Group #18076316 — subgroups

Subgroups — #18076316

Order 4864.

422 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 227 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	#14563795	C₂	1	2	yes	maximal
2	#14563763	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597275	—	2	4	no	—
5	#11926414	C₂²	1	4	yes	—
6	#11926307	—	2	8	no	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₈²×C₁₉	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₉	D₄	1	4	yes	—
11	C₂²×C₈×C₁₉	D₄	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	—	2	8	no	—
14	C₂×C₄⋊Dic₁₉	—	2	4	no	—
15	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
16	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₉	Q₈	1	4	yes	—
18	C₄×C₈×C₁₉	Q₈	1	2	yes	—
19	#10597275	—	4	8	no	—
20	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
22	C₂²×Dic₁₉	—	4	4	no	—
23	C₂×C₈×C₁₉	—	2	8	no	—
24	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
25	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
26	C₂×C₈×C₁₉	D₈	1	4	yes	—
27	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
28	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
29	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
30	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
31	C₄⋊Dic₁₉	—	4	8	no	—
32	C₄⋊Dic₁₉	—	4	16	no	—
33	#8816	—	19	1	no	maximal, Sylow
34	C₂³×C₁₉	#127	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
38	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
40	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
41	C₂×C₄×C₁₉	#135	1	8	yes	—
42	C₂×Dic₁₉	—	8	4	no	—
43	C₂×Dic₁₉	—	8	8	no	—
44	C₈×C₁₉	—	2	8	no	—
45	C₈×C₁₉	#107	1	8	yes	—
46	#1845	—	19	2	no	—
47	#1834	—	19	4	no	—
48	C₂×C₈²	D₁₉	1	1	yes	characteristic
49	C₂²×C₁₉	#384	1	1	yes	characteristic
50	C₂²×C₁₉	#493	1	1	yes	characteristic
51	C₂²×C₁₉	#494	1	1	yes	characteristic
52	C₂²×C₁₉	#495	1	4	yes	—
53	C₄×C₁₉	C₂×#107	1	2	yes	—
54	C₄×C₁₉	#427	1	4	yes	—
55	C₄×C₁₉	#499	1	4	yes	—
56	C₄×C₁₉	#500	1	2	yes	—
57	Dic₁₉	—	16	4	no	—
58	C₂×#107	—	38	4	no	—
59	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
60	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	#384	—	19	4	no	—
62	#340	—	38	8	no	—
63	C₈²	Dic₁₉	1	4	yes	complemented
64	C₂×C₁₉	#1709	1	2	yes	—
65	C₂×C₁₉	#1710	1	2	yes	—
66	C₂×C₁₉	#1845	1	1	yes	characteristic
67	C₂×C₁₉	#1846	1	2	yes	—
68	C₂²×C₈	D₇₆	1	4	yes	—
69	C₂²×C₈	D₇₆	1	2	yes	—
70	C₂×C₄⋊C₄	—	38	8	no	—
71	C₂×C₄⋊C₄	—	38	4	no	—
72	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
73	#107	—	76	8	no	—
74	C₄×C₈	Dic₃₈	1	4	yes	—
75	C₄×C₈	Dic₃₈	1	2	yes	—
76	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
77	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
78	C₁₉	#8816	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	—	76	4	no	—
80	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
81	C₂²×C₄	C₂×D₇₆	1	2	yes	—
82	C₂×C₈	—	2	8	no	—
83	C₂×C₈	D₁₅₂	1	4	yes	—
84	C₂×C₈	Dic₇₆	1	4	yes	—
85	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	—
86	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
87	C₄⋊C₄	—	76	8	no	—
88	C₄⋊C₄	—	76	16	no	—
89	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
90	C₄²	C₂×Dic₃₈	1	2	yes	—
91	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
92	C₂³	#10597320	1	1	yes	characteristic
93	C₂×C₄	—	152	4	no	—
94	C₂×C₄	—	152	8	no	—
95	C₂×C₄	#10597315	1	2	yes	—
96	C₂×C₄	#10597315	1	1	yes	characteristic
97	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
98	C₂×C₄	#10597350	1	8	yes	—
99	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
100	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
102	C₈	—	2	8	no	—
103	C₈	#10597275	1	8	yes	—
104	C₂²	#11926414	1	1	yes	characteristic
105	C₂²	#11926921	1	1	yes	characteristic
106	C₂²	#11926924	1	1	yes	characteristic
107	C₂²	#11926928	1	4	yes	—
108	C₄	—	304	4	no	—
109	C₄	C₂×#10597275	1	2	yes	—
110	C₄	#11926582	1	4	yes	—
111	C₄	#11926946	1	4	yes	—
112	C₄	#11926949	1	2	yes	—
113	C₂	#14563241	1	2	yes	—
114	C₂	#14563245	1	2	yes	—
115	C₂	#14563795	1	1	yes	characteristic
116	C₂	#14563799	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563795

