Group #18087589 — subgroups

Subgroups — #18087589

Order 4864.

526 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 165 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	#14564441	C₂	1	3	yes	maximal
2	#14563795	C₂	1	3	yes	maximal, complemented
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597320	C₂²	1	1	yes	characteristic
5	C₂×#10597275	—	2	6	no	—
6	C₂×#10597278	—	2	6	no	—
7	#11926414	C₂²	1	3	yes	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₂²×D₇₆	—	2	3	no	—
10	C₂²×C₈×C₁₉	D₄	1	6	yes	—
11	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	—	2	3	no	—
13	C₂×C₄⋊Dic₁₉	—	2	6	no	—
14	#10597320	—	2	3	no	—
15	#10597320	Q₈	1	2	yes	—
16	C₄×C₈×C₁₉	—	2	6	no	—
17	#10597278	—	4	12	no	—
18	#10597275	—	4	12	no	—
19	C₂³×D₁₉	—	4	1	no	—
20	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
21	C₂²×Dic₁₉	—	4	3	no	—
22	C₂×D₇₆	—	2	6	no	—
23	C₂×D₇₆	—	4	6	no	—
24	C₂×D₇₆	—	4	6	no	—
25	C₂×D₇₆	—	4	3	no	—
26	C₂×C₈×C₁₉	—	2	6	no	—
27	C₂×C₈×C₁₉	—	2	6	no	—
28	C₂×C₈×C₁₉	D₈	1	12	yes	—
29	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
30	C₄²×C₁₉	#41	1	3	yes	—
31	C₄⋊Dic₁₉	—	4	12	no	—
32	C₄⋊Dic₁₉	—	4	6	no	—
33	#10673	—	19	1	no	maximal, Sylow
34	C₂³×C₁₉	#127	1	1	yes	characteristic
35	C₂²×D₁₉	—	4	2	no	—
36	C₂²×D₁₉	—	8	3	no	—
37	C₂²×D₁₉	—	8	3	no	—
38	C₂×C₄×C₁₉	C₂²⋊Q₈	1	3	yes	—
39	C₂×C₄×C₁₉	#123	1	3	yes	—
40	C₂×C₄×C₁₉	C₂×D₈	1	6	yes	—
41	C₂×C₄×C₁₉	#137	1	6	yes	—
42	C₂×Dic₁₉	—	8	6	no	—
43	C₂×Dic₁₉	—	8	3	no	—
44	D₇₆	—	4	12	no	—
45	D₇₆	—	8	6	no	—
46	C₈×C₁₉	—	2	12	no	—
47	#1957	—	19	3	no	—
48	#1845	—	19	3	no	—
49	#1273	D₁₉	1	1	yes	characteristic, complemented
50	C₂²×C₁₉	#399	1	1	yes	characteristic
51	C₂²×C₁₉	#493	1	3	yes	—
52	C₂²×C₁₉	#497	1	3	yes	—
53	C₂×D₁₉	—	8	6	no	—
54	C₂×D₁₉	—	16	1	no	—
55	C₂×D₁₉	—	16	3	no	—
56	C₄×C₁₉	#474	1	6	yes	—
57	C₄×C₁₉	#480	1	6	yes	—
58	Dic₁₉	—	16	3	no	—
59	C₂×#127	—	19	1	no	—
60	C₂×#107	—	38	6	no	—
61	C₂×#102	—	38	6	no	—
62	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
63	#384	—	19	3	no	—
64	C₂×C₁₉	#1712	1	1	yes	characteristic
65	C₂×C₁₉	#1722	1	3	yes	—
66	C₂×C₁₉	#2093	1	3	yes	—
67	D₁₉	—	16	2	no	—
68	C₂²×D₄	—	38	3	no	—
69	C₂²×C₈	D₇₆	1	6	yes	—
70	#127	—	19	2	no	—
71	#127	—	38	3	no	—
72	C₂×C₄⋊C₄	—	38	3	no	—
73	C₂×C₄⋊C₄	—	38	6	no	—
74	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
75	#107	—	76	12	no	—
76	#102	—	76	12	no	—
77	C₄×C₈	—	2	6	no	—
78	C₁₉	#10673	1	1	yes	characteristic, complemented, Sylow
79	C₂⁴	—	76	1	no	—
80	C₂×D₄	—	38	6	no	—
81	C₂×D₄	—	76	3	no	—
82	C₂×D₄	—	76	6	no	—
83	C₂×D₄	—	76	6	no	—
84	C₂²×C₄	—	76	3	no	—
85	C₂²×C₄	C₂×D₇₆	1	3	yes	—
86	C₂×C₈	—	2	6	no	—
87	C₂×C₈	—	2	6	no	—
88	C₂×C₈	D₁₅₂	1	12	yes	—
89	C₄⋊C₄	—	76	6	no	—
90	C₄⋊C₄	—	76	12	no	—
91	C₄²	#64543	1	3	yes	—
92	C₄²	Q₈×D₁₉	1	1	yes	characteristic
93	C₂³	—	76	2	no	—
94	C₂³	—	152	3	no	—
95	C₂³	—	152	3	no	—
96	C₂³	#10597320	1	1	yes	characteristic
97	D₄	—	76	12	no	—
98	D₄	—	152	6	no	—
99	C₂×C₄	—	152	3	no	—
100	C₂×C₄	—	152	6	no	—
101	C₂×C₄	#10597332	1	3	yes	—
102	C₂×C₄	#10597343	1	3	yes	—
103	C₂×C₄	C₂×D₁₅₂	1	6	yes	—
104	C₂×C₄	#10597355	1	6	yes	—
105	C₈	—	2	12	no	—
106	C₂²	—	304	1	no	—
107	C₂²	—	304	3	no	—
108	C₂²	—	152	6	no	—
109	C₂²	#11926481	1	1	yes	characteristic
110	C₂²	#11926921	1	3	yes	—
111	C₂²	#11926938	1	3	yes	—
112	C₄	—	304	3	no	—
113	C₄	#11926825	1	6	yes	—
114	C₄	#11926858	1	6	yes	—
115	C₂	—	304	2	no	—
116	C₂	#14563250	1	1	yes	characteristic
117	C₂	#14563306	1	3	yes	—
118	C₂	#14565162	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564441

