Group #19137701 — subgroups

Subgroups — #19137701

Order 5504.

448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 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	#14582785	C₂	1	4	yes	maximal
2	#14582785	C₂	1	4	yes	maximal
3	C₄⋊C₄×Dic₄₃	C₂	1	4	yes	maximal
4	#14582745	C₂	1	2	yes	maximal
5	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
7	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
8	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
9	C₄₃⋊#95	C₂²	1	4	yes	—
10	C₄₃⋊#95	C₂²	1	2	yes	—
11	C₄₃⋊#95	C₂²	1	4	yes	—
12	C₄₃⋊#95	C₂²	1	4	yes	—
13	C₄₃⋊#95	C₂²	1	2	yes	—
14	#125×C₄₃	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
21	C₂²×Dic₄₃	C₂³	1	4	yes	—
22	C₂²×Dic₄₃	C₂³	1	4	yes	—
23	C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
24	C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
25	C₄²×C₄₃	C₂×C₄	1	4	yes	—
26	C₄⋊Dic₄₃	—	2	8	no	—
27	C₄×Dic₄₃	—	2	8	no	—
28	C₄×Dic₄₃	—	2	8	no	—
29	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	4	no	—
31	C₂×C₄×C₄₃	—	2	4	no	—
32	C₂×C₄×C₄₃	—	2	4	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
35	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
37	C₂×Dic₄₃	—	2	4	no	—
38	C₂×Dic₄₃	—	2	4	no	—
39	C₂×Dic₄₃	—	2	4	no	—
40	C₂×Dic₄₃	—	2	4	no	—
41	C₂×Dic₄₃	—	2	4	no	—
42	C₂×Dic₄₃	#41	1	8	yes	—
43	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
44	C₂²×C₄₃	C₂×#41	1	4	yes	—
45	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
46	C₄×C₄₃	—	2	4	no	—
47	C₄×C₄₃	—	2	8	no	—
48	C₄×C₄₃	—	2	2	no	—
49	Dic₄₃	—	2	8	no	—
50	Dic₄₃	—	4	4	no	—
51	#2371	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	C₄×#41	1	2	yes	—
53	C₂×C₄₃	#519	1	1	yes	characteristic
54	C₂×C₄₃	#552	1	4	yes	—
55	C₂×#125	D₄₃	1	1	yes	characteristic
56	#387	—	43	4	no	—
57	#387	—	43	4	no	—
58	C₄×C₄⋊C₄	—	43	4	no	—
59	#376	—	43	2	no	—
60	C₄₃	#2371	1	1	yes	characteristic, complemented, Sylow
61	#125	Dic₄₃	1	8	yes	complemented
62	C₂×C₄⋊C₄	—	43	4	no	—
63	C₂×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
64	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
65	C₂×C₄²	—	43	4	no	—
66	C₂×C₄²	—	43	4	no	—
67	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
68	#95	—	43	2	no	—
69	#95	—	43	4	no	—
70	#95	—	43	2	no	—
71	#95	—	43	4	no	—
72	#95	—	43	4	no	—
73	C₂²×C₄	—	43	4	no	—
74	C₂²×C₄	—	43	4	no	—
75	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
76	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
77	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
78	C₄⋊C₄	—	86	8	no	—
79	C₄⋊C₄	C₂×Dic₄₃	1	16	yes	—
80	C₄⋊C₄	C₂×Dic₄₃	1	8	yes	—
81	C₄²	—	86	8	no	—
82	C₄²	—	86	8	no	—
83	C₄²	C₂×Dic₄₃	1	4	yes	—
84	C₂³	C₂³×D₄₃	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	43	8	no	—
90	C₂×C₄	—	86	4	no	—
91	C₂×C₄	—	86	4	no	—
92	C₂×C₄	—	86	4	no	—
93	C₂×C₄	—	86	4	no	—
94	C₂×C₄	—	86	4	no	—
95	C₂×C₄	C₂²×Dic₄₃	1	4	yes	—
96	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
97	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
98	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
99	C₂²	#41×D₄₃	1	4	yes	—
100	C₂²	#13063373	1	2	yes	—
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	2	2	no	—
104	C₄	—	86	8	no	—
105	C₄	—	172	4	no	—
106	C₂	#41×Dic₄₃	1	2	yes	—
107	C₂	#14583377	1	1	yes	characteristic
108	C₂	#14583581	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582785

C₂

yes

maximal

#14582785

C₂

yes

maximal

C₄⋊C₄×Dic₄₃

C₂

yes

maximal

#14582745

C₂

yes

maximal

C₂×#125×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

#125×C₄₃

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#41

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2371

—

maximal, Sylow

C₂×C₄₃

C₄×#41

yes

—

C₂×C₄₃

#519

yes

characteristic

C₂×C₄₃

#552

yes

—

C₂×#125

D₄₃

yes

characteristic

#387

—

#387

—

C₄×C₄⋊C₄

—

#376

—

C₄₃

#2371

yes

characteristic, complemented, Sylow

#125

Dic₄₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×Dic₄₃

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂²

C₂³×Dic₄₃

yes

characteristic

C₂²

#41×D₄₃

yes

—

100

C₂²

#13063373

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

172

—

106

C₂

#41×Dic₄₃

yes

—

107

C₂

#14583377

yes

characteristic

108

C₂

#14583581

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₂×#125×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	#2371
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₂×#125×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
14. #125×C₄₃	C₄	semidirect
60. C₄₃	#2371	semidirect
61. #125	Dic₄₃	semidirect

H ≅ G/N

type

14. #125×C₄₃

C₄

semidirect

60. C₄₃

#2371

semidirect

61. #125

Dic₄₃

semidirect

Subgroups — #19137701

Conjugacy classes of subgroups

Complements