Group #18076313 — subgroups

Subgroups — #18076313

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	#14563792	C₂	1	2	yes	maximal
2	#14563763	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597274	—	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	#10597274	—	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	SD₁₆	1	8	yes	—
27	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
29	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
30	C₄⋊Dic₁₉	—	4	8	no	—
31	C₄⋊Dic₁₉	—	4	16	no	—
32	#8815	—	19	1	no	maximal, Sylow
33	C₂³×C₁₉	#127	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
38	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
39	C₂×C₄×C₁₉	#135	1	8	yes	—
40	C₂×Dic₁₉	—	8	4	no	—
41	C₂×Dic₁₉	—	8	8	no	—
42	C₈×C₁₉	—	2	8	no	—
43	C₈×C₁₉	#106	1	8	yes	—
44	#1844	—	19	2	no	—
45	#1834	—	19	4	no	—
46	C₂×C₈²	D₁₉	1	1	yes	characteristic
47	C₂²×C₁₉	#384	1	1	yes	characteristic
48	C₂²×C₁₉	#492	1	2	yes	—
49	C₂²×C₁₉	#495	1	4	yes	—
50	C₄×C₁₉	C₂×#106	1	2	yes	—
51	C₄×C₁₉	#427	1	4	yes	—
52	C₄×C₁₉	#498	1	2	yes	—
53	C₄×C₁₉	#499	1	4	yes	—
54	Dic₁₉	—	16	4	no	—
55	C₂×#106	—	38	4	no	—
56	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
57	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
58	#384	—	19	4	no	—
59	#340	—	38	8	no	—
60	C₈²	Dic₁₉	1	4	yes	complemented
61	C₂×C₁₉	#1708	1	4	yes	—
62	C₂×C₁₉	#1844	1	1	yes	characteristic
63	C₂×C₁₉	#1846	1	2	yes	—
64	C₂²×C₈	D₇₆	1	4	yes	—
65	C₂²×C₈	D₇₆	1	2	yes	—
66	C₂×C₄⋊C₄	—	38	8	no	—
67	C₂×C₄⋊C₄	—	38	4	no	—
68	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
69	#106	—	76	8	no	—
70	C₄×C₈	Dic₃₈	1	4	yes	—
71	C₄×C₈	Dic₃₈	1	2	yes	—
72	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
73	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
74	C₁₉	#8815	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	76	4	no	—
76	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
77	C₂²×C₄	C₂×D₇₆	1	2	yes	—
78	C₂×C₈	—	2	8	no	—
79	C₂×C₈	#64516	1	8	yes	—
80	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	—
81	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
82	C₄⋊C₄	—	76	8	no	—
83	C₄⋊C₄	—	76	16	no	—
84	C₄²	C₂×Dic₃₈	1	2	yes	—
85	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
86	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
87	C₂³	#10597320	1	1	yes	characteristic
88	C₂×C₄	—	152	4	no	—
89	C₂×C₄	—	152	8	no	—
90	C₂×C₄	#10597315	1	1	yes	characteristic
91	C₂×C₄	#10597315	1	2	yes	—
92	C₂×C₄	C₂×#64516	1	4	yes	—
93	C₂×C₄	#10597350	1	8	yes	—
94	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
96	C₈	—	2	8	no	—
97	C₈	#10597274	1	8	yes	—
98	C₂²	#11926414	1	1	yes	characteristic
99	C₂²	#11926917	1	2	yes	—
100	C₂²	#11926928	1	4	yes	—
101	C₄	—	304	4	no	—
102	C₄	C₂×#10597274	1	2	yes	—
103	C₄	#11926582	1	4	yes	—
104	C₄	#11926942	1	2	yes	—
105	C₄	#11926946	1	4	yes	—
106	C₂	#14563236	1	4	yes	—
107	C₂	#14563792	1	1	yes	characteristic
108	C₂	#14563799	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563792

C₂

yes

maximal

#14563763

C₂

yes

maximal

C₂×C₈²×C₁₉

C₂

yes

maximal, characteristic

C₂×#10597274

—

#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

—

#10597274

—

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

SD₁₆

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

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#106

yes

—

#1844

—

#1834

—

C₂×C₈²

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#495

yes

—

C₄×C₁₉

C₂×#106

yes

—

C₄×C₁₉

#427

yes

—

C₄×C₁₉

#498

yes

—

C₄×C₁₉

#499

yes

—

Dic₁₉

—

C₂×#106

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

—

#340

—

C₈²

Dic₁₉

yes

complemented

C₂×C₁₉

#1708

yes

—

C₂×C₁₉

#1844

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

#106

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₁₉

#8815

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

characteristic

C₂²×C₄

C₂×D₇₆

yes

—

C₂×C₈

—

C₂×C₈

#64516

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Dic₃₈

yes

—

C₄²

C₂×Dic₃₈

yes

characteristic

C₄²

C₂²×Dic₁₉

yes

characteristic

C₂³

#10597320

yes

characteristic

C₂×C₄

—

152

—

C₂×C₄

—

152

—

C₂×C₄

#10597315

yes

characteristic

C₂×C₄

#10597315

yes

—

C₂×C₄

C₂×#64516

yes

—

C₂×C₄

#10597350

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

—

C₈

—

C₈

#10597274

yes

—

C₂²

#11926414

yes

characteristic

C₂²

#11926917

yes

—

100

C₂²

#11926928

yes

—

101

C₄

—

304

—

102

C₄

C₂×#10597274

yes

—

103

C₄

#11926582

yes

—

104

C₄

#11926942

yes

—

105

C₄

#11926946

yes

—

106

C₂

#14563236

yes

—

107

C₂

#14563792

yes

characteristic

108

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	#8815
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

#8815

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
9. C₈²×C₁₉	C₄	semidirect
60. C₈²	Dic₁₉	semidirect
74. C₁₉	#8815	semidirect

H ≅ G/N

type

9. C₈²×C₁₉

C₄

semidirect

60. C₈²

Dic₁₉

semidirect

74. C₁₉

#8815

semidirect

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

subgroup	index
#14563792	2
#14563763	2
C₂×C₈²×C₁₉	2
#8815	19

subgroup

index

#14563792

#14563763

C₂×C₈²×C₁₉

#8815

Subgroups — #18076313

Conjugacy classes of subgroups

Complements

Maximal subgroups