Group #19132439 — subgroups

Subgroups — #19132439

Order 5504.

152 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 77 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	#14582952	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063236	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#431	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₈	C₄	1	2	yes	—
5	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
7	#13063236	—	2	1	no	—
8	#13063236	—	2	1	no	—
9	C₄×C₄₃⋊C₈	—	2	1	no	—
10	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₄₃	—	2	1	no	—
12	C₂²⋊C₈×C₄₃	C₄	1	2	yes	—
13	C₄×C₈×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	—	2	2	no	—
18	C₄²×C₄₃	D₄	1	1	yes	characteristic
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	C₄²×C₄₃	D₄	1	1	yes	characteristic
21	C₄²×C₄₃	Q₈	1	1	yes	characteristic
22	C₂×C₄₃⋊C₈	—	2	2	no	—
23	C₂×C₄₃⋊C₈	—	2	2	no	—
24	C₂×C₄₃⋊C₈	—	2	2	no	—
25	C₂×C₄₃⋊C₈	C₈	1	4	yes	complemented
26	C₂³×C₄₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	—	4	1	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₄₃	M₁₆	1	2	yes	—
37	C₈×C₄₃	—	4	2	no	—
38	C₄₃⋊C₈	—	2	4	no	—
39	C₄₃⋊C₈	—	4	2	no	—
40	C₂²×C₄₃	—	2	1	no	—
41	C₂²×C₄₃	—	2	1	no	—
42	C₂²×C₄₃	#95	1	1	yes	characteristic
43	C₂²×C₄₃	C₄×C₈	1	1	yes	characteristic
44	C₂²×C₄₃	#97	1	1	yes	characteristic
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
50	C₄×C₄₃	C₄⋊C₈	1	2	yes	—
51	#1281	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	—	2	1	no	—
53	C₂×C₄₃	—	2	1	no	—
54	C₂×C₄₃	#336	1	1	yes	characteristic
55	C₂×C₄₃	#344	1	1	yes	characteristic
56	C₂×C₄₃	#344	1	1	yes	characteristic
57	#431	—	43	1	no	—
58	#431	D₄₃	1	1	yes	characteristic
59	C₂×#97	—	43	1	no	—
60	C₄₃	#1281	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₈	—	43	2	no	—
62	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
63	C₄⋊C₈	—	2	1	no	—
64	C₄⋊C₈	—	86	1	no	—
65	C₂²⋊C₈	—	43	2	no	—
66	C₂²⋊C₈	Dic₄₃	1	2	yes	—
67	#97	—	86	1	no	—
68	#97	—	86	1	no	—
69	C₄×C₈	—	2	1	no	—
70	C₄×C₈	—	86	1	no	—
71	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
72	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
73	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	43	4	no	—
76	C₂×C₈	—	86	2	no	—
77	C₂×C₈	—	86	2	no	—
78	C₂×C₈	—	86	2	no	—
79	C₄²	Dic₈₆	1	1	yes	characteristic
80	C₄²	D₁₇₂	1	1	yes	characteristic
81	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
82	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
83	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	C₈×D₄₃	1	2	yes	—
87	C₂×C₄	#10621872	1	2	yes	—
88	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
89	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
90	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
91	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
92	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
93	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
94	C₈	—	4	2	no	—
95	C₈	—	86	4	no	—
96	C₈	—	172	2	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	C₄₃⋊#95	1	1	yes	characteristic
100	C₂²	C₈×Dic₄₃	1	1	yes	characteristic
101	C₂²	#13063235	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
107	C₄	Dic₄₃⋊C₈	1	2	yes	—
108	C₂	—	2	1	no	—
109	C₂	—	2	1	no	—
110	C₂	#14582653	1	1	yes	characteristic
111	C₂	#14582669	1	1	yes	characteristic
112	C₂	#14582671	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582952

C₂

yes

maximal, characteristic

C₂×#13063236

C₂

yes

maximal, characteristic

C₄₃×#431

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

C₄

yes

—

#13063236

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

C₄

yes

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₈

yes

complemented

C₂³×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

M₁₆

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#95

yes

characteristic

C₂²×C₄₃

C₄×C₈

yes

characteristic

C₂²×C₄₃

#97

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊C₈

yes

—

C₄×C₄₃

C₄⋊C₈

yes

—

#1281

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₂×#97

—

C₄₃

#1281

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₄₃

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₈₆

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₂³

C₄×Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

—

C₂×C₄

#10621872

yes

—

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

C₄₃⋊#95

yes

characteristic

100

C₂²

C₈×Dic₄₃

yes

characteristic

101

C₂²

#13063235

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

(C₂×D₄₃)⋊C₈

yes

—

107

C₄

Dic₄₃⋊C₈

yes

—

108

C₂

—

109

C₂

—

110

C₂

#14582653

yes

characteristic

111

C₂

#14582669

yes

characteristic

112

C₂

#14582671

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₄×C₈
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₄₃×#431	C₂
socle	C₂²×C₄₃	#95
hypercenter	#431	D₄₃
hypocenter	C₄₃	#1281
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

(C₂×D₄₃)⋊C₄

commutator

C₂²×C₄₃

C₄×C₈

Frattini

C₂×C₄²

C₂×D₄₃

Fitting

C₄₃×#431

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
25. C₂×C₄₃⋊C₈	C₈	semidirect
60. C₄₃	#1281	semidirect

H ≅ G/N

type

25. C₂×C₄₃⋊C₈

C₈

semidirect

60. C₄₃

#1281

semidirect

Subgroups — #19132439

Conjugacy classes of subgroups

Complements