Group #19132530 — subgroups

Subgroups — #19132530

Order 5504.

128 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 33 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	#14582862	C₂	1	1	yes	maximal, characteristic
2	#14582681	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄₃	C₄	1	1	yes	characteristic
5	C₂×#10621877	C₄	1	1	yes	characteristic
6	#13063265	—	2	1	no	—
7	(C₂×D₄₃)⋊C₈	—	2	1	no	—
8	(C₂×D₄₃)⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	M₃₂×C₄₃	—	2	1	no	—
11	C₂³×D₄₃	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₄₃	C₈	1	1	yes	characteristic
14	C₂×C₄×D₄₃	—	2	1	no	—
15	C₂×C₄×D₄₃	—	2	1	no	—
16	C₂×C₄×D₄₃	—	4	1	no	—
17	C₂×C₄×D₄₃	—	4	1	no	—
18	M₁₆×C₄₃	—	4	1	no	—
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	#10621877	—	4	1	no	—
22	C₂×C₄₃⋊C₈	—	2	1	no	—
23	C₁₆×C₄₃	—	4	1	no	—
24	C₄₃⋊C₁₆	—	4	1	no	—
25	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
26	C₂²×D₄₃	—	2	1	no	—
27	C₂²×D₄₃	—	4	2	no	—
28	C₂²×D₄₃	—	4	1	no	—
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
33	C₂×Dic₄₃	—	2	1	no	—
34	C₂×Dic₄₃	—	4	1	no	—
35	C₄×D₄₃	—	4	2	no	—
36	C₄×D₄₃	—	4	1	no	—
37	C₄×D₄₃	—	4	1	no	—
38	C₈×C₄₃	—	2	1	no	—
39	C₈×C₄₃	—	2	1	no	—
40	C₄₃⋊C₈	—	4	1	no	—
41	C₂²×C₄₃	—	2	1	no	—
42	C₂²×C₄₃	—	4	1	no	—
43	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₂×D₄₃	—	2	2	no	—
45	C₂×D₄₃	—	4	1	no	—
46	C₂×D₄₃	—	4	2	no	—
47	C₂×D₄₃	—	4	1	no	—
48	C₂×D₄₃	—	4	2	no	—
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	#99	1	1	yes	characteristic
51	C₄×C₄₃	#100	1	1	yes	characteristic
52	Dic₄₃	—	4	1	no	—
53	#1320	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	—	2	1	no	—
55	C₂×C₄₃	—	4	1	no	—
56	C₂×C₄₃	#323	1	1	yes	characteristic
57	D₄₃	—	4	2	no	—
58	#407	—	43	1	no	—
59	#349	—	43	1	no	—
60	#349	D₄₃	1	1	yes	characteristic, complemented
61	C₄₃	#1320	1	1	yes	characteristic, complemented, Sylow
62	C₂³×C₄	—	43	1	no	—
63	C₂×M₁₆	—	43	1	no	—
64	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
65	M₃₂	—	2	1	no	—
66	M₃₂	—	86	1	no	—
67	C₂²⋊C₈	—	86	1	no	—
68	C₂²⋊C₈	—	86	1	no	—
69	C₂⁴	—	43	1	no	—
70	C₂²×C₄	—	43	1	no	—
71	C₂²×C₄	—	86	1	no	—
72	C₂²×C₄	—	86	1	no	—
73	C₂²×C₄	—	172	1	no	—
74	C₂²×C₄	—	172	1	no	—
75	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
76	M₁₆	—	4	1	no	—
77	M₁₆	—	172	1	no	—
78	C₂×C₈	—	86	1	no	—
79	C₂×C₈	D₁₇₂	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₁₆	—	4	1	no	—
82	C₁₆	—	172	1	no	—
83	C₂³	—	86	1	no	—
84	C₂³	—	172	1	no	—
85	C₂³	—	172	2	no	—
86	C₂³	C₈×D₄₃	1	1	yes	characteristic
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	86	1	no	—
90	C₂×C₄	—	172	2	no	—
91	C₂×C₄	—	172	1	no	—
92	C₂×C₄	—	172	1	no	—
93	C₂×C₄	—	172	1	no	—
94	C₂×C₄	#10621872	1	1	yes	characteristic
95	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	2	1	no	—
98	C₈	—	172	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	4	1	no	—
101	C₂²	—	86	2	no	—
102	C₂²	—	172	1	no	—
103	C₂²	—	172	2	no	—
104	C₂²	—	172	2	no	—
105	C₂²	—	172	1	no	—
106	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	172	1	no	—
109	C₄	#13063239	1	1	yes	characteristic
110	C₄	#13063241	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	4	1	no	—
113	C₂	—	172	2	no	—
114	C₂	#14582622	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582862

C₂

yes

maximal, characteristic

#14582681

C₂

yes

maximal, characteristic, complemented

C₄₃×#349

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₄

yes

characteristic

C₂×#10621877

C₄

yes

characteristic

#13063265

—

(C₂×D₄₃)⋊C₈

—

(C₂×D₄₃)⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

—

C₂³×D₄₃

C₈

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₈

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1320

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#323

yes

characteristic

D₄₃

—

#407

—

#349

—

#349

D₄₃

yes

characteristic, complemented

C₄₃

#1320

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

172

—

C₂³

—

C₂³

—

172

—

C₂³

—

172

—

C₂³

C₈×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621872

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

172

—

103

C₂²

—

172

—

104

C₂²

—

172

—

105

C₂²

—

172

—

106

C₂²

(C₂×D₄₃)⋊C₈

yes

characteristic

107

C₄

—

108

C₄

—

172

—

109

C₄

#13063239

yes

characteristic

110

C₄

#13063241

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

—

172

—

114

C₂

#14582622

yes

characteristic

	subgroup	G/H
center	C₄	#13063239
commutator	C₂³×C₄₃	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₄₃
Fitting	C₄₃×#349	C₂
socle	C₂×C₄₃	#323
hypercenter	#349	D₄₃
hypocenter	C₄₃	#1320
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₄

#13063239

commutator

C₂³×C₄₃

C₂×C₈

Frattini

C₂×M₁₆

C₂×D₄₃

Fitting

C₄₃×#349

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
2. #14582681	C₂	semidirect
3. C₄₃×#349	C₂	semidirect
60. #349	D₄₃	semidirect
61. C₄₃	#1320	semidirect

H ≅ G/N

type

2. #14582681

C₂

semidirect

3. C₄₃×#349

C₂

semidirect

60. #349

D₄₃

semidirect

61. C₄₃

#1320

semidirect

Subgroups — #19132530

Conjugacy classes of subgroups

Complements