Group #18070172 — subgroups

Subgroups — #18070172

Order 4864.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	C₄⋊(C₁₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561707	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2246	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	—	2	1	no	—
5	#11926297	—	2	1	no	—
6	C₂×C₁₉×D₁₆	—	2	1	no	—
7	C₂×C₁₉×D₁₆	C₄	1	2	yes	—
8	C₁₉×#493	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×D₈×C₁₉	—	2	2	no	—
11	C₂×D₈×C₁₉	—	4	1	no	—
12	C₁₉×#127	—	4	1	no	—
13	C₁₉×D₁₆	—	4	2	no	—
14	C₁₉×D₁₆	—	4	1	no	—
15	C₁₉×D₁₆	—	4	1	no	—
16	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
20	C₁₉⋊C₃₂	—	4	1	no	—
21	C₂×D₄×C₁₉	—	4	2	no	—
22	C₂×D₄×C₁₉	—	8	1	no	—
23	C₂×D₄×C₁₉	—	8	1	no	—
24	D₈×C₁₉	—	4	2	no	—
25	D₈×C₁₉	—	4	2	no	—
26	D₈×C₁₉	—	8	2	no	—
27	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₄²×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₁₉⋊C₈	—	8	1	no	—
31	C₁₆×C₁₉	—	2	1	no	—
32	C₁₆×C₁₉	D₈	1	1	yes	characteristic
33	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
34	#7444	—	19	1	no	maximal, Sylow
35	C₂³×C₁₉	—	8	2	no	—
36	D₄×C₁₉	—	8	2	no	—
37	D₄×C₁₉	—	8	2	no	—
38	D₄×C₁₉	—	16	2	no	—
39	D₄×C₁₉	—	16	1	no	—
40	D₄×C₁₉	—	16	1	no	—
41	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
42	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
44	C₈×C₁₉	—	2	1	no	—
45	C₈×C₁₉	#100	1	1	yes	characteristic
46	C₈×C₁₉	#102	1	1	yes	characteristic
47	C₁₉⋊C₈	—	16	1	no	—
48	#2246	D₁₉	1	1	yes	characteristic
49	C₄⋊C₃₂	—	19	1	no	—
50	#1371	—	19	1	no	—
51	C₂²×C₁₉	—	16	2	no	—
52	C₂²×C₁₉	—	16	2	no	—
53	C₂²×C₁₉	—	16	2	no	—
54	C₂²×C₁₉	#357	1	1	yes	characteristic
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	#331	1	1	yes	characteristic
57	C₄×C₁₉	#361	1	1	yes	characteristic
58	C₄×C₁₉	D₃₂	1	1	yes	characteristic
59	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
60	C₂×D₁₆	—	2	1	no	—
61	C₂×D₁₆	Dic₁₉	1	2	yes	—
62	#493	—	2	1	no	—
63	C₂×C₃₂	—	38	1	no	—
64	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
65	#335	—	38	1	no	—
66	C₂×C₁₉	—	32	2	no	—
67	C₂×C₁₉	#1361	1	1	yes	characteristic
68	C₂×C₁₉	#1415	1	1	yes	characteristic
69	C₂×C₁₉	#1419	1	1	yes	characteristic
70	C₂×D₈	—	2	2	no	—
71	C₂×D₈	—	4	1	no	—
72	#127	—	4	1	no	—
73	D₁₆	—	4	2	no	—
74	D₁₆	—	4	1	no	—
75	D₁₆	—	4	1	no	—
76	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
77	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₄⋊C₈	—	76	1	no	—
79	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
80	C₃₂	—	76	1	no	—
81	C₁₉	#7444	1	1	yes	characteristic, complemented, Sylow
82	C₂×D₄	—	4	2	no	—
83	C₂×D₄	—	8	1	no	—
84	C₂×D₄	—	8	1	no	—
85	D₈	—	4	2	no	—
86	D₈	—	4	2	no	—
87	D₈	—	8	2	no	—
88	C₂×C₈	—	152	1	no	—
89	C₂×C₈	#64526	1	1	yes	characteristic
90	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
91	C₄²	#64525	1	1	yes	characteristic
92	C₁₆	—	2	1	no	—
93	C₁₆	#64525	1	1	yes	characteristic
94	C₁₆	#64526	1	1	yes	characteristic
95	C₂³	—	8	2	no	—
96	D₄	—	8	2	no	—
97	D₄	—	8	2	no	—
98	D₄	—	16	2	no	—
99	D₄	—	16	1	no	—
100	D₄	—	16	1	no	—
101	C₂×C₄	#10597283	1	1	yes	characteristic
102	C₂×C₄	#10597284	1	1	yes	characteristic
103	C₂×C₄	#10597289	1	1	yes	characteristic
104	C₈	—	2	1	no	—
105	C₈	—	304	1	no	—
106	C₈	#10597289	1	1	yes	characteristic
107	C₈	#10597290	1	1	yes	characteristic
108	C₂²	—	16	2	no	—
109	C₂²	—	16	2	no	—
110	C₂²	—	16	2	no	—
111	C₂²	#11926345	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	#11926288	1	1	yes	characteristic
114	C₄	#11926357	1	1	yes	characteristic
115	C₄	#11926379	1	1	yes	characteristic
116	C₄	#11926382	1	1	yes	characteristic
117	C₂	—	32	2	no	—
118	C₂	#14561681	1	1	yes	characteristic
119	C₂	#14561813	1	1	yes	characteristic
120	C₂	#14561825	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₁₉⋊C₃₂)

