Group #19132494 — subgroups

Subgroups — #19132494

Order 5504.

144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14582956	C₂	1	1	yes	maximal, characteristic
2	#14582952	C₂	1	1	yes	maximal, characteristic
3	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
5	C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
6	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
7	C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
8	#13063236	—	2	1	no	—
9	C₄×C₄₃⋊C₈	—	2	1	no	—
10	C₂²×C₈×C₄₃	—	2	1	no	—
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	#97×C₄₃	—	2	1	no	—
13	#97×C₄₃	C₄	1	2	yes	—
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₄₃	—	2	4	no	—
18	C₂×C₈×C₄₃	—	2	2	no	—
19	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₄₃⋊C₈	—	2	2	no	—
24	C₂×C₄₃⋊C₈	—	2	2	no	—
25	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₃	—	2	2	no	—
27	C₂×C₄×C₄₃	—	2	2	no	—
28	C₂×C₄×C₄₃	—	4	1	no	—
29	C₂×C₄×C₄₃	C₄²	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	C₂²⋊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	C₈×C₄₃	—	2	4	no	—
36	C₄₃⋊C₈	—	4	2	no	—
37	C₄₃⋊C₈	—	4	2	no	—
38	C₂²×C₄₃	—	2	1	no	—
39	C₂²×C₄₃	—	2	1	no	—
40	C₂²×C₄₃	#95	1	1	yes	characteristic
41	C₂²×C₄₃	#108	1	2	yes	—
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	#104	1	2	yes	—
48	#1302	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	2	no	—
50	C₂×C₄₃	#339	1	1	yes	characteristic
51	C₂×C₄₃	#341	1	1	yes	characteristic
52	C₂×C₄₃	#344	1	1	yes	characteristic
53	#432	—	43	1	no	—
54	#431	—	43	1	no	—
55	C₂×#97	D₄₃	1	1	yes	characteristic
56	C₄₃	#1302	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	2	1	no	—
58	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
59	C₄⋊C₈	—	43	2	no	—
60	C₄⋊C₈	—	86	1	no	—
61	C₂²⋊C₈	—	43	2	no	—
62	C₂²⋊C₈	—	86	1	no	—
63	#97	—	2	1	no	—
64	#97	—	86	1	no	—
65	#97	Dic₄₃	1	2	yes	—
66	C₄×C₈	—	86	1	no	—
67	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
69	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
70	C₂×C₈	—	2	4	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	86	2	no	—
73	C₂×C₈	—	86	2	no	—
74	C₄²	C₄×D₄₃	1	1	yes	characteristic
75	C₄²	D₁₇₂	1	1	yes	characteristic
76	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
77	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
78	C₂³	Dic₄₃⋊C₄	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
83	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
84	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
85	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
86	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
88	C₈	—	2	4	no	—
89	C₈	—	172	2	no	—
90	C₈	—	172	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	C₄₃⋊#95	1	1	yes	characteristic
94	C₂²	#13063260	1	2	yes	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	2	1	no	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	#13063253	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	#14582659	1	1	yes	characteristic
103	C₂	#14582663	1	1	yes	characteristic
104	C₂	#14582671	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582956

C₂

yes

maximal, characteristic

#14582952

C₂

yes

maximal, characteristic

C₂×#97×C₄₃

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

C₄

yes

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

—

#97×C₄₃

C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

characteristic

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

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#95

yes

characteristic

C₂²×C₄₃

#108

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#104

yes

—

#1302

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

C₂×#97

D₄₃

yes

characteristic

C₄₃

#1302

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#97

Dic₄₃

yes

—

C₄×C₈

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₄×D₄₃

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₂³

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₃

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

—

172

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

C₄₃⋊#95

yes

characteristic

C₂²

#13063260

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₄

#13063253

yes

—

101

C₂

—

102

C₂

#14582659

yes

characteristic

103

C₂

#14582663

yes

characteristic

104

C₂

#14582671

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₄²
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂²×C₄₃	#95
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	#1302
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₄²

Frattini

C₂×C₄²

C₂×D₄₃

Fitting

C₂×#97×C₄₃

C₂

socle

C₂²×C₄₃

#95

hypercenter

C₂×#97

D₄₃

hypocenter

C₄₃

#1302

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
56. C₄₃	#1302	semidirect

H ≅ G/N

type

56. C₄₃

#1302

semidirect

Subgroups — #19132494

Conjugacy classes of subgroups

Complements