Group #19134764 — subgroups

Subgroups — #19134764

Order 5504.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13063258	C₂	1	2	yes	maximal
2	C₂×#13063256	C₂	1	2	yes	maximal
3	C₂×#13063236	C₂	1	1	yes	maximal, characteristic
4	#14582769	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#382	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	—	2	2	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	#13063258	—	2	4	no	—
10	#13063256	—	2	4	no	—
11	#13063236	C₄	1	4	yes	complemented
12	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	#95×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄×C₄₃	D₄	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₃	—	2	2	no	—
21	C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₄⋊C₄×C₄₃	—	2	2	no	—
23	C₄²×C₄₃	C₂×C₄	1	2	yes	—
24	C₄²×C₄₃	Q₈	1	2	yes	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄⋊Dic₄₃	—	4	4	no	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
30	C₂×C₄₃⋊C₈	Q₈	1	4	yes	—
31	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	4	1	no	—
35	C₂×C₄×C₄₃	—	4	1	no	—
36	C₂×C₄×C₄₃	—	4	2	no	—
37	C₂×C₄×C₄₃	—	4	2	no	—
38	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
43	C₂×Dic₄₃	—	4	2	no	—
44	C₂×Dic₄₃	—	4	4	no	—
45	C₄₃⋊C₈	C₄⋊C₄	1	8	yes	complemented
46	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₄₃	#127	1	1	yes	characteristic
48	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
49	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
50	C₂²×C₄₃	#137	1	2	yes	—
51	C₄×C₄₃	—	2	4	no	—
52	C₄×C₄₃	—	8	1	no	—
53	C₄×C₄₃	—	8	1	no	—
54	C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
55	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
56	Dic₄₃	—	8	2	no	—
57	#1847	—	43	1	no	maximal, Sylow
58	C₂×C₄₃	#384	1	1	yes	characteristic
59	C₂×C₄₃	#428	1	2	yes	—
60	C₂×C₄₃	#496	1	1	yes	characteristic
61	C₂×C₄₃	#497	1	1	yes	characteristic
62	C₂×C₄₃	#501	1	2	yes	—
63	C₂×#107	—	43	2	no	—
64	C₂×#106	—	43	2	no	—
65	C₂×#97	—	43	1	no	—
66	#384	—	43	1	no	—
67	#382	D₄₃	1	1	yes	characteristic
68	C₄₃	#1847	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	43	2	no	—
70	C₂×C₄⋊C₄	—	43	2	no	—
71	C₂×C₄⋊C₄	—	86	2	no	—
72	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
73	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
74	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
75	#107	—	86	4	no	—
76	#106	—	86	4	no	—
77	#97	—	43	4	no	—
78	#95	—	2	2	no	—
79	C₂²×C₄	—	2	1	no	—
80	C₂²×C₄	—	2	1	no	—
81	C₂²×C₄	—	86	2	no	—
82	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
83	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
84	C₂×C₈	—	43	4	no	—
85	C₂×C₈	—	43	4	no	—
86	C₂×C₈	—	43	4	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	86	2	no	—
90	C₄⋊C₄	—	86	2	no	—
91	C₄⋊C₄	—	172	4	no	—
92	C₄²	Dic₈₆	1	2	yes	—
93	C₄²	C₄×D₄₃	1	2	yes	—
94	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	172	2	no	—
102	C₂×C₄	—	172	4	no	—
103	C₂×C₄	Dic₄₃⋊C₄	1	4	yes	—
104	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
105	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
106	C₂×C₄	D₄×D₄₃	1	2	yes	—
107	C₂×C₄	Q₈×D₄₃	1	2	yes	—
108	C₈	—	43	8	no	—
109	C₂²	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
110	C₂²	#13063321	1	1	yes	characteristic
111	C₂²	#13063323	1	1	yes	characteristic
112	C₂²	#13063350	1	2	yes	—
113	C₂²	#13063355	1	2	yes	—
114	C₄	—	2	4	no	—
115	C₄	—	8	1	no	—
116	C₄	—	8	1	no	—
117	C₄	—	344	2	no	—
118	C₄	C₄⋊C₄×D₄₃	1	2	yes	—
119	C₄	#13063324	1	2	yes	—
120	C₂	#14582768	1	1	yes	characteristic
121	C₂	#14582942	1	2	yes	—
122	C₂	#14583289	1	1	yes	characteristic
123	C₂	#14583294	1	1	yes	characteristic
124	C₂	#14583309	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063258

C₂

yes

maximal

C₂×#13063256

C₂

yes

maximal

C₂×#13063236

C₂

yes

maximal, characteristic

#14582769

C₂

yes

maximal, characteristic

C₄₃×#382

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063258

—

#13063256

—

#13063236

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

C₄⋊C₄

yes

complemented

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

#127

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₂²×C₄₃

#137

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₄×C₄₃

C₄⋊Q₈

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×#107

—

C₂×#106

—

C₂×#97

—

#384

—

#382

D₄₃

yes

characteristic

C₄₃

#1847

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

Dic₈₆

yes

—

C₄²

C₄×D₄₃

yes

—

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

172

—

102

C₂×C₄

—

172

—

103

C₂×C₄

Dic₄₃⋊C₄

yes

—

104

C₂×C₄

C₂×Dic₈₆

yes

characteristic

105

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

106

C₂×C₄

D₄×D₄₃

yes

—

107

C₂×C₄

Q₈×D₄₃

yes

—

108

C₈

—

109

C₂²

C₂×Dic₄₃⋊C₄

yes

characteristic

110

C₂²

#13063321

yes

characteristic

111

C₂²

#13063323

yes

characteristic

112

C₂²

#13063350

yes

—

113

C₂²

#13063355

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

344

—

118

C₄

C₄⋊C₄×D₄₃

yes

—

119

C₄

#13063324

yes

—

120

C₂

#14582768

yes

characteristic

121

C₂

#14582942

yes

—

122

C₂

#14583289

yes

characteristic

123

C₂

#14583294

yes

characteristic

124

C₂

#14583309

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#382	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#382	D₄₃
hypocenter	C₄₃	#1847
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#382

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
11. #13063236	C₄	semidirect
45. C₄₃⋊C₈	C₄⋊C₄	semidirect
68. C₄₃	#1847	semidirect

H ≅ G/N

type

11. #13063236

C₄

semidirect

45. C₄₃⋊C₈

C₄⋊C₄

semidirect

68. C₄₃

#1847

semidirect

Subgroups — #19134764

Conjugacy classes of subgroups

Complements