Group #18069987 — subgroups

Subgroups — #18069987

Order 4864.

118 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14565473	C₂	1	1	yes	maximal, characteristic
2	#14561833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926960	—	2	1	no	—
5	#11926662	C₄	1	1	yes	characteristic
6	#11926378	—	2	1	no	—
7	#11926365	C₄	1	1	yes	characteristic
8	#11926327	—	2	1	no	—
9	C₂×C₁₉×C₃₂	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	#10597350	C₈	1	1	yes	characteristic
12	#10597347	—	2	1	no	—
13	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	#10597276	C₈	1	1	yes	characteristic
17	#10597269	—	2	1	no	—
18	#10597262	—	2	1	no	—
19	#10597255	—	4	1	no	—
20	C₁₆×D₁₉	—	4	1	no	—
21	C₁₉×C₃₂	—	2	2	no	—
22	C₁₉⋊C₃₂	—	4	1	no	—
23	#64541	—	2	1	no	—
24	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
27	#64520	—	2	1	no	—
28	Dic₇₆	C₁₆	1	1	yes	characteristic
29	D₁₅₂	C₁₆	1	1	yes	characteristic
30	#64516	—	2	1	no	—
31	#64515	—	4	1	no	—
32	C₈×D₁₉	—	4	1	no	—
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₆×C₁₉	D₈	1	1	yes	characteristic
35	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₁₉⋊C₁₆	—	4	1	no	—
37	#7382	—	19	1	no	maximal, Sylow
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₂²⋊D₁₉	—	4	1	no	—
41	D₇₆	—	2	1	no	—
42	C₄×D₁₉	—	4	1	no	—
43	Dic₃₈	—	2	1	no	—
44	C₈×C₁₉	#102	1	1	yes	characteristic
45	C₈×C₁₉	#104	1	1	yes	characteristic
46	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
47	C₈×C₁₉	M₃₂	1	1	yes	characteristic
48	C₁₉⋊C₈	—	4	1	no	—
49	#2170	—	19	1	no	—
50	#1422	—	19	1	no	—
51	#1397	D₁₉	1	1	yes	characteristic, complemented
52	C₂²×C₁₉	#350	1	1	yes	characteristic
53	C₂×D₁₉	—	4	1	no	—
54	C₄×C₁₉	—	4	1	no	—
55	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
56	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
57	Dic₁₉	—	4	1	no	—
58	#504	—	38	1	no	—
59	#443	—	19	1	no	—
60	M₆₄	—	38	1	no	—
61	C₂×C₃₂	—	2	1	no	—
62	#364	—	19	1	no	—
63	#350	—	38	1	no	—
64	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	D₄⋊C₁₆	1	1	yes	characteristic
67	D₁₉	—	8	1	no	—
68	#135	—	19	1	no	—
69	#131	—	38	1	no	—
70	M₃₂	—	38	1	no	—
71	M₃₂	—	76	1	no	—
72	C₂×C₁₆	—	76	1	no	—
73	C₂×C₁₆	D₇₆	1	1	yes	characteristic
74	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
75	#108	—	19	1	no	—
76	#104	—	38	1	no	—
77	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
78	C₃₂	—	2	2	no	—
79	C₃₂	—	76	1	no	—
80	C₁₉	#7382	1	1	yes	characteristic, complemented, Sylow
81	#41	—	38	1	no	—
82	Q₁₆	—	19	1	no	—
83	SD₁₆	—	38	1	no	—
84	D₈	—	19	1	no	—
85	M₁₆	—	38	1	no	—
86	M₁₆	—	76	1	no	—
87	C₂×C₈	—	76	1	no	—
88	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
89	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
90	C₄²	#64515	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	76	1	no	—
93	C₁₆	#64516	1	1	yes	characteristic
94	C₁₆	D₁₅₂	1	1	yes	characteristic
95	Q₈	—	38	1	no	—
96	D₄	—	38	1	no	—
97	D₄	—	76	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	76	1	no	—
100	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
101	C₈	—	76	1	no	—
102	C₈	C₁₆×D₁₉	1	1	yes	characteristic
103	C₈	#10597255	1	1	yes	characteristic
104	C₈	#10597262	1	1	yes	characteristic
105	C₈	#10597278	1	1	yes	characteristic
106	C₂²	—	76	1	no	—
107	C₂²	#11926327	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	76	1	no	—
110	C₄	#11926273	1	1	yes	characteristic
111	C₄	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
112	C₂	—	2	1	no	—
113	C₂	—	152	1	no	—
114	C₂	#14561591	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565473

C₂

yes

maximal, characteristic

#14561833

C₂

yes

maximal, characteristic, complemented

C₁₉×#1397

C₂

yes

maximal, characteristic, complemented

#11926960

—

#11926662

C₄

yes

characteristic

#11926378

—

#11926365

C₄

yes

characteristic

#11926327

—

C₂×C₁₉×C₃₂

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

#10597350

C₈

yes

characteristic

#10597347

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

#10597276

C₈

yes

—

—

—

C₁₆×D₁₉

—

C₁₉×C₃₂

—

C₁₉⋊C₃₂

—

#64541

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

#64520

—

Dic₇₆

C₁₆

yes

characteristic

D₁₅₂

C₁₆

yes

characteristic

#64516

—

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7382

—

maximal, Sylow

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

C₂×C₁₆

yes

characteristic

C₈×C₁₉

M₃₂

yes

characteristic

C₁₉⋊C₈

—

#2170

—

#1422

—

#1397

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#350

yes

characteristic

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

C₂²⋊C₁₆

yes

characteristic

Dic₁₉

—

#504

—

#443

—

M₆₄

—

C₂×C₃₂

—

#364

—

#350

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

D₄⋊C₁₆

yes

characteristic

D₁₉

—

#135

—

#131

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

D₇₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

#108

—

#104

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₃₂

—

C₃₂

—

C₁₉

#7382

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₈×D₁₉

yes

characteristic

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₄²

#64515

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

#64516

yes

characteristic

C₁₆

D₁₅₂

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

101

C₈

—

102

C₈

C₁₆×D₁₉

yes

characteristic

103

C₈

#10597255

yes

characteristic

104

C₈

#10597262

yes

characteristic

105

C₈

#10597278

yes

characteristic

106

C₂²

—

107

C₂²

#11926327

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

#11926273

yes

characteristic

111

C₄

(C₂×D₁₉)⋊C₁₆

yes

characteristic

112

C₂

—

113

C₂

—

152

—

114

C₂

#14561591

yes

characteristic

	subgroup	G/H
center	C₈	#10597278
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1397	C₂
socle	C₂×C₁₉	D₄⋊C₁₆
prime radical	#10597350	C₈
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1397	D₁₉
hypocenter	C₁₉	#7382
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₈

#10597278

commutator

C₈×C₁₉

C₂×C₁₆

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1397

C₂

socle

C₂×C₁₉

D₄⋊C₁₆

prime radical

#10597350

C₈

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
2. #14561833	C₂	semidirect
3. C₁₉×#1397	C₂	semidirect
51. #1397	D₁₉	semidirect
80. C₁₉	#7382	semidirect

H ≅ G/N

type

2. #14561833

C₂

semidirect

3. C₁₉×#1397

C₂

semidirect

51. #1397

D₁₉

semidirect

80. C₁₉

#7382

semidirect

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

subgroup	index
#14565473	2
#14561833	2
C₁₉×#1397	2
#7382	19

subgroup

index

#14565473

#14561833

C₁₉×#1397

#7382

Subgroups — #18069987

Conjugacy classes of subgroups

Complements

Maximal subgroups