
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13063259	C₂²	1	1	yes	characteristic
12	#13063259	C₂²	1	1	yes	characteristic
13	#13063257	—	2	1	no	—
14	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×D₄×C₄₃	—	2	1	no	—
16	#107×C₄₃	C₂²	1	1	yes	characteristic
17	#102×C₄₃	—	2	1	no	—
18	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₃	—	2	1	no	—
20	C₂²×C₄×C₄₃	—	4	1	no	—
21	D₈×C₄₃	—	2	1	no	—
22	D₈×C₄₃	Q₈	1	2	yes	—
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₃	—	2	1	no	—
26	C₂²⋊C₄×C₄₃	—	4	1	no	—
27	C₄²×C₄₃	D₄	1	1	yes	characteristic
28	C₄⋊Dic₄₃	—	2	1	no	—
29	C₄⋊Dic₄₃	—	2	1	no	—
30	Dic₄₃⋊C₄	—	4	1	no	—
31	Dic₄₃⋊C₄	—	4	1	no	—
32	C₄₃⋊C₁₆	—	2	1	no	—
33	C₄₃⋊C₁₆	—	2	1	no	—
34	C₂³×C₄₃	—	4	1	no	—
35	D₄×C₄₃	—	2	2	no	—
36	D₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	—	8	2	no	—
39	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
40	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	C₈×C₄₃	—	2	1	no	—
45	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
46	C₈×C₄₃	#41	1	1	yes	characteristic
47	C₂²×C₄₃	—	4	2	no	—
48	C₂²×C₄₃	—	8	1	no	—
49	C₂²×C₄₃	—	8	1	no	—
50	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	—	2	1	no	—
53	C₄×C₄₃	—	8	1	no	—
54	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
55	C₄×C₄₃	#137	1	1	yes	characteristic
56	Dic₄₃	—	8	1	no	—
57	Dic₄₃	—	8	1	no	—
58	#2228	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	—	8	2	no	—
60	C₂×C₄₃	#474	1	1	yes	characteristic
61	C₂×C₄₃	#508	1	1	yes	characteristic
62	C₂×C₄₃	#509	1	1	yes	characteristic
63	#499	—	43	1	no	—
64	C₄×D₈	D₄₃	1	1	yes	characteristic
65	#367	—	43	1	no	—
66	#366	—	43	1	no	—
67	C₄⋊C₁₆	—	43	1	no	—
68	#357	—	43	1	no	—
69	#357	—	43	1	no	—
70	C₄₃	#2228	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
72	#125	—	86	1	no	—
73	C₄×D₄	—	2	1	no	—
74	C₂×C₁₆	—	43	1	no	—
75	C₂×C₁₆	—	43	1	no	—
76	#107	—	43	1	no	—
77	#107	—	43	1	no	—
78	#107	C₂×D₄₃	1	1	yes	characteristic
79	#106	—	86	1	no	—
80	#102	—	2	1	no	—
81	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
82	C₂×D₄	—	2	1	no	—
83	C₂²×C₄	—	4	1	no	—
84	D₈	—	2	1	no	—
85	D₈	Dic₈₆	1	2	yes	—
86	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
88	C₄⋊C₄	—	2	1	no	—
89	C₄⋊C₄	—	86	1	no	—
90	C₄⋊C₄	—	86	1	no	—
91	C₄⋊C₄	—	172	1	no	—
92	C₄⋊C₄	—	172	1	no	—
93	C₂²⋊C₄	—	4	1	no	—
94	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
95	C₁₆	—	86	1	no	—
96	C₁₆	—	86	1	no	—
97	C₂³	—	4	1	no	—
98	D₄	—	2	2	no	—
99	D₄	—	4	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	8	2	no	—
102	C₂×C₄	—	172	1	no	—
103	C₂×C₄	—	172	1	no	—
104	C₂×C₄	#10621882	1	1	yes	characteristic
105	C₂×C₄	#10621882	1	1	yes	characteristic
106	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	C₂×Dic₈₆	1	1	yes	characteristic
109	C₈	#10621898	1	1	yes	characteristic
110	C₂²	—	4	2	no	—
111	C₂²	—	8	1	no	—
112	C₂²	—	8	1	no	—
113	C₂²	C₂×#10621882	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	2	1	no	—
116	C₄	—	8	1	no	—
117	C₄	—	344	1	no	—
118	C₄	—	344	1	no	—
119	C₄	#13063304	1	1	yes	characteristic
120	C₄	#13063355	1	1	yes	characteristic
121	C₂	—	8	2	no	—
122	C₂	#14583179	1	1	yes	characteristic
123	C₂	#14583329	1	1	yes	characteristic
124	C₂	#14583335	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583301

C₂

yes

maximal, characteristic, complemented

#14582726

C₂

yes

maximal, characteristic, complemented

#14582724

C₂

yes

maximal, characteristic, complemented

C₄⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#14582700

C₂

yes

maximal, characteristic

#14582700

C₂

yes

maximal, characteristic

C₄×D₈×C₄₃

C₂

yes

maximal, characteristic

#13063317

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063257

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₄×D₄×C₄₃

—

#107×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2228

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₄×D₈

D₄₃

yes

characteristic

#367

—

#366

—

C₄⋊C₁₆

—

#357

—

#357

—

C₄₃

#2228

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₃

yes

characteristic

#125

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₄₃

yes

characteristic

#106

—

#102

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

Dic₈₆

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

172

—

103

C₂×C₄

—

172

—

104

C₂×C₄

#10621882

yes

characteristic

105

C₂×C₄

#10621882

yes

characteristic

106

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

107

C₈

—

108

C₈

C₂×Dic₈₆

yes

characteristic

109

C₈

#10621898

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×#10621882

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

344

—

118

C₄

—

344

—

119

C₄

#13063304

yes

characteristic

120

C₄

#13063355

yes

characteristic

121

C₂

—

122

C₂

#14583179

yes

characteristic

123

C₂

#14583329

yes

characteristic

124

C₂

#14583335

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₄×D₈	D₄₃
hypocenter	C₄₃	#2228
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×D₈×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₄×D₈

D₄₃

hypocenter

C₄₃

#2228

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
1. #14583301	C₂	semidirect
2. #14582726	C₂	semidirect
3. #14582724	C₂	semidirect
4. C₄⋊(C₄₃⋊C₁₆)	C₂	semidirect
70. C₄₃	#2228	semidirect

H ≅ G/N

type

1. #14583301

C₂

semidirect

2. #14582726

C₂

semidirect

3. #14582724

C₂

semidirect

4. C₄⋊(C₄₃⋊C₁₆)

C₂

semidirect

70. C₄₃

#2228

semidirect

Subgroups — #19136752

Conjugacy classes of subgroups

Complements