C₂

yes

maximal

#14563763

C₂

yes

maximal

C₂×C₈²×C₁₉

C₂

yes

maximal, characteristic

C₂×#10597275

—

#11926414

C₂²

yes

—

#11926307

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₈²×C₁₉

C₄

yes

complemented

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597275

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#107

yes

—

#1845

—

#1834

—

C₂×C₈²

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#427

yes

—

C₄×C₁₉

#499

yes

—

C₄×C₁₉

#500

yes

—

Dic₁₉

—

C₂×#107

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

—

#340

—

C₈²

Dic₁₉

yes

complemented

C₂×C₁₉

#1709

yes

—

C₂×C₁₉

#1710

yes

—

C₂×C₁₉

#1845

yes

characteristic

C₂×C₁₉

#1846

yes

—

C₂²×C₈

D₇₆

yes

—

C₂²×C₈

D₇₆

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#107

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₁₉

#8816

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

characteristic

C₂²×C₄

C₂×D₇₆

yes

—

C₂×C₈

—

C₂×C₈

D₁₅₂

yes

—

C₂×C₈

Dic₇₆

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Dic₃₈

yes

characteristic

C₄²

C₂×Dic₃₈

yes

—

C₄²

C₂²×Dic₁₉

yes

characteristic

C₂³

#10597320

yes

characteristic

C₂×C₄

—

152

—

C₂×C₄

—

152

—

C₂×C₄

#10597315

yes

—

C₂×C₄

#10597315

yes

characteristic

C₂×C₄

C₂×D₁₅₂

yes

—

C₂×C₄

#10597350

yes

—

C₂×C₄

C₂×Dic₇₆

yes

—

100

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

101

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

—

102

C₈

—

103

C₈

#10597275

yes

—

104

C₂²

#11926414

yes

characteristic

105

C₂²

#11926921

yes

characteristic

106

C₂²

#11926924

yes

characteristic

107

C₂²

#11926928

yes

—

108

C₄

—

304

—

109

C₄

C₂×#10597275

yes

—

110

C₄

#11926582

yes

—

111

C₄

#11926946

yes

—

112

C₄

#11926949

yes

—

113

C₂

#14563241

yes

—

114

C₂

#14563245

yes

—

115

C₂

#14563795

yes

characteristic

116

C₂

#14563799

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈²×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#8816
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center

C₂³

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₈²×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₂×C₈²

D₁₉

hypocenter

C₁₉

#8816

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
9. C₈²×C₁₉	C₄	semidirect
63. C₈²	Dic₁₉	semidirect
78. C₁₉	#8816	semidirect

H ≅ G/N

type

9. C₈²×C₁₉

C₄

semidirect

63. C₈²

Dic₁₉

semidirect

78. C₁₉

#8816

semidirect

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

subgroup	index
#14563795	2
#14563763	2
C₂×C₈²×C₁₉	2
#8816	19

subgroup

index

#14563795

#14563763

C₂×C₈²×C₁₉

#8816

Subgroups — #18076316

Conjugacy classes of subgroups

Complements

Maximal subgroups