Group #19133491 — subgroups

Subgroups — #19133491

Order 5504.

152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14583026	C₂	1	2	yes	maximal
2	C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#14582629	C₂	1	2	yes	maximal
4	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₄	1	1	yes	characteristic
7	C₄×Dic₈₆	C₂²	1	2	yes	—
8	#13063259	C₄	1	1	yes	characteristic
9	Dic₄₃⋊C₈	—	2	2	no	—
10	#13063250	C₄	1	2	yes	—
11	#13063235	—	2	2	no	—
12	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₃	—	2	2	no	—
18	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₄₃	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
22	Dic₄₃⋊C₄	—	2	2	no	—
23	C₄×Dic₄₃	—	2	2	no	—
24	C₂×C₄₃⋊C₈	—	2	1	no	—
25	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
26	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
27	Dic₁₇₂	—	2	2	no	—
28	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
31	C₂×Dic₄₃	—	2	2	no	—
32	C₂×Dic₄₃	—	2	2	no	—
33	Dic₈₆	—	2	2	no	—
34	Dic₈₆	—	2	2	no	—
35	C₈×C₄₃	—	2	1	no	—
36	C₈×C₄₃	—	4	2	no	—
37	C₈×C₄₃	M₁₆	1	2	yes	—
38	C₄₃⋊C₈	—	2	2	no	—
39	C₄₃⋊C₈	—	2	1	no	—
40	C₄₃⋊C₈	Q₁₆	1	2	yes	complemented
41	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₄₃	#131	1	1	yes	characteristic
45	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₄₃	#135	1	1	yes	characteristic
47	Dic₄₃	—	4	2	no	—
48	Dic₄₃	—	4	2	no	—
49	#1591	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	#436	1	1	yes	characteristic
51	C₂×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₄₃	#443	1	1	yes	characteristic
53	#446	—	43	2	no	—
54	C₄×Q₁₆	—	43	1	no	—
55	#335	D₄₃	1	1	yes	characteristic
56	Q₈⋊C₈	—	43	2	no	—
57	C₈²	—	43	1	no	—
58	C₄₃	#1591	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	43	1	no	—
60	C₄×Q₈	—	43	2	no	—
61	#107	—	43	1	no	—
62	C₄⋊C₈	—	86	2	no	—
63	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
64	#103	—	43	2	no	—
65	#97	—	86	2	no	—
66	C₄×C₈	—	43	1	no	—
67	C₄×C₈	—	43	1	no	—
68	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
69	C₂×Q₈	—	43	2	no	—
70	Q₁₆	—	86	2	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	43	1	no	—
73	C₂×C₈	—	43	1	no	—
74	C₂×C₈	—	86	1	no	—
75	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
76	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
77	C₄⋊C₄	—	43	2	no	—
78	C₄⋊C₄	—	86	2	no	—
79	C₄²	—	86	2	no	—
80	C₄²	C₂²×D₄₃	1	1	yes	characteristic
81	Q₈	—	86	2	no	—
82	Q₈	—	86	2	no	—
83	C₂×C₄	—	86	2	no	—
84	C₂×C₄	—	86	2	no	—
85	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
86	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
87	C₂×C₄	#10621902	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	4	2	no	—
90	C₈	—	43	2	no	—
91	C₈	—	86	2	no	—
92	C₈	—	86	1	no	—
93	C₈	#10621872	1	2	yes	—
94	C₂²	#13063287	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	172	2	no	—
97	C₄	—	172	2	no	—
98	C₄	C₂×#10621872	1	1	yes	characteristic
99	C₄	#13063333	1	1	yes	characteristic
100	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
101	C₄	#13063344	1	1	yes	characteristic
102	C₂	#14582976	1	1	yes	characteristic
103	C₂	#14582993	1	1	yes	characteristic
104	C₂	#14583015	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583026

C₂

yes

maximal

C₄×Dic₁₇₂

C₂

yes

maximal, characteristic

#14582629

C₂

yes

maximal

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄₃×#335

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₄

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

#13063259

C₄

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

C₄

yes

—

#13063235

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

M₁₆

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

Q₁₆

yes

complemented

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₄×C₄₃

#131

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₄×Q₁₆

yes

C₂×C₄₃

yes

—

C₄×Q₁₆

—

#335

D₄₃

yes

characteristic

Q₈⋊C₈

—

C₈²

—

C₄₃

#1591

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621902

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

#10621872

yes

—

C₂²

#13063287

yes

characteristic

C₄

—

C₄

—

172

—

C₄

—

172

—

C₄

yes

C₄

yes

100

C₄

Q₁₆×D₄₃

yes

characteristic

101

C₄

#13063344

yes

characteristic

102

C₂

#14582976

yes

characteristic

103

C₂

#14582993

yes

characteristic

104

C₂

#14583015

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#335	C₂
socle	C₂²×C₄₃	C₄×D₄
hypercenter	#335	D₄₃
hypocenter	C₄₃	#1591
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#335

C₂

socle

C₂²×C₄₃

C₄×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
40. C₄₃⋊C₈	Q₁₆	semidirect
58. C₄₃	#1591	semidirect

H ≅ G/N

type

40. C₄₃⋊C₈

Q₁₆

semidirect

58. C₄₃

#1591

semidirect

Subgroups — #19133491

Conjugacy classes of subgroups

Complements