Group #19137181 — subgroups

Subgroups — #19137181

Order 5504.

784 conjugacy classes of subgroups; only the 309 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 309 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×#13063284	C₂	1	2	yes	maximal
2	#14582806	C₂	1	8	yes	maximal, complemented
3	#14582762	C₂	1	4	yes	maximal
4	C₂³×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	#13063284	—	2	8	no	—
6	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
7	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
8	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
9	C₄₃⋊#95	C₂²	1	16	yes	—
10	C₂²×Q₈×C₄₃	—	2	8	no	—
11	C₂²×Q₈×C₄₃	C₄	1	8	yes	complemented
12	C₂²×Q₈×C₄₃	C₂²	1	4	yes	—
13	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
14	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×Q₈×C₄₃	—	2	32	no	—
17	C₂×Q₈×C₄₃	—	2	8	no	—
18	C₂×Q₈×C₄₃	—	2	8	no	—
19	C₂×Q₈×C₄₃	C₂×C₄	1	16	yes	—
20	C₂²×C₄×C₄₃	—	2	8	no	—
21	C₂²×C₄×C₄₃	C₂×C₄	1	8	yes	—
22	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₄₃	D₄	1	8	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂²×Dic₄₃	C₂³	1	8	yes	—
27	C₂²⋊Dic₄₃	—	2	8	no	—
28	C₄⋊Dic₄₃	—	2	8	no	—
29	C₄×Dic₄₃	—	2	8	no	—
30	C₂³×C₄₃	—	2	4	no	—
31	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
32	C₂³×C₄₃	C₂×D₄	1	4	yes	—
33	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
34	Q₈×C₄₃	—	2	32	no	—
35	C₂×C₄×C₄₃	—	2	16	no	—
36	C₂×C₄×C₄₃	—	2	8	no	—
37	C₂×C₄×C₄₃	C₂²⋊C₄	1	16	yes	—
38	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
40	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
42	C₂×Dic₄₃	—	2	8	no	—
43	C₂×Dic₄₃	—	2	16	no	—
44	C₂²×C₄₃	—	2	4	no	—
45	C₂²×C₄₃	—	2	8	no	—
46	C₂²×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
47	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
48	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
49	C₂²×C₄₃	2₋¹⁺⁴	1	4	yes	—
50	C₄×C₄₃	—	2	8	no	—
51	C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
52	Dic₄₃	—	4	8	no	—
53	#2310	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	—	2	4	no	—
55	C₂×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄₃	#519	1	2	yes	—
57	C₂×C₄₃	#536	1	4	yes	—
58	C₂³×Q₈	D₄₃	1	1	yes	characteristic
59	C₂×#117	—	43	2	no	—
60	#391	—	43	8	no	—
61	#381	—	43	4	no	—
62	C₄₃	#2310	1	1	yes	characteristic, complemented, Sylow
63	C₂²×Q₈	—	2	8	no	—
64	C₂²×Q₈	Dic₄₃	1	8	yes	complemented
65	C₂²×Q₈	C₂×D₄₃	1	4	yes	—
66	C₂³×C₄	C₂×D₄₃	1	2	yes	—
67	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
68	#117	—	86	8	no	—
69	C₂×C₄⋊C₄	—	43	4	no	—
70	C₂×C₂²⋊C₄	—	43	4	no	—
71	C₂×C₄²	—	43	4	no	—
72	#95	—	43	16	no	—
73	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
74	C₂×Q₈	—	2	32	no	—
75	C₂×Q₈	—	2	8	no	—
76	C₂×Q₈	—	2	8	no	—
77	C₂×Q₈	C₂×Dic₄₃	1	16	yes	—
78	C₂²×C₄	—	2	8	no	—
79	C₂²×C₄	—	43	8	no	—
80	C₂²×C₄	C₂×Dic₄₃	1	8	yes	—
81	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
82	C₂²×C₄	C₂²⋊D₄₃	1	8	yes	—
83	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
84	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
85	C₄⋊C₄	—	86	8	no	—
86	C₂²⋊C₄	—	86	8	no	—
87	C₄²	—	86	8	no	—
88	C₂³	—	2	4	no	—
89	C₂³	C₂²×Dic₄₃	1	2	yes	—
90	C₂³	C₂×C₂²⋊D₄₃	1	4	yes	—
91	C₂³	C₂³×D₄₃	1	1	yes	characteristic
92	Q₈	—	2	32	no	—
93	C₂×C₄	—	2	16	no	—
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	86	8	no	—
96	C₂×C₄	—	86	16	no	—
97	C₂×C₄	C₂²⋊Dic₄₃	1	16	yes	—
98	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
99	C₂×C₄	C₂²×Dic₄₃	1	4	yes	—
100	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
102	C₂²	—	2	4	no	—
103	C₂²	—	2	8	no	—
104	C₂²	C₂×C₂²⋊Dic₄₃	1	4	yes	—
105	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
106	C₂²	C₂²×C₂²⋊D₄₃	1	2	yes	—
107	C₂²	#13063373	1	4	yes	—
108	C₄	—	2	8	no	—
109	C₄	—	172	8	no	—
110	C₄	C₂×C₂²⋊Dic₄₃	1	8	yes	—
111	C₂	—	2	4	no	—
112	C₂	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
113	C₂	#14583377	1	2	yes	—
114	C₂	#14583473	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal

#14582806

C₂

yes

maximal, complemented

#14582762

C₂

yes

maximal

C₂³×Q₈×C₄₃

C₂

yes

maximal, characteristic

#13063284

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

C₄

yes

complemented

C₂²×Q₈×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

Q₈×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×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

Dic₄₃

—

#2310

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₄₃

#519

yes

—

C₂×C₄₃

#536

yes

—

C₂³×Q₈

D₄₃

yes

—

—

—

C₄₃

#2310

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

Dic₄₃

yes

complemented

C₂²×Q₈

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#95

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂²×Dic₄₃

yes

—

C₂³

C₂×C₂²⋊D₄₃

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

100

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

101

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊Dic₄₃

yes

—

105

C₂²

C₂³×Dic₄₃

yes

characteristic

106

C₂²

C₂²×C₂²⋊D₄₃

yes

—

107

C₂²

#13063373

yes

—

108

C₄

—

109

C₄

—

172

—

110

C₄

C₂×C₂²⋊Dic₄₃

yes

—

111

C₂

—

112

C₂

C₂²×C₂²⋊Dic₄₃

yes

characteristic

113

C₂

#14583377

yes

—

114

C₂

#14583473

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₂³×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂³×Q₈	D₄₃
hypocenter	C₄₃	#2310
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₂³×Q₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

hypercenter

C₂³×Q₈

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂³×Q₈

N	H ≅ G/N	type
2. #14582806	C₂	semidirect
11. C₂²×Q₈×C₄₃	C₄	semidirect
62. C₄₃	#2310	semidirect
64. C₂²×Q₈	Dic₄₃	semidirect

H ≅ G/N

type

2. #14582806

C₂

semidirect

11. C₂²×Q₈×C₄₃

C₄

semidirect

62. C₄₃

#2310

semidirect

64. C₂²×Q₈

Dic₄₃

semidirect

Subgroups — #19137181

Conjugacy classes of subgroups

Complements