C₂

yes

maximal, characteristic, complemented

#14561707

C₂

yes

maximal, characteristic, complemented

C₁₉×#2246

C₂

yes

maximal, characteristic

C₂×C₁₉⋊C₃₂

—

#11926297

—

C₂×C₁₉×D₁₆

—

C₂×C₁₉×D₁₆

C₄

yes

—

C₁₉×#493

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×#127

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄⋊(C₁₉⋊C₈)

—

C₁₉⋊C₃₂

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

#7444

—

maximal, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2246

D₁₉

yes

characteristic

C₄⋊C₃₂

—

#1371

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

D₃₂

yes

characteristic

C₄×C₁₉

SD₆₄

yes

characteristic

C₂×D₁₆

—

C₂×D₁₆

Dic₁₉

yes

—

#493

—

C₂×C₃₂

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

#335

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×D₈

—

C₂×D₈

—

#127

—

D₁₆

—

D₁₆

—

D₁₆

—

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7444

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

—

152

—

C₂×C₈

#64526

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄²

#64525

yes

characteristic

C₁₆

—

C₁₆

yes

C₁₆

yes

C₂³

—

D₄

—

D₄

—

D₄

—

D₄

—

100

D₄

—

101

C₂×C₄

#10597283

yes

characteristic

102

C₂×C₄

#10597284

yes

characteristic

103

C₂×C₄

#10597289

yes

characteristic

104

C₈

—

105

C₈

—

304

—

106

C₈

#10597289

yes

characteristic

107

C₈

#10597290

yes

characteristic

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

#11926345

yes

characteristic

112

C₄

—

113

C₄

#11926288

yes

characteristic

114

C₄

#11926357

yes

characteristic

115

C₄

#11926379

yes

characteristic

116

C₄

#11926382

yes

characteristic

117

C₂

—

118

C₂

#14561681

yes

characteristic

119

C₂

#14561813

yes

characteristic

120

C₂

#14561825

yes

characteristic

	subgroup	G/H
center	C₂²	#11926345
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting, prime radical	C₁₉×#2246	C₂
socle	C₂²×C₁₉	#357
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#2246	D₁₉
hypocenter	C₁₉	#7444
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2246

subgroup

G/H

center

C₂²

#11926345

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting, prime radical

C₁₉×#2246

C₂

socle

C₂²×C₁₉

#357

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2246

N	H ≅ G/N	type
1. C₄⋊(C₁₉⋊C₃₂)	C₂	semidirect
2. #14561707	C₂	semidirect
81. C₁₉	#7444	semidirect

H ≅ G/N

type

1. C₄⋊(C₁₉⋊C₃₂)

C₂

semidirect

2. #14561707

C₂

semidirect

81. C₁₉

#7444

semidirect

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

subgroup	index
C₄⋊(C₁₉⋊C₃₂)	2
#14561707	2
C₁₉×#2246	2
#7444	19

subgroup

index

C₄⋊(C₁₉⋊C₃₂)

#14561707

C₁₉×#2246

#7444

Subgroups — #18070172

Conjugacy classes of subgroups

Complements

Maximal subgroups