Group #14562415 — subgroups

Subgroups — #14562415

Order 2432.

150 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 81 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	#11926601	C₂	1	1	yes	maximal, characteristic
2	#11926597	C₂	1	1	yes	maximal, characteristic
3	#11926297	C₂	1	2	yes	maximal, complemented
4	#11926295	C₂	1	2	yes	maximal, complemented
5	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊C₈	C₄	1	2	yes	—
8	C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
9	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
12	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
15	#10597260	—	2	1	no	—
16	C₄×C₁₉⋊C₈	—	2	1	no	—
17	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₄²×C₁₉	Q₈	1	1	yes	characteristic
25	C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₁₉⋊C₈	—	2	2	no	—
27	C₂×C₁₉⋊C₈	—	2	2	no	—
28	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₈×C₁₉	—	2	2	no	—
39	C₈×C₁₉	—	2	2	no	—
40	C₁₉⋊C₈	—	4	2	no	—
41	C₁₉⋊C₈	—	4	2	no	—
42	#1572	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	2	1	no	—
46	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	#131	1	2	yes	—
52	C₄×C₁₉	#135	1	2	yes	—
53	#432	—	19	1	no	—
54	#431	—	19	1	no	—
55	#431	D₁₉	1	1	yes	characteristic
56	#335	—	19	2	no	—
57	#334	—	19	2	no	—
58	C₂×C₁₉	—	4	1	no	—
59	C₂×C₁₉	#424	1	1	yes	characteristic
60	C₂×C₁₉	#427	1	1	yes	characteristic
61	C₂×C₁₉	#430	1	1	yes	characteristic
62	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
63	C₄⋊C₈	—	19	2	no	—
64	C₄⋊C₈	—	19	2	no	—
65	C₄⋊C₈	Dic₁₉	1	2	yes	—
66	C₂²⋊C₈	—	38	1	no	—
67	C₂²⋊C₈	—	38	1	no	—
68	C₂²⋊C₈	Dic₁₉	1	2	yes	—
69	#97	—	38	1	no	—
70	C₄×C₈	—	38	1	no	—
71	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
72	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₁₉	#1572	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
75	C₂²×C₄	D₇₆	1	1	yes	characteristic
76	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
77	C₂×C₈	—	38	2	no	—
78	C₂×C₈	—	38	2	no	—
79	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
80	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
81	C₄²	Dic₃₈	1	1	yes	characteristic
82	C₄²	D₇₆	1	1	yes	characteristic
83	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
84	C₄²	C₂²×D₁₉	1	1	yes	characteristic
85	C₂³	C₄⋊Dic₁₉	1	1	yes	characteristic
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	4	1	no	—
89	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
90	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
92	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
93	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
94	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
95	C₈	—	2	2	no	—
96	C₈	—	2	2	no	—
97	C₈	—	76	2	no	—
98	C₈	—	76	2	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	#10597350	1	2	yes	—
108	C₄	#10597394	1	2	yes	—
109	C₂	—	4	1	no	—
110	C₂	#11926571	1	1	yes	characteristic
111	C₂	#11926582	1	1	yes	characteristic
112	C₂	#11926593	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic

#11926597

C₂

yes

maximal, characteristic

#11926297

C₂

yes

maximal, complemented

#11926295

C₂

yes

maximal, complemented

C₁₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₄

yes

—

C₁₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

Q₈

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1572

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

#135

yes

—

#432

—

#431

—

#431

D₁₉

yes

characteristic

#335

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

Dic₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₁₉

yes

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1572

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₄²

Dic₃₈

yes

characteristic

C₄²

D₇₆

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₂×Dic₃₈

yes

characteristic

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

#10597350

yes

—

108

C₄

#10597394

yes

—

109

C₂

—

110

C₂

#11926571

yes

characteristic

111

C₂

#11926582

yes

characteristic

112

C₂

#11926593

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#431	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₄⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#431	D₁₉
hypocenter	C₁₉	#1572
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#431

C₂

socle

C₂²×C₁₉

C₂×C₄⋊C₄

prime radical

C₂³×C₁₉

C₄⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
3. #11926297	C₂	semidirect
4. #11926295	C₂	semidirect
73. C₁₉	#1572	semidirect

H ≅ G/N

type

3. #11926297

C₂

semidirect

4. #11926295

C₂

semidirect

73. C₁₉

#1572

semidirect

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

subgroup	index
#11926601	2
#11926597	2
#11926297	2
#11926295	2
C₁₉×#431	2
#1572	19

subgroup

index

C₁₉×#431

Subgroups — #14562415

Conjugacy classes of subgroups

Complements

Maximal subgroups