Group #18069373 — subgroups

Subgroups — #18069373

Order 4864.

262 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 151 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	C₄×#10597269	C₂	1	2	yes	maximal
2	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597269	C₄	1	4	yes	—
4	#11926320	—	2	2	no	—
5	C₄×C₁₉⋊C₁₆	—	2	2	no	—
6	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#322	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₈	1	4	yes	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	—	2	2	no	—
13	C₄×C₈×C₁₉	—	2	2	no	—
14	C₄×C₈×C₁₉	D₄	1	2	yes	—
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
17	#10597269	—	2	4	no	—
18	#10597269	C₈	1	8	yes	complemented
19	C₂×C₁₉⋊C₁₆	—	2	4	no	—
20	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₁₉	—	2	4	no	—
23	C₂×C₈×C₁₉	—	4	4	no	—
24	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
27	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
28	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
30	C₄²×C₁₉	M₁₆	1	2	yes	—
31	C₁₉⋊C₁₆	—	2	8	no	—
32	#7139	—	19	1	no	maximal, Sylow
33	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
37	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#97	1	2	yes	—
39	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
40	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
41	C₈×C₁₉	—	4	4	no	—
42	C₈×C₁₉	C₂²⋊C₈	1	4	yes	—
43	C₈×C₁₉	C₄⋊C₈	1	4	yes	—
44	C₄×M₃₂	—	19	2	no	—
45	C₂×#322	D₁₉	1	1	yes	characteristic
46	C₂²×C₁₉	—	2	2	no	—
47	C₂²×C₁₉	C₈²	1	1	yes	characteristic
48	C₂²×C₁₉	#322	1	1	yes	characteristic
49	C₂²×C₁₉	#336	1	1	yes	characteristic
50	C₄×C₁₉	—	2	2	no	—
51	C₄×C₁₉	#322	1	2	yes	—
52	C₄×C₁₉	#336	1	2	yes	—
53	C₄×C₁₉	#349	1	4	yes	—
54	C₂×M₃₂	—	19	4	no	—
55	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
56	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
57	#346	—	38	2	no	—
58	C₄×C₁₆	—	38	2	no	—
59	#322	—	2	2	no	—
60	C₂×C₁₉	—	2	1	no	—
61	C₂×C₁₉	—	2	1	no	—
62	C₂×C₁₉	#1273	1	1	yes	characteristic
63	C₂×C₁₉	#1377	1	2	yes	—
64	C₂²×C₈	C₁₉⋊C₈	1	4	yes	—
65	C₂²×C₈	C₄×D₁₉	1	2	yes	—
66	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
67	M₃₂	—	19	8	no	—
68	M₃₂	—	38	4	no	—
69	C₂×C₁₆	—	38	4	no	—
70	C₄×C₈	—	2	2	no	—
71	C₄×C₈	—	2	2	no	—
72	C₄×C₈	Dic₃₈	1	1	yes	characteristic
73	C₄×C₈	D₇₆	1	1	yes	characteristic
74	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
75	C₁₉	#7139	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
77	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	—	4	4	no	—
80	C₂×C₈	C₈×D₁₉	1	4	yes	—
81	C₂×C₈	#64515	1	4	yes	—
82	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
83	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
84	C₄²	#64520	1	2	yes	—
85	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
86	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
87	C₁₆	—	38	8	no	—
88	C₂³	C₄×C₁₉⋊C₈	1	1	yes	characteristic
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	#10597260	1	1	yes	characteristic
91	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
92	C₂×C₄	C₈×Dic₁₉	1	2	yes	—
93	C₂×C₄	#10597272	1	2	yes	—
94	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
95	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
96	C₈	—	4	4	no	—
97	C₈	Dic₁₉⋊C₈	1	4	yes	—
98	C₈	(C₂×D₁₉)⋊C₈	1	4	yes	—
99	C₂²	—	2	2	no	—
100	C₂²	C₈×C₁₉⋊C₈	1	1	yes	characteristic
101	C₂²	#11926265	1	1	yes	characteristic
102	C₂²	#11926299	1	1	yes	characteristic
103	C₄	—	2	2	no	—
104	C₄	#11926266	1	2	yes	—
105	C₄	#11926298	1	2	yes	—
106	C₄	#11926326	1	4	yes	—
107	C₂	—	2	1	no	—
108	C₂	—	2	1	no	—
109	C₂	C₁₉⋊#1273	1	1	yes	characteristic
110	C₂	#14561719	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597269

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₂×#10597269

C₄

yes

—

#11926320

—

C₄×C₁₉⋊C₁₆

—

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂²×C₈×C₁₉

C₈

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

#10597269

—

#10597269

C₈

yes

complemented

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

M₁₆

yes

—

C₁₉⋊C₁₆

—

#7139

—

maximal, Sylow

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

—

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

#97

yes

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

—

C₈×C₁₉

C₄⋊C₈

yes

—

C₄×M₃₂

—

C₂×#322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

C₈²

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

#322

yes

—

C₄×C₁₉

#336

yes

—

C₄×C₁₉

#349

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#346

—

C₄×C₁₆

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1273

yes

characteristic

C₂×C₁₉

#1377

yes

—

C₂²×C₈

C₁₉⋊C₈

yes

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7139

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₉

yes

—

C₂×C₈

#64515

yes

—

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

C₄²

#64520

yes

—

C₄²

C₄⋊Dic₁₉

yes

characteristic

C₄²

C₂²⋊Dic₁₉

yes

characteristic

C₁₆

—

C₂³

C₄×C₁₉⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

#10597260

yes

characteristic

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

C₂×C₄

C₈×Dic₁₉

yes

—

C₂×C₄

#10597272

yes

—

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

C₂×C₄

C₁₉⋊#95

yes

characteristic

C₈

—

C₈

Dic₁₉⋊C₈

yes

—

C₈

(C₂×D₁₉)⋊C₈

yes

—

C₂²

—

100

C₂²

C₈×C₁₉⋊C₈

yes

characteristic

101

C₂²

#11926265

yes

characteristic

102

C₂²

#11926299

yes

characteristic

103

C₄

—

104

C₄

#11926266

yes

—

105

C₄

#11926298

yes

—

106

C₄

#11926326

yes

—

107

C₂

—

108

C₂

—

109

C₂

C₁₉⋊#1273

yes

characteristic

110

C₂

#14561719

yes

—

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₉
commutator	C₂²×C₁₉	C₈²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄×C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#7139
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

subgroup

G/H

center

C₄²

C₂²⋊Dic₁₉

commutator

C₂²×C₁₉

C₈²

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₄×C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

N	H ≅ G/N	type
18. #10597269	C₈	semidirect
75. C₁₉	#7139	semidirect

H ≅ G/N

type

18. #10597269

C₈

semidirect

75. C₁₉

#7139

semidirect

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

subgroup	index
C₄×#10597269	2
C₂×C₁₉×#322	2
#7139	19

subgroup

index

C₄×#10597269

C₂×C₁₉×#322

#7139

Subgroups — #18069373

Conjugacy classes of subgroups

Complements

Maximal subgroups