Group #14572244 — subgroups

Subgroups — #14572244

Order 2432.

440 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 249 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	#11927311	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597394	C₂	1	1	yes	maximal, characteristic
3	#11926592	C₂	1	6	yes	maximal, complemented
4	C₂×#10597279	C₂	1	6	yes	maximal, complemented
5	C₁₉×#568	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#131	—	2	4	no	—
8	C₂×M₁₆×C₁₉	C₂²	1	6	yes	—
9	#10597394	—	2	4	no	—
10	#10597394	C₄	1	8	yes	—
11	C₂×#64520	C₂²	1	6	yes	—
12	C₂×#64520	C₂²	1	3	yes	—
13	C₂²×C₁₉⋊C₈	C₂²	1	3	yes	—
14	#10597279	C₂²	1	4	yes	—
15	#10597279	C₂²	1	12	yes	—
16	#41×C₁₉	C₂×C₄	1	4	yes	—
17	#41×C₁₉	D₄	1	4	yes	—
18	C₂×Q₈×C₁₉	Q₈	1	1	yes	characteristic
19	C₂×D₄×C₁₉	Q₈	1	3	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
21	M₁₆×C₁₉	—	2	6	no	—
22	M₁₆×C₁₉	C₂³	1	4	yes	—
23	C₂×C₈×C₁₉	—	2	6	no	—
24	#64520	—	2	6	no	—
25	#64520	C₂×C₄	1	12	yes	—
26	#64520	C₂³	1	4	yes	—
27	C₂×C₁₉⋊C₈	—	2	6	no	—
28	C₂×C₁₉⋊C₈	C₂×C₄	1	12	yes	—
29	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
30	C₂×C₁₉⋊C₈	C₂³	1	3	yes	—
31	C₂³×C₁₉	C₂×Q₈	1	3	yes	—
32	Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
33	D₄×C₁₉	C₄⋊C₄	1	12	yes	—
34	C₂×C₄×C₁₉	C₂²×C₄	1	6	yes	—
35	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
36	C₂×C₄×C₁₉	C₂×Q₈	1	3	yes	—
37	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
38	C₈×C₁₉	—	2	4	no	—
39	C₁₉⋊C₈	—	2	4	no	—
40	C₁₉⋊C₈	C₂²×C₄	1	2	yes	—
41	C₁₉⋊C₈	C₂²×C₄	1	6	yes	—
42	#2916	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	4	3	no	—
44	C₂²×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
45	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
46	C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
47	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
48	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
49	#568	—	19	1	no	—
50	#568	D₁₉	1	1	yes	characteristic
51	C₂×#131	—	19	1	no	—
52	#430	—	19	6	no	—
53	C₂×#108	—	19	6	no	—
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	—	2	6	no	—
56	C₂×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
57	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
58	#131	—	2	4	no	—
59	#131	—	19	8	no	—
60	#131	—	38	4	no	—
61	C₂×M₁₆	—	19	3	no	—
62	C₂×M₁₆	—	19	6	no	—
63	C₂×M₁₆	C₂×D₁₉	1	6	yes	—
64	C₂²×C₈	—	19	3	no	—
65	#108	—	19	4	no	—
66	#108	—	19	12	no	—
67	C₁₉	#2916	1	1	yes	characteristic, complemented, Sylow
68	#41	C₄×D₁₉	1	4	yes	—
69	#41	C₂²⋊D₁₉	1	4	yes	—
70	C₂×Q₈	Dic₃₈	1	1	yes	characteristic
71	C₂×D₄	Dic₃₈	1	3	yes	—
72	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
73	M₁₆	—	2	6	no	—
74	M₁₆	—	19	12	no	—
75	M₁₆	—	19	4	no	—
76	M₁₆	—	38	6	no	—
77	M₁₆	C₂²×D₁₉	1	4	yes	—
78	C₂×C₈	—	2	6	no	—
79	C₂×C₈	—	19	12	no	—
80	C₂×C₈	—	19	1	no	—
81	C₂×C₈	—	19	3	no	—
82	C₂×C₈	—	38	6	no	—
83	C₂³	C₂×Dic₃₈	1	3	yes	—
84	Q₈	Dic₁₉⋊C₄	1	4	yes	—
85	D₄	Dic₁₉⋊C₄	1	12	yes	—
86	C₂×C₄	C₂×Dic₃₈	1	3	yes	—
87	C₂×C₄	C₂×C₄×D₁₉	1	6	yes	—
88	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
89	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	19	2	no	—
92	C₈	—	19	6	no	—
93	C₈	—	38	4	no	—
94	C₂²	—	4	3	no	—
95	C₂²	C₂×Dic₁₉⋊C₄	1	6	yes	—
96	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
97	C₄	C₂×Dic₁₉⋊C₄	1	6	yes	—
98	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
99	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	2	6	no	—
102	C₂	C₂²×Dic₁₉⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927311

