Group #18076292 — subgroups

Subgroups — #18076292

Order 4864.

402 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 211 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	#14563787	C₂	1	2	yes	maximal
2	C₂×#11926295	C₂	1	4	yes	maximal
3	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	#11926295	—	2	8	no	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
8	C₄³×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#336	C₄	1	4	yes	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₉	D₄	1	2	yes	—
13	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	4	no	—
16	C₄×C₈×C₁₉	D₄	1	4	yes	—
17	C₄×C₈×C₁₉	Q₈	1	4	yes	—
18	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	8	no	—
20	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
21	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₈×C₁₉	—	2	8	no	—
25	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
26	C₄²×C₁₉	—	2	4	no	—
27	C₄²×C₁₉	—	4	2	no	—
28	C₄²×C₁₉	SD₁₆	1	8	yes	—
29	C₄²×C₁₉	C₂×D₄	1	2	yes	—
30	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	C₂×C₁₉⋊C₈	—	4	8	no	—
33	#8809	—	19	1	no	maximal, Sylow
34	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	#106	1	8	yes	—
39	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
42	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#131	1	4	yes	—
44	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
45	C₈×C₁₉	—	2	8	no	—
46	C₁₉⋊C₈	—	8	4	no	—
47	#1842	—	19	2	no	—
48	#1744	D₁₉	1	1	yes	characteristic
49	C₂×#334	—	19	4	no	—
50	C₂²×C₁₉	#384	1	1	yes	characteristic
51	C₂²×C₁₉	#424	1	2	yes	—
52	C₂²×C₁₉	C₂×#106	1	2	yes	—
53	C₂²×C₁₉	#430	1	2	yes	—
54	C₄×C₁₉	—	2	8	no	—
55	C₄×C₁₉	—	2	2	no	—
56	C₄×C₁₉	#424	1	4	yes	—
57	C₄×C₁₉	#492	1	2	yes	—
58	C₄×C₁₉	#498	1	2	yes	—
59	C₂×C₄⋊C₈	—	19	4	no	—
60	C₂×C₄⋊C₈	—	38	4	no	—
61	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
62	C₄³	C₂×D₁₉	1	1	yes	characteristic
63	#336	Dic₁₉	1	4	yes	—
64	#334	—	38	8	no	—
65	C₂×C₁₉	#1570	1	4	yes	—
66	C₂×C₁₉	#1843	1	1	yes	characteristic
67	C₂×C₁₉	#1844	1	1	yes	characteristic
68	C₂×C₁₉	#1849	1	1	yes	characteristic
69	C₂²×C₈	—	38	4	no	—
70	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
71	C₂×C₄²	Dic₃₈	1	2	yes	—
72	C₂×C₄²	D₇₆	1	2	yes	—
73	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
74	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
75	C₄⋊C₈	—	38	8	no	—
76	C₄⋊C₈	—	76	8	no	—
77	C₄×C₈	Dic₃₈	1	4	yes	—
78	C₄×C₈	D₇₆	1	4	yes	—
79	C₁₉	#8809	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
81	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
82	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
83	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
84	C₂×C₈	—	2	8	no	—
85	C₂×C₈	—	76	4	no	—
86	C₂×C₈	—	76	8	no	—
87	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	—
88	C₄²	—	2	4	no	—
89	C₄²	—	4	2	no	—
90	C₄²	#64516	1	8	yes	—
91	C₄²	C₂×Dic₃₈	1	2	yes	—
92	C₄²	C₂×D₇₆	1	2	yes	—
93	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	#10597274	1	8	yes	—
98	C₂×C₄	#10597315	1	2	yes	—
99	C₂×C₄	#10597315	1	1	yes	characteristic
100	C₂×C₄	#10597320	1	1	yes	characteristic
101	C₂×C₄	C₂×#64516	1	4	yes	—
102	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
103	C₂×C₄	#10597394	1	4	yes	—
104	C₈	—	2	8	no	—
105	C₈	—	152	4	no	—
106	C₂²	#11926414	1	1	yes	characteristic
107	C₂²	#11926571	1	2	yes	—
108	C₂²	C₂×#10597274	1	2	yes	—
109	C₂²	#11926593	1	2	yes	—
110	C₄	—	2	8	no	—
111	C₄	—	2	2	no	—
112	C₄	#11926571	1	4	yes	—
113	C₄	#11926917	1	2	yes	—
114	C₄	#11926942	1	2	yes	—
115	C₂	#14562406	1	4	yes	—
116	C₂	#14563789	1	1	yes	characteristic
117	C₂	#14563792	1	1	yes	characteristic
118	C₂	#14563810	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563787

C₂

yes

maximal

C₂×#11926295

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926295

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8809

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#106

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1842

—

#1744

D₁₉

yes

characteristic

C₂×#334

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#424

yes

—

C₂²×C₁₉

C₂×#106

yes

—

C₂²×C₁₉

#430

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

#492

yes

—

C₄×C₁₉

#498

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#336

Dic₁₉

yes

—

#334

—

C₂×C₁₉

#1570

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

Dic₃₈

yes

—

C₂×C₄²

D₇₆

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

D₇₆

yes

—

C₁₉

#8809

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄⋊Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

C₂²×C₄

C₂×D₇₆

yes

characteristic

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄²

—

C₄²

—

C₄²

#64516

yes

—

C₄²

C₂×Dic₃₈

yes

—

C₄²

C₂×D₇₆

yes

—

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597274

yes

—

C₂×C₄

#10597315

yes

—

C₂×C₄

#10597315

yes

characteristic

100

C₂×C₄

#10597320

yes

characteristic

101

C₂×C₄

C₂×#64516

yes

—

102

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

—

103

C₂×C₄

#10597394

yes

—

104

C₈

—

105

C₈

—

152

—

106

C₂²

#11926414

yes

characteristic

107

C₂²

#11926571

yes

—

108

C₂²

C₂×#10597274

yes

—

109

C₂²

#11926593

yes

—

110

C₄

—

111

C₄

—

112

C₄

#11926571

yes

—

113

C₄

#11926917

yes

—

114

C₄

#11926942

yes

—

115

C₂

#14562406

yes

—

116

C₂

#14563789

yes

characteristic

117

C₂

#14563792

yes

characteristic

118

C₂

#14563810

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#8809
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₇₆

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1744

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
79. C₁₉	#8809	semidirect

H ≅ G/N

type

79. C₁₉

#8809

semidirect

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

subgroup	index
#14563787	2
C₂×#11926295	2
C₁₉×#1744	2
#8809	19

subgroup

index

#14563787

C₂×#11926295

C₁₉×#1744

#8809

Subgroups — #18076292

Conjugacy classes of subgroups

Complements

Maximal subgroups