Group #18076246 — subgroups

Subgroups — #18076246

Order 4864.

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

normal subgroups only

This group has 228 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	#14562398	C₂	1	2	yes	maximal
2	#14561497	C₂	1	4	yes	maximal
3	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic
4	#11926601	C₂²	1	4	yes	—
5	#11926297	—	2	2	no	—
6	#11926295	—	2	2	no	—
7	C₁₉×#431	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#322	C₄	1	2	yes	—
10	C₈²×C₁₉	C₄	1	2	yes	—
11	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₁₉×C₄⋊C₈	—	2	2	no	—
15	C₁₉×C₂²⋊C₈	—	2	2	no	—
16	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
22	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
23	#10597260	—	2	4	no	—
24	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	#41	1	2	yes	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	4	no	—
29	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₄²×C₁₉	#41	1	2	yes	—
36	C₂×C₁₉⋊C₈	—	4	4	no	—
37	#8796	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	#125	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	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	2	yes	—
44	C₂×C₄×C₁₉	#124	1	2	yes	—
45	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
46	C₈×C₁₉	—	2	1	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	—	4	4	no	—
49	C₈×C₁₉	#108	1	2	yes	—
50	C₈×C₁₉	#108	1	2	yes	—
51	C₁₉⋊C₈	—	8	4	no	—
52	#1568	—	19	2	no	—
53	#1450	D₁₉	1	1	yes	characteristic
54	#1287	—	19	4	no	—
55	C₂²×C₁₉	—	2	2	no	—
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	#382	1	1	yes	characteristic
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
62	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
63	#432	—	19	4	no	—
64	#431	C₂×D₁₉	1	2	yes	—
65	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
66	#335	—	38	2	no	—
67	#334	—	38	2	no	—
68	#322	Dic₁₉	1	2	yes	—
69	C₈²	Dic₁₉	1	2	yes	—
70	C₂×C₁₉	—	4	1	no	—
71	C₂×C₁₉	#1833	1	2	yes	—
72	C₂×C₁₉	#1837	1	1	yes	characteristic
73	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
74	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
75	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
76	C₄⋊C₈	—	2	2	no	—
77	C₄⋊C₈	—	38	4	no	—
78	C₂²⋊C₈	—	2	2	no	—
79	C₂²⋊C₈	—	38	4	no	—
80	#97	—	38	4	no	—
81	C₄×C₈	D₇₆	1	1	yes	characteristic
82	C₄×C₈	D₇₆	1	1	yes	characteristic
83	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
84	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
85	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
86	C₁₉	#8796	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
88	C₂²×C₄	#64541	1	2	yes	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	76	4	no	—
93	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
95	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
96	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
97	C₄²	C₂×D₇₆	1	1	yes	characteristic
98	C₄²	#64541	1	2	yes	—
99	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
100	C₂³	#10597316	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	#10597316	1	1	yes	characteristic
105	C₂×C₄	#10597321	1	2	yes	—
106	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
107	C₂×C₄	#10597372	1	2	yes	—
108	C₈	—	2	1	no	—
109	C₈	—	2	1	no	—
110	C₈	—	4	4	no	—
111	C₈	—	152	4	no	—
112	C₈	#10597276	1	2	yes	—
113	C₈	#10597276	1	2	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	1	no	—
116	C₂²	#11926410	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	2	2	no	—
119	C₄	—	2	1	no	—
120	C₄	C₂×#10597276	1	1	yes	characteristic
121	C₄	C₂×#10597276	1	1	yes	characteristic
122	C₂	—	4	1	no	—
123	C₂	#14563759	1	2	yes	—
124	C₂	#14563773	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562398

C₂

yes

maximal

#14561497

C₂

yes

maximal

C₁₉×#1450

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926297

—

#11926295

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

C₄

yes

—

C₈²×C₁₉

C₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

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

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#125

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#108

yes

—

C₈×C₁₉

#108

yes

—

C₁₉⋊C₈

—

#1568

—

#1450

D₁₉

yes

characteristic

#1287

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×D₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

Dic₁₉

yes

—

C₈²

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#1833

yes

—

C₂×C₁₉

#1837

yes

characteristic

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

Dic₃₈

yes

characteristic

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₁₉

#8796

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

C₂²×C₄

#64541

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

C₄²

C₂×D₇₆

yes

characteristic

C₄²

#64541

yes

—

C₄²

C₂²×Dic₁₉

yes

characteristic

100

C₂³

#10597316

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#10597316

yes

characteristic

105

C₂×C₄

#10597321

yes

—

106

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

107

C₂×C₄

#10597372

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

152

—

112

C₈

#10597276

yes

—

113

C₈

#10597276

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

#11926410

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

C₂×#10597276

yes

characteristic

121

C₄

C₂×#10597276

yes

characteristic

122

C₂

—

123

C₂

#14563759

yes

—

124

C₂

#14563773

yes

characteristic

	subgroup	G/H
center	C₂²	#11926410
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1450	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#125
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1450	D₁₉
hypocenter	C₁₉	#8796
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

subgroup

G/H

center

C₂²

#11926410

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1450

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

N	H ≅ G/N	type
86. C₁₉	#8796	semidirect

H ≅ G/N

type

86. C₁₉

#8796

semidirect

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

subgroup	index
#14562398	2
#14561497	2
C₁₉×#1450	2
#8796	19

subgroup

index

#14562398

#14561497

C₁₉×#1450

#8796

Subgroups — #18076246

Conjugacy classes of subgroups

Complements

Maximal subgroups