Group #19132680 — subgroups

Subgroups — #19132680

Order 5504.

132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13063265	C₂	1	1	yes	maximal, characteristic
2	#14582854	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	C₄	1	1	yes	characteristic
5	#13063284	C₄	1	1	yes	characteristic
6	#13063265	—	2	1	no	—
7	#13063265	C₄	1	2	yes	complemented
8	C₂×C₄₃⋊C₁₆	—	2	1	no	—
9	#13063235	—	2	1	no	—
10	C₈×Dic₄₃	—	2	1	no	—
11	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	M₃₂×C₄₃	—	2	1	no	—
13	M₃₂×C₄₃	—	2	1	no	—
14	C₂×C₁₆×C₄₃	C₄	1	2	yes	complemented
15	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
22	C₂²⋊Dic₄₃	C₈	1	2	yes	—
23	C₄⋊Dic₄₃	—	2	1	no	—
24	C₄×Dic₄₃	—	2	1	no	—
25	#10621877	—	2	1	no	—
26	#10621877	C₈	1	2	yes	—
27	C₂×C₄₃⋊C₈	—	2	1	no	—
28	C₁₆×C₄₃	—	2	2	no	—
29	C₄₃⋊C₁₆	—	2	2	no	—
30	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
37	C₂×Dic₄₃	—	2	2	no	—
38	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
42	C₄₃⋊C₈	—	2	2	no	—
43	C₂²×C₄₃	—	4	1	no	—
44	C₂²×C₄₃	C₄×C₈	1	1	yes	characteristic
45	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₄₃	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₄₃	#95	1	1	yes	characteristic
48	C₄×C₄₃	#97	1	1	yes	characteristic
49	C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
50	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
51	Dic₄₃	—	4	2	no	—
52	#1378	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	—	2	1	no	—
54	C₂×C₄₃	—	2	1	no	—
55	C₂×C₄₃	—	2	1	no	—
56	C₂×C₄₃	#336	1	1	yes	characteristic
57	C₂×M₃₂	—	43	1	no	—
58	C₂×M₃₂	D₄₃	1	1	yes	characteristic
59	#405	—	43	1	no	—
60	C₄₃	#1378	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	43	1	no	—
62	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
63	#117	—	43	1	no	—
64	M₃₂	—	2	1	no	—
65	M₃₂	—	2	1	no	—
66	M₃₂	—	43	2	no	—
67	M₃₂	—	86	1	no	—
68	C₂×C₁₆	—	86	1	no	—
69	C₂×C₁₆	Dic₄₃	1	2	yes	complemented
70	#97	—	86	1	no	—
71	C₄×C₈	—	86	1	no	—
72	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
73	M₁₆	—	43	2	no	—
74	M₁₆	—	86	1	no	—
75	C₂×C₈	—	86	1	no	—
76	C₂×C₈	Dic₈₆	1	1	yes	characteristic
77	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
78	C₂×C₈	D₁₇₂	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
82	C₄⋊C₄	—	86	1	no	—
83	C₂²⋊C₄	—	43	2	no	—
84	C₄²	—	86	1	no	—
85	C₁₆	—	2	2	no	—
86	C₁₆	—	86	2	no	—
87	C₂³	C₈×D₄₃	1	1	yes	characteristic
88	C₂×C₄	—	86	2	no	—
89	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
90	C₂×C₄	#10621872	1	1	yes	characteristic
91	C₂×C₄	#10621872	1	1	yes	characteristic
92	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
93	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
94	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
95	C₈	—	86	2	no	—
96	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
97	C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
98	C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
99	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
100	C₂²	—	4	1	no	—
101	C₂²	C₈×Dic₄₃	1	1	yes	characteristic
102	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
103	C₂²	Dic₄₃⋊C₈	1	1	yes	characteristic
104	C₄	—	172	2	no	—
105	C₄	C₄₃⋊#95	1	1	yes	characteristic
106	C₄	#13063235	1	1	yes	characteristic
107	C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
108	C₄	Dic₄₃⋊C₈	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#14582653	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063265

C₂

yes

maximal, characteristic

#14582854

C₂

yes

maximal, characteristic

C₂×M₃₂×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₄

yes

characteristic

#13063284

C₄

yes

characteristic

#13063265

—

#13063265

C₄

yes

complemented

C₂×C₄₃⋊C₁₆

—

#13063235

—

C₈×Dic₄₃

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₄

yes

complemented

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

characteristic

C₂²⋊Dic₄₃

C₈

yes

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

C₈

yes

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×C₈

yes

characteristic

C₂²×C₄₃

C₂²⋊C₈

yes

characteristic

C₂²×C₄₃

C₄⋊C₈

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₄×C₄₃

C₄⋊C₈

yes

characteristic

Dic₄₃

—

#1378

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#336

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

D₄₃

yes

characteristic

#405

—

C₄₃

#1378

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

Dic₄₃

yes

complemented

#97

—

C₄×C₈

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

C₈×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

Dic₄₃⋊C₄

yes

characteristic

C₈

C₄⋊Dic₄₃

yes

characteristic

C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

C₂²⋊Dic₄₃

yes

characteristic

100

C₂²

—

101

C₂²

C₈×Dic₄₃

yes

characteristic

102

C₂²

(C₂×D₄₃)⋊C₈

yes

characteristic

103

C₂²

Dic₄₃⋊C₈

yes

characteristic

104

C₄

—

172

—

105

C₄

C₄₃⋊#95

yes

characteristic

106

C₄

#13063235

yes

characteristic

107

C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

108

C₄

Dic₄₃⋊C₈

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#14582653

yes

characteristic

	subgroup	G/H
center	C₈	C₂²⋊Dic₄₃
commutator	C₂²×C₄₃	C₄×C₈
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₂×M₃₂×C₄₃	C₂
socle	C₂×C₄₃	#336
hypercenter	C₂×M₃₂	D₄₃
hypocenter	C₄₃	#1378
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₈

C₂²⋊Dic₄₃

commutator

C₂²×C₄₃

C₄×C₈

Frattini

C₂²×C₈

C₂×D₄₃

Fitting

C₂×M₃₂×C₄₃

C₂

socle

C₂×C₄₃

#336

hypercenter

C₂×M₃₂

D₄₃

hypocenter

C₄₃

#1378

LCS

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
7. #13063265	C₄	semidirect
14. C₂×C₁₆×C₄₃	C₄	semidirect
60. C₄₃	#1378	semidirect
69. C₂×C₁₆	Dic₄₃	semidirect

H ≅ G/N

type

7. #13063265

C₄

semidirect

14. C₂×C₁₆×C₄₃

C₄

semidirect

60. C₄₃

#1378

semidirect

69. C₂×C₁₆

Dic₄₃

semidirect

Subgroups — #19132680

Conjugacy classes of subgroups

Complements