Group #18076353 — subgroups

Subgroups — #18076353

Order 4864.

338 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 187 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	#14563807	C₂	1	2	yes	maximal
2	#14562394	C₂	1	4	yes	maximal
3	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	4	no	—
5	#11926568	C₂²	1	4	yes	—
6	#11926297	—	2	8	no	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#322	C₄	1	4	yes	—
10	C₂²×C₈×C₁₉	D₄	1	2	yes	—
11	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	C₂×#64520	—	2	4	no	—
14	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
15	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₉	D₄	1	4	yes	—
17	C₄×C₈×C₁₉	Q₈	1	2	yes	—
18	#10597276	—	4	8	no	—
19	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
20	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
22	C₂×C₈×C₁₉	—	4	4	no	—
23	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
24	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
25	C₂×C₈×C₁₉	D₈	1	4	yes	—
26	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
27	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₁₉	C₂×D₄	1	2	yes	—
29	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
30	#64520	—	4	8	no	—
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	#8826	—	19	1	no	maximal, Sylow
33	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	4	no	—
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	#127	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
39	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
40	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
41	C₈×C₁₉	—	2	8	no	—
42	C₈×C₁₉	#107	1	8	yes	—
43	C₁₉⋊C₈	—	8	4	no	—
44	#1848	—	19	2	no	—
45	#1567	—	19	4	no	—
46	C₂×#322	D₁₉	1	1	yes	characteristic
47	C₂²×C₁₉	—	2	2	no	—
48	C₂²×C₁₉	#384	1	1	yes	characteristic
49	C₂²×C₁₉	#500	1	2	yes	—
50	C₄×C₁₉	—	2	2	no	—
51	C₄×C₁₉	C₂×#107	1	2	yes	—
52	C₄×C₁₉	#430	1	4	yes	—
53	C₄×C₁₉	#493	1	1	yes	characteristic
54	C₄×C₁₉	#494	1	1	yes	characteristic
55	C₂×#108	—	38	4	no	—
56	#423	—	19	4	no	—
57	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
58	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
59	#335	—	38	8	no	—
60	#322	Dic₁₉	1	4	yes	—
61	C₂×C₁₉	—	2	2	no	—
62	C₂×C₁₉	#1845	1	1	yes	characteristic
63	C₂×C₁₉	#1849	1	2	yes	—
64	C₂×M₁₆	—	38	4	no	—
65	C₂²×C₈	Dic₃₈	1	4	yes	—
66	C₂²×C₈	D₇₆	1	2	yes	—
67	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
68	#108	—	76	8	no	—
69	C₄⋊C₈	—	38	8	no	—
70	C₄×C₈	Dic₃₈	1	2	yes	—
71	C₄×C₈	D₇₆	1	4	yes	—
72	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
73	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
74	C₁₉	#8826	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	C₂×Dic₃₈	1	2	yes	—
76	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
77	M₁₆	—	76	8	no	—
78	C₂×C₈	—	4	4	no	—
79	C₂×C₈	—	76	4	no	—
80	C₂×C₈	D₁₅₂	1	4	yes	—
81	C₂×C₈	Dic₇₆	1	4	yes	—
82	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	—
83	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
84	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
85	C₄²	C₂×D₇₆	1	2	yes	—
86	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
87	C₂³	#10597315	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	#10597315	1	2	yes	—
90	C₂×C₄	#10597320	1	1	yes	characteristic
91	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
92	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
93	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	—	152	4	no	—
97	C₈	#10597275	1	8	yes	—
98	C₂²	—	2	2	no	—
99	C₂²	#11926414	1	1	yes	characteristic
100	C₂²	#11926949	1	2	yes	—
101	C₄	—	2	2	no	—
102	C₄	C₂×#10597275	1	2	yes	—
103	C₄	#11926593	1	4	yes	—
104	C₄	#11926921	1	1	yes	characteristic
105	C₄	#11926924	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	#14563795	1	1	yes	characteristic
108	C₂	#14563810	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563807

C₂

yes

maximal

#14562394

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926568

C₂²

yes

—

#11926297

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₁₉×#322

C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

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×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

#8826

—

maximal, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

#107

yes

—

C₁₉⋊C₈

—

#1848

—

#1567

—

C₂×#322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#500

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#430

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

—

#335

—

#322

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#1845

yes

characteristic

C₂×C₁₉

#1849

yes

—

C₂×M₁₆

—

C₂²×C₈

Dic₃₈

yes

—

C₂²×C₈

D₇₆

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

D₇₆

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₁₉

#8826

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₃₈

yes

—

C₂²×C₄

C₂×D₇₆

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₅₂

yes

—

C₂×C₈

Dic₇₆

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄²

C₂×Dic₃₈

yes

characteristic

C₄²

C₂×D₇₆

yes

—

C₄²

C₂²×Dic₁₉

yes

characteristic

C₂³

#10597315

yes

characteristic

C₂×C₄

—

C₂×C₄

#10597315

yes

—

C₂×C₄

#10597320

yes

characteristic

C₂×C₄

C₂×D₁₅₂

yes

—

C₂×C₄

C₂×Dic₇₆

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

—

C₈

—

C₈

—

152

—

C₈

#10597275

yes

—

C₂²

—

C₂²

#11926414

yes

characteristic

100

C₂²

#11926949

yes

—

101

C₄

—

102

C₄

C₂×#10597275

yes

—

103

C₄

#11926593

yes

—

104

C₄

#11926921

yes

characteristic

105

C₄

#11926924

yes

characteristic

106

C₂

—

107

C₂

#14563795

yes

characteristic

108

C₂

#14563810

yes

—

	subgroup	G/H
center	C₂×C₄	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#8826
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
74. C₁₉	#8826	semidirect

H ≅ G/N

type

74. C₁₉

#8826

semidirect

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

subgroup	index
#14563807	2
#14562394	2
C₂×C₁₉×#322	2
#8826	19

subgroup

index

#14563807

#14562394

C₂×C₁₉×#322

#8826

Subgroups — #18076353

Conjugacy classes of subgroups

Complements

Maximal subgroups