Group #18069274 — subgroups

Subgroups — #18069274

Order 4864.

142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14563253	C₂	1	1	yes	maximal, characteristic
2	#14561705	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1370	C₂	1	1	yes	maximal, characteristic
4	#11926949	—	2	1	no	—
5	#11926949	—	2	1	no	—
6	#11926924	C₄	1	2	yes	—
7	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
8	C₁₉×C₄⋊C₁₆	—	2	1	no	—
9	C₈²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₆	—	4	2	no	—
11	#10597315	—	2	2	no	—
12	C₂×C₁₆×C₁₉	—	4	1	no	—
13	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	#10597275	—	4	1	no	—
17	#10597275	—	4	1	no	—
18	#10597275	—	4	1	no	—
19	#10597275	—	4	1	no	—
20	C₂×C₁₉⋊C₁₆	—	4	1	no	—
21	C₂×Dic₃₈	—	4	2	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
24	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
25	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
26	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₄⋊Dic₁₉	—	4	2	no	—
29	C₄⋊Dic₁₉	—	4	2	no	—
30	Dic₇₆	—	8	4	no	—
31	C₁₆×C₁₉	—	8	1	no	—
32	C₁₉⋊C₁₆	—	8	1	no	—
33	#7098	—	19	1	no	maximal, Sylow
34	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
35	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
36	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
37	C₂×Dic₁₉	—	8	2	no	—
38	Dic₃₈	—	8	4	no	—
39	C₈×C₁₉	—	2	2	no	—
40	C₈×C₁₉	—	2	1	no	—
41	C₈×C₁₉	—	2	1	no	—
42	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
43	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
44	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
45	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
46	#1713	—	19	1	no	—
47	#1370	—	19	1	no	—
48	#1370	D₁₉	1	1	yes	characteristic
49	C₂²×C₁₉	#331	1	1	yes	characteristic
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	#358	1	1	yes	characteristic
52	C₄×C₁₉	#358	1	1	yes	characteristic
53	C₄×C₁₉	#362	1	1	yes	characteristic
54	C₄×C₁₉	#362	1	1	yes	characteristic
55	Dic₁₉	—	16	2	no	—
56	#500	—	38	1	no	—
57	#500	—	38	1	no	—
58	#494	—	19	2	no	—
59	C₄⋊C₁₆	—	2	1	no	—
60	C₄⋊C₁₆	—	38	1	no	—
61	C₈²	C₂×D₁₉	1	1	yes	characteristic
62	C₂×C₁₉	#1357	1	1	yes	characteristic
63	C₂×C₁₉	#1362	1	1	yes	characteristic
64	C₂×C₁₉	#1362	1	1	yes	characteristic
65	C₂×Q₁₆	—	76	2	no	—
66	C₄⋊Q₈	—	38	2	no	—
67	C₂×C₁₆	—	4	1	no	—
68	C₂×C₁₆	—	76	1	no	—
69	#107	—	76	1	no	—
70	#107	—	76	1	no	—
71	#107	—	76	1	no	—
72	#107	—	76	1	no	—
73	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
74	C₄×C₈	D₇₆	1	1	yes	characteristic
75	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
76	C₁₉	#7098	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	76	2	no	—
78	Q₁₆	—	152	4	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	#64516	1	1	yes	characteristic
81	C₂×C₈	D₁₅₂	1	1	yes	characteristic
82	C₂×C₈	#64525	1	1	yes	characteristic
83	C₂×C₈	#64527	1	1	yes	characteristic
84	C₄⋊C₄	—	76	2	no	—
85	C₄⋊C₄	—	76	2	no	—
86	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
87	C₁₆	—	8	1	no	—
88	C₁₆	—	152	1	no	—
89	Q₈	—	152	4	no	—
90	C₂×C₄	—	152	2	no	—
91	C₂×C₄	#10597266	1	1	yes	characteristic
92	C₂×C₄	#10597278	1	1	yes	characteristic
93	C₂×C₄	#10597280	1	1	yes	characteristic
94	C₈	—	2	2	no	—
95	C₈	—	2	1	no	—
96	C₈	—	2	1	no	—
97	C₈	#10597257	1	1	yes	characteristic
98	C₈	Dic₁₅₂	1	1	yes	characteristic
99	C₈	#10597284	1	1	yes	characteristic
100	C₈	#10597286	1	1	yes	characteristic
101	C₂²	#11926287	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	304	2	no	—
104	C₄	#11926347	1	1	yes	characteristic
105	C₄	#11926349	1	1	yes	characteristic
106	C₄	#11926359	1	1	yes	characteristic
107	C₄	#11926361	1	1	yes	characteristic
108	C₂	#14561671	1	1	yes	characteristic
109	C₂	#14561683	1	1	yes	characteristic
110	C₂	#14561685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563253

C₂

yes

maximal, characteristic

#14561705

C₂

yes

maximal, characteristic

C₁₉×#1370

C₂

yes

maximal, characteristic

#11926949

—

#11926949

—

#11926924

C₄

yes

—

C₄⋊(C₁₉⋊C₁₆)

—

C₁₉×C₄⋊C₁₆

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

—

#10597315

—

C₂×C₁₆×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

—

—

—

C₂×C₁₉⋊C₁₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

Q₃₂

yes

characteristic

C₈×C₁₉

Q₃₂

yes

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

#331

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#500

—

#500

—

#494

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7098

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

152

—

C₂×C₈

—

C₂×C₈

#64516

yes

characteristic

C₂×C₈

D₁₅₂

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

C₁₆

—

C₁₆

—

152

—

Q₈

—

152

—

C₂×C₄

—

152

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

—

C₈

#10597257

yes

characteristic

C₈

Dic₁₅₂

yes

characteristic

C₈

#10597284

yes

characteristic

100

C₈

#10597286

yes

characteristic

101

C₂²

#11926287

yes

characteristic

102

C₄

—

103

C₄

—

304

—

104

C₄

#11926347

yes

characteristic

105

C₄

#11926349

yes

characteristic

106

C₄

#11926359

yes

characteristic

107

C₄

#11926361

yes

characteristic

108

C₂

#14561671

yes

characteristic

109

C₂

#14561683

yes

characteristic

110

C₂

#14561685

yes

characteristic

	subgroup	G/H
center	C₂²	#11926287
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1370	C₂
socle, prime radical	C₂²×C₁₉	#331
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1370	D₁₉
hypocenter	C₁₉	#7098
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1370

subgroup

G/H

center

C₂²

#11926287

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1370

C₂

socle, prime radical

C₂²×C₁₉

#331

cosocle

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1370

N	H ≅ G/N	type
76. C₁₉	#7098	semidirect

H ≅ G/N

type

76. C₁₉

#7098

semidirect

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

subgroup	index
#14563253	2
#14561705	2
C₁₉×#1370	2
#7098	19

subgroup

index

#14563253

#14561705

C₁₉×#1370

#7098

Subgroups — #18069274

Conjugacy classes of subgroups

Complements

Maximal subgroups