Group #19136170 — subgroups

Subgroups — #19136170

Order 5504.

158 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14582948	C₂	1	1	yes	maximal, characteristic
2	#14582671	C₂	1	2	yes	maximal
3	#14582659	C₂	1	2	yes	maximal
4	#14582656	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#423	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	#13063284	C₂²	1	2	yes	—
8	#13063261	—	2	2	no	—
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₄₃	—	2	2	no	—
13	C₂²×C₄×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
15	M₁₆×C₄₃	—	2	2	no	—
16	M₁₆×C₄₃	—	2	2	no	—
17	C₂×C₈×C₄₃	—	2	1	no	—
18	C₂×C₈×C₄₃	D₄	1	2	yes	—
19	C₄²×C₄₃	—	2	1	no	—
20	C₄²×C₄₃	Q₈	1	1	yes	characteristic
21	C₄²×C₄₃	Q₈	1	1	yes	characteristic
22	C₂²⋊Dic₄₃	—	2	2	no	—
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄×Dic₄₃	—	2	2	no	—
25	#10621877	—	2	2	no	—
26	#10621877	—	2	2	no	—
27	C₂×C₄₃⋊C₈	—	2	2	no	—
28	C₂³×C₄₃	#41	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	—	4	2	no	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₄₃	#41	1	2	yes	—
35	C₂×C₄×C₄₃	#41	1	2	yes	—
36	C₂×Dic₄₃	—	4	2	no	—
37	C₈×C₄₃	—	2	2	no	—
38	C₈×C₄₃	—	4	1	no	—
39	C₄₃⋊C₈	—	4	2	no	—
40	C₂²×C₄₃	—	4	1	no	—
41	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²×C₄₃	#126	1	2	yes	—
43	C₄×C₄₃	—	2	2	no	—
44	C₄×C₄₃	—	4	1	no	—
45	C₄×C₄₃	#123	1	1	yes	characteristic
46	C₄×C₄₃	#124	1	1	yes	characteristic
47	C₄×C₄₃	#125	1	2	yes	—
48	Dic₄₃	—	8	2	no	—
49	#2102	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	2	no	—
51	C₂×C₄₃	—	2	1	no	—
52	C₂×C₄₃	#400	1	1	yes	characteristic
53	#430	—	43	1	no	—
54	#423	D₄₃	1	1	yes	characteristic
55	#344	—	43	2	no	—
56	#339	—	43	2	no	—
57	H(3,ℤ/4)	—	43	1	no	—
58	C₄₃	#2102	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	43	2	no	—
60	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
61	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
62	#117	—	43	2	no	—
63	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
64	#108	—	86	2	no	—
65	C₄⋊C₈	—	2	2	no	—
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	86	2	no	—
71	M₁₆	—	86	2	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	86	2	no	—
74	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
75	C₄⋊C₄	—	86	2	no	—
76	C₂²⋊C₄	—	86	2	no	—
77	C₄²	—	2	1	no	—
78	C₄²	—	86	2	no	—
79	C₄²	Dic₈₆	1	1	yes	characteristic
80	C₄²	Dic₈₆	1	1	yes	characteristic
81	C₂³	#10621898	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	172	2	no	—
86	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
87	C₂×C₄	#10621900	1	2	yes	—
88	C₂×C₄	#10621902	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	4	1	no	—
92	C₈	—	172	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#13063304	1	1	yes	characteristic
95	C₂²	#13063320	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	—	4	1	no	—
98	C₄	—	344	2	no	—
99	C₄	#13063306	1	1	yes	characteristic
100	C₄	#13063314	1	1	yes	characteristic
101	C₄	#13063316	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#14582838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582948

C₂

yes

maximal, characteristic

#14582671

C₂

yes

maximal

#14582659

C₂

yes

maximal

#14582656

C₂

yes

maximal, characteristic

C₄₃×#423

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063284

C₂²

yes

—

#13063261

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

Q₈

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#41

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

#126

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

#2102

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

D₄₃

yes

—

—

—

C₄₃

#2102

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#117

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#108

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

Dic₈₆

yes

characteristic

C₄²

Dic₈₆

yes

characteristic

C₂³

#10621898

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

#10621900

yes

—

C₂×C₄

#10621902

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

C₂²

#13063304

yes

characteristic

C₂²

#13063320

yes

—

C₄

—

C₄

—

C₄

—

344

—

C₄

#13063306

yes

characteristic

100

C₄

#13063314

yes

characteristic

101

C₄

#13063316

yes

—

102

C₂

—

103

C₂

—

104

C₂

#14582838

yes

characteristic

	subgroup	G/H
center	C₄	#13063314
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂×C₄₃	#400
hypercenter	#423	D₄₃
hypocenter	C₄₃	#2102
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #423

subgroup

G/H

center

C₄

#13063314

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#423

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #423

N	H ≅ G/N	type
58. C₄₃	#2102	semidirect

H ≅ G/N

type

58. C₄₃

#2102

semidirect

Subgroups — #19136170

Conjugacy classes of subgroups

Complements