Group #18076193 — subgroups

Subgroups — #18076193

Order 4864.

262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14562383	C₂	1	2	yes	maximal
2	#14561480	C₂	1	2	yes	maximal
3	#14561464	C₂	1	2	yes	maximal
4	C₁₉×#1746	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926297	—	2	2	no	—
7	#11926295	—	2	2	no	—
8	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#376	C₂²	1	1	yes	characteristic
11	C₁₉×#336	C₄	1	4	yes	—
12	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
16	C₁₉×#97	—	2	2	no	—
17	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	Q₈	1	2	yes	—
20	C₁₉×#95	—	2	2	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
22	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
23	C₄×C₁₉⋊C₈	—	2	4	no	—
24	C₂²×C₄×C₁₉	—	2	2	no	—
25	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	#41	1	2	yes	—
27	C₂×C₈×C₁₉	—	2	4	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	4	no	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₄²×C₁₉	—	2	4	no	—
33	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₄²×C₁₉	#41	1	2	yes	—
36	C₂×C₁₉⋊C₈	—	4	4	no	—
37	#8782	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	#117	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	4	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#124	1	2	yes	—
45	C₂×C₄×C₁₉	#125	1	2	yes	—
46	C₂×C₄×C₁₉	#131	1	4	yes	—
47	C₈×C₁₉	—	2	2	no	—
48	C₈×C₁₉	—	2	2	no	—
49	C₈×C₁₉	—	4	2	no	—
50	C₁₉⋊C₈	—	8	4	no	—
51	#1746	D₁₉	1	1	yes	characteristic
52	#1564	—	19	2	no	—
53	#1281	—	19	2	no	—
54	#1274	—	19	2	no	—
55	C₂²×C₁₉	—	2	2	no	—
56	C₂²×C₁₉	#382	1	1	yes	characteristic
57	C₂²×C₁₉	#433	1	2	yes	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	8	2	no	—
61	C₄×C₁₉	#424	1	2	yes	—
62	C₄×C₁₉	#433	1	2	yes	—
63	#431	—	19	4	no	—
64	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
66	#376	C₂×D₁₉	1	1	yes	characteristic
67	#336	Dic₁₉	1	4	yes	—
68	#335	—	38	2	no	—
69	#334	—	38	2	no	—
70	C₂×C₁₉	—	2	2	no	—
71	C₂×C₁₉	#1832	1	1	yes	characteristic
72	C₂×C₁₉	#1833	1	2	yes	—
73	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
74	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
75	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
76	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
77	C₄⋊C₈	—	38	4	no	—
78	C₂²⋊C₈	—	38	4	no	—
79	#97	—	2	2	no	—
80	C₄×C₈	—	38	4	no	—
81	C₄×C₈	Dic₃₈	1	2	yes	—
82	C₄×C₈	D₇₆	1	1	yes	characteristic
83	C₄×C₈	D₇₆	1	1	yes	characteristic
84	#95	—	2	2	no	—
85	C₁₉	#8782	1	1	yes	characteristic, complemented, Sylow
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	#64541	1	2	yes	—
88	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
89	C₂×C₈	—	2	4	no	—
90	C₂×C₈	—	2	4	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	76	4	no	—
93	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
94	C₂×C₈	C₄⋊Dic₁₉	1	2	yes	—
95	C₄²	—	2	4	no	—
96	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
97	C₄²	C₂×D₇₆	1	1	yes	characteristic
98	C₄²	#64541	1	2	yes	—
99	C₂³	#10597372	1	1	yes	characteristic
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	4	no	—
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	#10597316	1	2	yes	—
104	C₂×C₄	#10597321	1	2	yes	—
105	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
106	C₂×C₄	#10597372	1	1	yes	characteristic
107	C₂×C₄	#10597394	1	4	yes	—
108	C₈	—	2	2	no	—
109	C₈	—	2	2	no	—
110	C₈	—	4	2	no	—
111	C₈	—	152	4	no	—
112	C₂²	—	2	2	no	—
113	C₂²	#11926410	1	1	yes	characteristic
114	C₂²	#11926605	1	2	yes	—
115	C₄	—	2	2	no	—
116	C₄	—	2	2	no	—
117	C₄	—	8	2	no	—
118	C₄	#11926571	1	2	yes	—
119	C₄	#11926605	1	2	yes	—
120	C₂	—	2	2	no	—
121	C₂	#14563755	1	1	yes	characteristic
122	C₂	#14563759	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562383

C₂

yes

maximal

#14561480

C₂

yes

maximal

#14561464

C₂

yes

maximal

C₁₉×#1746

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926297

—

#11926295

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#97

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1746

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

#433

yes

—

#431

—

C₂×#97

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#376

C₂×D₁₉

yes

characteristic

#336

Dic₁₉

yes

—

#335

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

#1832

yes

characteristic

C₂×C₁₉

#1833

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

#95

—

C₁₉

#8782

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

#64541

yes

—

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄²

—

C₄²

C₂×Dic₃₈

yes

characteristic

C₄²

C₂×D₇₆

yes

characteristic

C₄²

#64541

yes

—

C₂³

#10597372

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#10597316

yes

—

104

C₂×C₄

#10597321

yes

—

105

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

106

C₂×C₄

#10597372

yes

characteristic

107

C₂×C₄

#10597394

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

152

—

112

C₂²

—

113

C₂²

#11926410

yes

characteristic

114

C₂²

#11926605

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#11926571

yes

—

119

C₄

#11926605

yes

—

120

C₂

—

121

C₂

#14563755

yes

characteristic

122

C₂

#14563759

yes

—

	subgroup	G/H
center	C₂×C₄	#10597372
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1746	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1746	D₁₉
hypocenter	C₁₉	#8782
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ #1746

subgroup

G/H

center

C₂×C₄

#10597372

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1746

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ #376 ◁ #1746

N	H ≅ G/N	type
85. C₁₉	#8782	semidirect

H ≅ G/N

type

85. C₁₉

#8782

semidirect

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

subgroup	index
#14562383	2
#14561480	2
#14561464	2
C₁₉×#1746	2
#8782	19

subgroup

index

C₁₉×#1746

Subgroups — #18076193

Conjugacy classes of subgroups

Complements

Maximal subgroups