Group #14561928 — subgroups

Subgroups — #14561928

Order 2432.

196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11926597	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#11926266	C₂	1	2	yes	maximal, complemented
4	#11926265	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	C₂²×C₁₉⋊C₈	C₄	1	2	yes	—
8	C₁₉×C₄⋊C₈	C₄	1	2	yes	—
9	C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
12	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
13	C₄×C₁₉⋊C₈	C₄	1	2	yes	—
14	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
21	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₁₉⋊C₈	—	2	4	no	—
26	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
27	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
28	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₂³×C₁₉	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	2	2	no	—
32	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
35	C₂×C₄×C₁₉	M₁₆	1	4	yes	—
36	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₈×C₁₉	—	2	4	no	—
40	C₁₉⋊C₈	—	2	2	no	—
41	C₁₉⋊C₈	—	2	2	no	—
42	C₁₉⋊C₈	—	2	4	no	—
43	#1452	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	2	1	no	—
46	C₂²×C₁₉	#97	1	2	yes	—
47	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	#97	1	2	yes	—
51	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
52	C₄×C₁₉	#131	1	2	yes	—
53	C₄×C₁₉	#131	1	2	yes	—
54	#431	—	19	1	no	—
55	#431	D₁₉	1	1	yes	characteristic
56	C₂×C₄×C₈	—	19	1	no	—
57	#322	—	19	2	no	—
58	#322	—	19	2	no	—
59	C₂×C₁₉	—	2	2	no	—
60	C₂×C₁₉	C₂×#97	1	1	yes	characteristic
61	C₂×C₁₉	#405	1	1	yes	characteristic
62	C₂×C₁₉	#405	1	1	yes	characteristic
63	C₂²×C₈	—	19	2	no	—
64	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
65	C₄⋊C₈	—	19	2	no	—
66	C₄⋊C₈	Dic₁₉	1	2	yes	—
67	C₂²⋊C₈	—	19	2	no	—
68	C₂²⋊C₈	Dic₁₉	1	2	yes	—
69	C₄×C₈	—	19	2	no	—
70	C₄×C₈	—	19	1	no	—
71	C₄×C₈	—	19	1	no	—
72	C₄×C₈	—	19	2	no	—
73	C₄×C₈	C₂×D₁₉	1	2	yes	—
74	C₁₉	#1452	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
76	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
77	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
78	C₂×C₈	—	19	2	no	—
79	C₂×C₈	—	19	2	no	—
80	C₂×C₈	—	19	4	no	—
81	C₂×C₈	—	38	4	no	—
82	C₂×C₈	C₂×Dic₁₉	1	4	yes	—
83	C₄²	C₄×D₁₉	1	1	yes	characteristic
84	C₄²	C₄×D₁₉	1	1	yes	characteristic
85	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
86	C₄²	C₂²×D₁₉	1	1	yes	characteristic
87	C₂³	C₄×Dic₁₉	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	#64515	1	4	yes	—
91	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
92	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
93	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
94	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
96	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
97	C₈	—	2	4	no	—
98	C₈	—	38	2	no	—
99	C₈	—	38	2	no	—
100	C₈	—	38	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	#10597272	1	2	yes	—
104	C₂²	C₂×C₄×Dic₁₉	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	#10597272	1	2	yes	—
108	C₄	C₂×#64515	1	2	yes	—
109	C₄	#10597353	1	2	yes	—
110	C₄	#10597394	1	2	yes	—
111	C₂	—	2	2	no	—
112	C₂	C₂×#10597272	1	1	yes	characteristic
113	C₂	#11926500	1	1	yes	characteristic
114	C₂	#11926502	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926597

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#11926266

C₂

yes

maximal, complemented

#11926265

C₂

yes

maximal, complemented

C₁₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₄

yes

—

C₁₉×C₄⋊C₈

C₄

yes

—

C₁₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₁₉

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₄×C₁₉⋊C₈

C₄

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1452

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#97

yes

—

C₂²×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#97

yes

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

#131

yes

—

#431

—

#431

D₁₉

yes

characteristic

C₂×C₄×C₈

—

#322

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#97

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

Dic₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₁₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

—

C₁₉

#1452

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₄²

C₄×D₁₉

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

C₄×Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64515

yes

—

C₂×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

100

C₈

—

101

C₂²

—

102

C₂²

—

103

C₂²

#10597272

yes

—

104

C₂²

C₂×C₄×Dic₁₉

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

#10597272

yes

—

108

C₄

C₂×#64515

yes

—

109

C₄

#10597353

yes

—

110

C₄

#10597394

yes

—

111

C₂

—

112

C₂

C₂×#10597272

yes

characteristic

113

C₂

#11926500

yes

characteristic

114

C₂

#11926502

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂×C₄²
Fitting	C₁₉×#431	C₂
prime radical	C₂³×C₁₉	C₄²
cosocle	C₄²×C₁₉	C₂³
hypercenter	#431	D₁₉
hypocenter	C₁₉	#1452
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ #431

subgroup

G/H

center, Frattini

C₄²

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂×C₄²

Fitting

C₁₉×#431

C₂

prime radical

C₂³×C₁₉

C₄²

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₄² ◁ #431

N	H ≅ G/N	type
3. #11926266	C₂	semidirect
4. #11926265	C₂	semidirect
74. C₁₉	#1452	semidirect

H ≅ G/N

type

3. #11926266

C₂

semidirect

4. #11926265

C₂

semidirect

74. C₁₉

#1452

semidirect

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

subgroup	index
#11926597	2
C₂×C₄×C₁₉⋊C₈	2
#11926266	2
#11926265	2
C₁₉×#431	2
#1452	19

subgroup

index

C₂×C₄×C₁₉⋊C₈

C₁₉×#431

Subgroups — #14561928

Conjugacy classes of subgroups

Complements

Maximal subgroups