Group #19134751 — subgroups

Subgroups — #19134751

Order 5504.

280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063256	C₂	1	4	yes	maximal
2	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#14582769	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₄₃	—	2	2	no	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	#13063256	—	2	8	no	—
9	C₄×C₄₃⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
11	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₄₃	—	2	2	no	—
14	C₂²×C₄×C₄₃	D₄	1	2	yes	—
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	—	2	2	no	—
17	C₄⋊C₄×C₄₃	—	2	4	no	—
18	C₄⋊C₄×C₄₃	—	4	4	no	—
19	C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₄²×C₄₃	Q₈	1	2	yes	—
21	C₄⋊Dic₄₃	—	2	4	no	—
22	C₄⋊Dic₄₃	—	4	4	no	—
23	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
25	C₂×C₄₃⋊C₈	Q₈	1	4	yes	—
26	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₄₃	—	4	2	no	—
28	C₂×C₄×C₄₃	—	4	4	no	—
29	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₄₃	SD₁₆	1	4	yes	—
31	C₂×C₄×C₄₃	SD₁₆	1	4	yes	—
32	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
36	C₂×Dic₄₃	—	4	2	no	—
37	C₂×Dic₄₃	—	4	4	no	—
38	C₄₃⋊C₈	C₄⋊C₄	1	8	yes	complemented
39	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄₃	#127	1	1	yes	characteristic
41	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₄₃	C₂×SD₁₆	1	2	yes	—
43	C₂²×C₄₃	C₂×SD₁₆	1	2	yes	—
44	C₄×C₄₃	—	8	2	no	—
45	C₄×C₄₃	#106	1	8	yes	complemented
46	C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
47	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
48	Dic₄₃	—	8	2	no	—
49	#1844	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	#384	1	1	yes	characteristic
51	C₂×C₄₃	C₂×#106	1	2	yes	—
52	C₂×C₄₃	#492	1	1	yes	characteristic
53	C₂×C₄₃	#492	1	1	yes	characteristic
54	C₂×C₄₃	#498	1	2	yes	—
55	C₂×#106	—	43	4	no	—
56	C₂×C₄×C₈	—	43	1	no	—
57	#384	—	43	1	no	—
58	#384	D₄₃	1	1	yes	characteristic
59	C₄₃	#1844	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	43	2	no	—
61	C₂×C₄⋊C₄	—	2	2	no	—
62	C₂×C₄⋊C₄	—	43	2	no	—
63	C₂×C₄⋊C₄	—	86	2	no	—
64	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
65	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
66	#106	—	86	8	no	—
67	C₄×C₈	—	43	4	no	—
68	C₂²×C₄	—	2	2	no	—
69	C₂²×C₄	—	86	2	no	—
70	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
71	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
72	C₂×C₈	—	43	4	no	—
73	C₂×C₈	—	43	4	no	—
74	C₂×C₈	—	43	4	no	—
75	C₄⋊C₄	—	2	4	no	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	86	4	no	—
78	C₄⋊C₄	—	172	4	no	—
79	C₄²	Dic₈₆	1	2	yes	—
80	C₄²	C₄×D₄₃	1	2	yes	—
81	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	—	172	2	no	—
85	C₂×C₄	—	172	4	no	—
86	C₂×C₄	Dic₄₃⋊C₄	1	4	yes	—
87	C₂×C₄	#10621883	1	4	yes	—
88	C₂×C₄	#10621884	1	4	yes	—
89	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
91	C₂×C₄	D₄×D₄₃	1	2	yes	—
92	C₂×C₄	Q₈×D₄₃	1	2	yes	—
93	C₈	—	43	8	no	—
94	C₂²	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
95	C₂²	#13063321	1	1	yes	characteristic
96	C₂²	#13063323	1	1	yes	characteristic
97	C₂²	C₂×#10621884	1	2	yes	—
98	C₂²	C₂×#10621883	1	2	yes	—
99	C₄	—	8	2	no	—
100	C₄	—	344	2	no	—
101	C₄	#13063256	1	8	yes	complemented
102	C₄	C₄⋊C₄×D₄₃	1	2	yes	—
103	C₄	#13063324	1	2	yes	—
104	C₂	#14582768	1	1	yes	characteristic
105	C₂	C₂×#13063256	1	2	yes	—
106	C₂	#14583271	1	1	yes	characteristic
107	C₂	#14583273	1	1	yes	characteristic
108	C₂	#14583295	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063256

C₂

yes

maximal

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

#14582769

C₂

yes

maximal, characteristic

C₄₃×#384

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063256

—

C₄×C₄₃⋊C₈

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

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

—

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

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

SD₁₆

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

C₂×SD₁₆

yes

—

C₂²×C₄₃

C₂×SD₁₆

yes

—

C₄×C₄₃

—

C₄×C₄₃

#106

yes

complemented

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×#106

—

C₂×C₄×C₈

—

#384

—

#384

D₄₃

yes

characteristic

C₄₃

#1844

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#106

—

C₄×C₈

—

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

—

172

—

C₄²

Dic₈₆

yes

—

C₄²

C₄×D₄₃

yes

—

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

Dic₄₃⋊C₄

yes

—

C₂×C₄

#10621883

yes

—

C₂×C₄

#10621884

yes

—

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

—

C₂×C₄

Q₈×D₄₃

yes

—

C₈

—

C₂²

C₂×Dic₄₃⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×#10621883

yes

—

C₄

—

100

C₄

—

344

—

101

C₄

#13063256

yes

complemented

102

C₄

C₄⋊C₄×D₄₃

yes

—

103

C₄

#13063324

yes

—

104

C₂

#14582768

yes

characteristic

105

C₂

C₂×#13063256

yes

—

106

C₂

#14583271

yes

characteristic

107

C₂

#14583273

yes

characteristic

108

C₂

#14583295

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#384	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#384	D₄₃
hypocenter	C₄₃	#1844
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#384

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
9. C₄×C₄₃⋊C₈	C₄	semidirect
38. C₄₃⋊C₈	C₄⋊C₄	semidirect
45. C₄×C₄₃	#106	semidirect
59. C₄₃	#1844	semidirect
101. C₄	#13063256	semidirect

H ≅ G/N

type

9. C₄×C₄₃⋊C₈

C₄

semidirect

38. C₄₃⋊C₈

C₄⋊C₄

semidirect

45. C₄×C₄₃

#106

semidirect

59. C₄₃

#1844

semidirect

101. C₄

#13063256

semidirect

Subgroups — #19134751

Conjugacy classes of subgroups

Complements