Group #18076227 — subgroups

Subgroups — #18076227

Order 4864.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563773	C₂	1	1	yes	maximal, characteristic
2	#14561918	C₂	1	1	yes	maximal, characteristic
3	#14561493	C₂	1	4	yes	maximal
4	C₁₉×#1835	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	2	yes	—
6	#11926568	C₂²	1	2	yes	—
7	#11926309	—	2	2	no	—
8	#11926265	C₄	1	2	yes	complemented
9	C₈×C₁₉⋊C₈	C₄	1	2	yes	complemented
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#382	C₂²	1	2	yes	—
12	C₁₉×#340	—	2	2	no	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
16	C₂×#64520	—	2	2	no	—
17	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	Q₈	1	2	yes	—
20	C₁₉×#95	—	2	4	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
24	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₁₉	—	4	2	no	—
26	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	#41	1	2	yes	—
28	C₂×C₈×C₁₉	—	2	4	no	—
29	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₄⋊C₄×C₁₉	—	4	4	no	—
32	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₄²×C₁₉	#41	1	2	yes	—
35	#64520	—	4	4	no	—
36	C₂×C₁₉⋊C₈	—	2	4	no	—
37	C₂×C₁₉⋊C₈	—	4	2	no	—
38	#8792	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#124	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	—	8	4	no	—
42	C₂×C₄×C₁₉	—	8	2	no	—
43	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#117	1	2	yes	—
45	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#125	1	2	yes	—
47	C₂×C₄×C₁₉	#135	1	4	yes	—
48	C₈×C₁₉	—	2	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₁₉⋊C₈	—	4	4	no	—
51	C₁₉⋊C₈	—	8	2	no	—
52	#1837	—	19	1	no	—
53	#1835	D₁₉	1	1	yes	characteristic
54	#1450	—	19	1	no	—
55	#1286	—	19	4	no	—
56	C₂²×C₁₉	—	2	2	no	—
57	C₂²×C₁₉	#382	1	1	yes	characteristic
58	C₂²×C₁₉	#488	1	2	yes	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	—	16	2	no	—
62	C₄×C₁₉	#427	1	2	yes	—
63	C₄×C₁₉	#488	1	2	yes	—
64	#431	—	19	2	no	—
65	#423	—	19	2	no	—
66	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
67	#382	C₂×D₁₉	1	2	yes	—
68	#341	—	38	2	no	—
69	#340	—	2	2	no	—
70	#322	—	19	2	no	—
71	C₈²	—	19	2	no	—
72	C₂×C₁₉	—	2	2	no	—
73	C₂×C₁₉	#1833	1	2	yes	—
74	C₂×C₁₉	#1835	1	1	yes	characteristic
75	C₂×M₁₆	—	38	2	no	—
76	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
77	C₂×C₄⋊C₄	—	2	2	no	—
78	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
79	C₄⋊C₈	—	38	2	no	—
80	C₄⋊C₈	—	38	4	no	—
81	C₂²⋊C₈	—	38	2	no	—
82	C₄×C₈	—	19	4	no	—
83	C₄×C₈	Dic₃₈	1	2	yes	—
84	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
85	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
86	#95	—	2	4	no	—
87	C₁₉	#8792	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	4	2	no	—
89	C₂²×C₄	#64543	1	2	yes	—
90	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
91	M₁₆	—	76	4	no	—
92	C₂×C₈	—	2	4	no	—
93	C₂×C₈	—	38	4	no	—
94	C₂×C₈	—	76	2	no	—
95	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
96	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
97	C₄⋊C₄	—	4	4	no	—
98	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
99	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
100	C₄²	#64545	1	2	yes	—
101	C₂³	#10597382	1	1	yes	characteristic
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	—	8	4	no	—
104	C₂×C₄	—	8	2	no	—
105	C₂×C₄	#10597336	1	2	yes	—
106	C₂×C₄	#10597338	1	2	yes	—
107	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
108	C₂×C₄	#10597393	1	1	yes	characteristic
109	C₂×C₄	#10597396	1	4	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	2	2	no	—
112	C₈	—	76	4	no	—
113	C₈	—	152	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#11926409	1	1	yes	characteristic
116	C₂²	#11926898	1	2	yes	—
117	C₄	—	2	2	no	—
118	C₄	—	2	2	no	—
119	C₄	—	16	2	no	—
120	C₄	#11926580	1	2	yes	—
121	C₄	#11926901	1	2	yes	—
122	C₂	—	2	2	no	—
123	C₂	#14563758	1	2	yes	—
124	C₂	#14563765	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563773

C₂

yes

maximal, characteristic

#14561918

C₂

yes

maximal, characteristic

#14561493

C₂

yes

maximal

C₁₉×#1835

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

#11926309

—

#11926265

C₄

yes

complemented

C₈×C₁₉⋊C₈

C₄

yes

complemented

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#382

C₂²

yes

—

C₁₉×#340

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1837

—

#1835

D₁₉

yes

characteristic

#1450

—

#1286

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#488

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#427

yes

—

C₄×C₁₉

#488

yes

—

#431

—

#423

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#382

C₂×D₁₉

yes

—

#341

—

#340

—

#322

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

#1833

yes

—

C₂×C₁₉

#1835

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

C₄×D₁₉

yes

characteristic

#95

—

C₁₉

#8792

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

#64543

yes

—

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₄⋊C₄

—

C₄²

C₂×Dic₃₈

yes

characteristic

C₄²

C₂×C₄×D₁₉

yes

characteristic

100

C₄²

#64545

yes

—

101

C₂³

#10597382

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

#10597336

yes

—

106

C₂×C₄

#10597338

yes

—

107

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

108

C₂×C₄

#10597393

yes

characteristic

109

C₂×C₄

#10597396

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

152

—

114

C₂²

—

115

C₂²

#11926409

yes

characteristic

116

C₂²

#11926898

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

#11926580

yes

—

121

C₄

#11926901

yes

—

122

C₂

—

123

C₂

#14563758

yes

—

124

C₂

#14563765

yes

characteristic

	subgroup	G/H
center	C₂²	#11926409
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1835	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1835	D₁₉
hypocenter	C₁₉	#8792
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#11926409

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1835

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
8. #11926265	C₄	semidirect
9. C₈×C₁₉⋊C₈	C₄	semidirect
87. C₁₉	#8792	semidirect

H ≅ G/N

type

8. #11926265

C₄

semidirect

9. C₈×C₁₉⋊C₈

C₄

semidirect

87. C₁₉

#8792

semidirect

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

subgroup	index
#14563773	2
#14561918	2
#14561493	2
C₁₉×#1835	2
#8792	19

subgroup

index

C₁₉×#1835

Subgroups — #18076227

Conjugacy classes of subgroups

Complements

Maximal subgroups