C₂

yes

maximal, characteristic

C₂×#10597394

C₂

yes

maximal, characteristic

#11926592

C₂

yes

maximal, complemented

C₂×#10597279

C₂

yes

maximal, complemented

C₁₉×#568

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₁₉×#131

—

C₂×M₁₆×C₁₉

C₂²

yes

—

#10597394

—

#10597394

C₄

yes

—

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597279

C₂²

yes

—

#10597279

C₂²

yes

—

#41×C₁₉

C₂×C₄

yes

—

#41×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

Q₈

yes

characteristic

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

—

#64520

—

#64520

C₂×C₄

yes

—

#64520

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

Q₈×C₁₉

C₄⋊C₄

yes

—

D₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²×C₄

yes

—

C₁₉⋊C₈

C₂²×C₄

yes

—

#2916

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₄×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

#568

—

#568

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×C₄⋊C₄

yes

characteristic

C₂×#41

C₂×D₁₉

yes

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

#108

—

#108

—

C₁₉

#2916

yes

characteristic, complemented, Sylow

#41

C₄×D₁₉

yes

—

#41

C₂²⋊D₁₉

yes

—

C₂×Q₈

Dic₃₈

yes

characteristic

C₂×D₄

Dic₃₈

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂²×D₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂³

C₂×Dic₃₈

yes

—

Q₈

Dic₁₉⋊C₄

yes

—

D₄

Dic₁₉⋊C₄

yes

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×C₄×D₁₉

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

C₂×C₄

C₂³×D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₂×Dic₁₉⋊C₄

yes

—

C₂²

C₂²×Dic₃₈

yes

characteristic

C₄

C₂×Dic₁₉⋊C₄

yes

—

C₄

C₂²×C₄×D₁₉

yes

characteristic

C₄

C₂²×C₂²⋊D₁₉

yes

characteristic

100

C₂

—

101

C₂

—

102

C₂

C₂²×Dic₁₉⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₂²×C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#568	C₂
socle	C₂×C₁₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#568	D₁₉
hypocenter	C₁₉	#2916
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #568

subgroup

G/H

center

C₄

C₂²×C₂²⋊D₁₉

commutator

C₄×C₁₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#568

C₂

socle

C₂×C₁₉

C₂²×C₄⋊C₄

prime radical

C₂×#41×C₁₉

C₂²

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×#41 ◁ #568

N	H ≅ G/N	type
3. #11926592	C₂	semidirect
4. C₂×#10597279	C₂	semidirect
67. C₁₉	#2916	semidirect

H ≅ G/N

type

3. #11926592

C₂

semidirect

4. C₂×#10597279

C₂

semidirect

67. C₁₉

#2916

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11927311	2
C₂×#10597394	2
#11926592	2
C₂×#10597279	2
C₁₉×#568	2
#2916	19

subgroup

index

C₁₉×#568

Subgroups — #14572244

Conjugacy classes of subgroups

Complements

Maximal subgroups