Group #18069411 — subgroups

Subgroups — #18069411

Order 4864.

222 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 127 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	#14562383	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926597	—	2	2	no	—
4	#11926297	C₄	1	4	yes	—
5	#11926295	—	2	2	no	—
6	C₂²×C₁₆×C₁₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₄×C₁₆×C₁₉	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	—	2	2	no	—
13	C₂×C₁₆×C₁₉	—	2	2	no	—
14	C₂×C₁₆×C₁₉	C₈	1	4	yes	complemented
15	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₉	D₄	1	2	yes	—
17	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
19	C₄×C₁₉⋊C₈	—	4	2	no	—
20	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
27	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
28	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
29	C₄²×C₁₉	D₈	1	1	yes	characteristic
30	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	C₁₆×C₁₉	—	2	4	no	—
33	#7155	—	19	1	no	maximal, Sylow
34	C₂³×C₁₉	#106	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
37	C₂×C₄×C₁₉	#102	1	2	yes	—
38	C₂×C₄×C₁₉	#103	1	2	yes	—
39	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
40	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#108	1	2	yes	—
42	C₈×C₁₉	—	2	2	no	—
43	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
44	C₈×C₁₉	#97	1	1	yes	characteristic
45	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
46	C₁₉⋊C₈	—	8	4	no	—
47	C₂×C₄×C₁₆	D₁₉	1	1	yes	characteristic
48	#1564	—	19	2	no	—
49	C₂²×C₁₉	—	2	2	no	—
50	C₂²×C₁₉	#334	1	2	yes	—
51	C₂²×C₁₉	#340	1	1	yes	characteristic
52	C₄×C₁₉	—	2	2	no	—
53	C₄×C₁₉	#335	1	2	yes	—
54	C₄×C₁₉	#336	1	1	yes	characteristic
55	C₄×C₁₉	#341	1	1	yes	characteristic
56	C₄×C₁₉	#359	1	4	yes	—
57	C₂²×C₁₆	Dic₁₉	1	2	yes	—
58	#431	—	38	2	no	—
59	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
60	C₄×C₁₆	—	2	2	no	—
61	#335	—	19	4	no	—
62	#334	—	38	2	no	—
63	C₂×C₁₉	—	2	2	no	—
64	C₂×C₁₉	#1277	1	1	yes	characteristic
65	C₂×C₁₉	#1382	1	2	yes	—
66	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
67	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
68	C₂×C₄²	D₇₆	1	1	yes	characteristic
69	C₂×C₁₆	—	2	2	no	—
70	C₂×C₁₆	—	2	2	no	—
71	C₂×C₁₆	C₁₉⋊C₈	1	4	yes	complemented
72	C₄⋊C₈	—	38	4	no	—
73	C₂²⋊C₈	—	76	2	no	—
74	C₄×C₈	—	76	2	no	—
75	C₄×C₈	C₄×D₁₉	1	2	yes	—
76	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
77	C₁₉	#7155	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	#64516	1	2	yes	—
79	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	76	4	no	—
82	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
83	C₂×C₈	#64520	1	2	yes	—
84	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
85	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
86	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
87	C₄²	D₁₅₂	1	1	yes	characteristic
88	C₄²	Dic₇₆	1	1	yes	characteristic
89	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
90	C₁₆	—	2	4	no	—
91	C₂³	#10597274	1	1	yes	characteristic
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
94	C₂×C₄	#10597273	1	2	yes	—
95	C₂×C₄	#10597275	1	1	yes	characteristic
96	C₂×C₄	#10597276	1	2	yes	—
97	C₂×C₄	#10597278	1	2	yes	—
98	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	152	4	no	—
101	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
102	C₈	#10597260	1	1	yes	characteristic
103	C₈	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#11926295	1	2	yes	—
106	C₂²	#11926307	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	#11926297	1	2	yes	—
109	C₄	#11926299	1	1	yes	characteristic
110	C₄	#11926309	1	1	yes	characteristic
111	C₄	#11926352	1	4	yes	—
112	C₂	—	2	2	no	—
113	C₂	#14561470	1	1	yes	characteristic
114	C₂	#14561731	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562383

C₂

yes

maximal

C₂×C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic

#11926597

—

#11926297

C₄

yes

—

#11926295

—

C₂²×C₁₆×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₈

yes

complemented

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

#107

yes

characteristic

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

—

C₁₉⋊C₈

—

C₂×C₄×C₁₆

D₁₉

yes

characteristic

#1564

—

C₂²×C₁₉

—

C₂²×C₁₉

#334

yes

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#335

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂²×C₁₆

Dic₁₉

yes

—

#431

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₁₆

—

#335

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

#1277

yes

characteristic

C₂×C₁₉

#1382

yes

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₁₉⋊C₈

yes

complemented

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7155

yes

characteristic, complemented, Sylow

C₂²×C₄

#64516

yes

—

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

C₂×C₈

#64520

yes

—

C₂×C₈

C₄×Dic₁₉

yes

characteristic

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄²

D₁₅₂

yes

characteristic

C₄²

Dic₇₆

yes

characteristic

C₄²

(C₂×D₁₉)⋊C₄

yes

—

C₁₆

—

C₂³

#10597274

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

C₂×C₄

#10597273

yes

—

C₂×C₄

#10597275

yes

characteristic

C₂×C₄

#10597276

yes

—

C₂×C₄

#10597278

yes

—

C₂×C₄

C₁₉⋊#95

yes

characteristic

C₈

—

100

C₈

—

152

—

101

C₈

C₄×C₁₉⋊C₈

yes

characteristic

102

C₈

#10597260

yes

characteristic

103

C₈

C₂²⋊(C₁₉⋊C₈)

yes

—

104

C₂²

—

105

C₂²

#11926295

yes

—

106

C₂²

#11926307

yes

characteristic

107

C₄

—

108

C₄

#11926297

yes

—

109

C₄

#11926299

yes

characteristic

110

C₄

#11926309

yes

characteristic

111

C₄

#11926352

yes

—

112

C₂

—

113

C₂

#14561470

yes

characteristic

114

C₂

#14561731

yes

—

	subgroup	G/H
center	C₄²	D₁₅₂
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₄×C₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#106
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×C₄×C₁₆	D₁₉
hypocenter	C₁₉	#7155
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₄²

D₁₅₂

commutator

C₈×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₄×C₁₆×C₁₉

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

hypercenter

C₂×C₄×C₁₆

D₁₉

hypocenter

C₁₉

#7155

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
14. C₂×C₁₆×C₁₉	C₈	semidirect
71. C₂×C₁₆	C₁₉⋊C₈	semidirect
77. C₁₉	#7155	semidirect

H ≅ G/N

type

14. C₂×C₁₆×C₁₉

C₈

semidirect

71. C₂×C₁₆

C₁₉⋊C₈

semidirect

77. C₁₉

#7155

semidirect

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

subgroup	index
#14562383	2
C₂×C₄×C₁₆×C₁₉	2
#7155	19

subgroup

index

#14562383

C₂×C₄×C₁₆×C₁₉

#7155

Subgroups — #18069411

Conjugacy classes of subgroups

Complements

Maximal subgroups