C₂

yes

maximal

#14563795

C₂

yes

maximal, complemented

C₁₉×#1273

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

—

—

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597320

—

#10597320

Q₈

yes

—

C₄×C₈×C₁₉

—

#10597278

—

#10597275

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

#1957

—

#1845

—

#1273

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#399

yes

characteristic

C₂²×C₁₉

#493

yes

—

C₂²×C₁₉

#497

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#474

yes

—

C₄×C₁₉

#480

yes

—

Dic₁₉

—

C₂×#127

—

C₂×#107

—

C₂×#102

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

#384

—

C₂×C₁₉

#1712

yes

characteristic

C₂×C₁₉

#1722

yes

—

C₂×C₁₉

#2093

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×C₈

D₇₆

yes

—

#127

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#107

—

#102

—

C₄×C₈

—

C₁₉

#10673

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₅₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#64543

yes

—

C₄²

Q₈×D₁₉

yes

characteristic

C₂³

—

C₂³

—

152

—

C₂³

—

152

—

C₂³

#10597320

yes

characteristic

D₄

—

D₄

—

152

—

C₂×C₄

—

152

—

100

C₂×C₄

—

152

—

101

C₂×C₄

#10597332

yes

—

102

C₂×C₄

#10597343

yes

—

103

C₂×C₄

C₂×D₁₅₂

yes

—

104

C₂×C₄

#10597355

yes

—

105

C₈

—

106

C₂²

—

304

—

107

C₂²

—

304

—

108

C₂²

—

152

—

109

C₂²

#11926481

yes

characteristic

110

C₂²

#11926921

yes

—

111

C₂²

#11926938

yes

—

112

C₄

—

304

—

113

C₄

#11926825

yes

—

114

C₄

#11926858

yes

—

115

C₂

—

304

—

116

C₂

#14563250

yes

characteristic

117

C₂

#14563306

yes

—

118

C₂

#14565162

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1273	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#10673
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1273

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. #14563795	C₂	semidirect
3. C₁₉×#1273	C₂	semidirect
49. #1273	D₁₉	semidirect
78. C₁₉	#10673	semidirect

H ≅ G/N

type

2. #14563795

C₂

semidirect

3. C₁₉×#1273

C₂

semidirect

49. #1273

D₁₉

semidirect

78. C₁₉

#10673

semidirect

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

subgroup	index
#14564441	2
#14563795	2
C₁₉×#1273	2
#10673	19

subgroup

index

#14564441

#14563795

C₁₉×#1273

#10673

Subgroups — #18087589

Conjugacy classes of subgroups

Complements

Maximal subgroups