Group #19134637 — subgroups

Subgroups — #19134637

Order 5504.

272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13063261	C₂	1	2	yes	maximal, complemented
2	#14582863	C₂	1	2	yes	maximal
3	#14582664	C₂	1	2	yes	maximal, complemented
4	C₂²×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	C₂²	1	4	yes	—
6	#13063261	—	2	4	no	—
7	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
8	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₄₃	—	2	4	no	—
10	C₂×M₁₆×C₄₃	C₄	1	4	yes	—
11	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄₃	Q₈	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	—	2	2	no	—
15	C₂²×C₄×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₄₃	D₄	1	2	yes	—
18	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	M₁₆×C₄₃	—	2	8	no	—
21	C₂×C₈×C₄₃	—	2	2	no	—
22	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₃	D₄	1	4	yes	—
25	#10621877	—	2	4	no	—
26	#10621877	—	2	4	no	—
27	C₂×C₄₃⋊C₈	—	2	4	no	—
28	C₂³×C₄₃	—	2	2	no	—
29	C₂³×C₄₃	—	4	2	no	—
30	C₂³×C₄₃	C₄⋊C₄	1	2	yes	—
31	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
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×D₄	1	2	yes	—
40	C₂×C₄×C₄₃	#41	1	2	yes	—
41	C₈×C₄₃	—	2	2	no	—
42	C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
43	C₄₃⋊C₈	—	4	4	no	—
44	C₂²×C₄₃	—	2	2	no	—
45	C₂²×C₄₃	—	2	2	no	—
46	C₂²×C₄₃	—	2	4	no	—
47	C₂²×C₄₃	—	4	4	no	—
48	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄₃	C₂²⋊Q₈	1	2	yes	—
50	C₄×C₄₃	—	2	2	no	—
51	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₄×C₄₃	#117	1	1	yes	characteristic
53	C₄×C₄₃	#121	1	2	yes	—
54	#1811	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	—	2	2	no	—
56	C₂×C₄₃	—	4	2	no	—
57	C₂×C₄₃	#380	1	1	yes	characteristic
58	C₂×C₄₃	#430	1	2	yes	—
59	C₂²×M₁₆	D₄₃	1	1	yes	characteristic
60	C₂×#108	—	43	2	no	—
61	#407	—	43	2	no	—
62	#341	—	43	2	no	—
63	C₄₃	#1811	1	1	yes	characteristic, complemented, Sylow
64	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
65	C₂×M₁₆	—	2	4	no	—
66	C₂×M₁₆	—	43	4	no	—
67	C₂×M₁₆	Dic₄₃	1	4	yes	—
68	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
69	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
70	#108	—	86	4	no	—
71	C₂²⋊C₈	—	86	4	no	—
72	C₂⁴	Dic₈₆	1	1	yes	characteristic
73	C₂²×C₄	—	2	2	no	—
74	C₂²×C₄	—	2	2	no	—
75	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
76	C₂²×C₄	D₁₇₂	1	2	yes	—
77	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
78	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
79	M₁₆	—	2	8	no	—
80	M₁₆	—	86	4	no	—
81	M₁₆	—	86	4	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	86	4	no	—
84	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
85	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
86	C₂×C₈	C₂²⋊D₄₃	1	4	yes	—
87	C₂³	—	2	2	no	—
88	C₂³	—	4	2	no	—
89	C₂³	C₄⋊Dic₄₃	1	2	yes	—
90	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
96	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
97	C₂×C₄	#10621898	1	2	yes	—
98	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
100	C₈	—	2	2	no	—
101	C₈	—	172	4	no	—
102	C₈	C₂²⋊Dic₄₃	1	4	yes	—
103	C₂²	—	2	2	no	—
104	C₂²	—	2	4	no	—
105	C₂²	—	2	2	no	—
106	C₂²	—	4	4	no	—
107	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
108	C₂²	#13063304	1	2	yes	—
109	C₄	—	2	2	no	—
110	C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
111	C₄	#13063284	1	1	yes	characteristic
112	C₄	#13063299	1	2	yes	—
113	C₂	—	2	2	no	—
114	C₂	—	4	2	no	—
115	C₂	#14582759	1	1	yes	characteristic
116	C₂	#14582948	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063261

C₂

yes

maximal, complemented

#14582863

C₂

yes

maximal

#14582664

C₂

yes

maximal, complemented

C₂²×M₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063261

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

—

C₂×M₁₆×C₄₃

C₄

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₄⋊C₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

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

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₂²⋊C₄

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

#1811

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#380

yes

characteristic

C₂×C₄₃

#430

yes

—

C₂²×M₁₆

D₄₃

yes

—

—

—

C₄₃

#1811

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

Dic₄₃

yes

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

#108

—

C₂²⋊C₈

—

C₂⁴

Dic₈₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₂³

—

C₂³

—

C₂³

C₄⋊Dic₄₃

yes

—

C₂³

C₂×Dic₈₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₄₃

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

#10621898

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

100

C₈

—

101

C₈

—

172

—

102

C₈

C₂²⋊Dic₄₃

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

108

C₂²

#13063304

yes

—

109

C₄

—

110

C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

111

C₄

#13063284

yes

characteristic

112

C₄

#13063299

yes

—

113

C₂

—

114

C₂

—

115

C₂

#14582759

yes

characteristic

116

C₂

#14582948

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂²×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂²×M₁₆	D₄₃
hypocenter	C₄₃	#1811
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂²×M₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

hypercenter

C₂²×M₁₆

D₄₃

hypocenter

C₄₃

#1811

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

N	H ≅ G/N	type
1. C₂×#13063261	C₂	semidirect
3. #14582664	C₂	semidirect
63. C₄₃	#1811	semidirect

H ≅ G/N

type

1. C₂×#13063261

C₂

semidirect

3. #14582664

C₂

semidirect

63. C₄₃

#1811

semidirect

Subgroups — #19134637

Conjugacy classes of subgroups

Complements