Group #18069710 — subgroups

Subgroups — #18069710

Order 4864.

238 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 111 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	C₂×#11926365	C₂	1	2	yes	maximal
2	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597269	—	2	2	no	—
4	#11926365	—	2	2	no	—
5	#11926365	C₄	1	4	yes	complemented
6	C₂×C₁₉×#106	—	2	2	no	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#384	C₄	1	2	yes	—
9	C₂²×C₈×C₁₉	D₄	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
12	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₁₉×#106	—	4	2	no	—
14	C₁₉×#106	—	4	2	no	—
15	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
18	#10597269	—	2	4	no	—
19	#10597269	—	4	2	no	—
20	C₂×C₁₉⋊C₁₆	—	4	2	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	4	2	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₉	D₈	1	2	yes	—
27	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
28	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
29	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	4	4	no	—
31	C₄⋊C₄×C₁₉	—	8	4	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	C₄²	1	1	yes	characteristic
34	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₁₉⋊C₁₆	—	4	4	no	—
36	#7268	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	#100	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	8	4	no	—
42	C₂×C₄×C₁₉	—	8	2	no	—
43	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#102	1	2	yes	—
46	C₂×C₄×C₁₉	#103	1	2	yes	—
47	C₈×C₁₉	#102	1	2	yes	—
48	C₈×C₁₉	#103	1	2	yes	—
49	C₈×C₁₉	#106	1	2	yes	—
50	C₈×C₁₉	#107	1	2	yes	—
51	C₂×#364	—	19	2	no	—
52	#1844	D₁₉	1	1	yes	characteristic
53	C₂²×C₁₉	—	2	2	no	—
54	C₂²×C₁₉	#331	1	1	yes	characteristic
55	C₂²×C₁₉	#333	1	1	yes	characteristic
56	C₂²×C₁₉	#343	1	1	yes	characteristic
57	C₄×C₁₉	—	2	2	no	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	16	2	no	—
60	C₄×C₁₉	#332	1	2	yes	—
61	C₄×C₁₉	#340	1	2	yes	—
62	C₂×M₃₂	—	38	2	no	—
63	C₂×#106	—	2	2	no	—
64	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	#384	Dic₁₉	1	2	yes	—
66	#364	—	19	4	no	—
67	#364	—	38	2	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	#1296	1	1	yes	characteristic
71	C₂×C₁₉	#1359	1	2	yes	—
72	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
73	C₂×C₄⋊C₄	—	2	2	no	—
74	C₂×C₄⋊C₄	—	4	2	no	—
75	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
76	M₃₂	—	38	4	no	—
77	M₃₂	—	76	2	no	—
78	C₂×C₁₆	—	76	2	no	—
79	#106	—	4	2	no	—
80	#106	—	4	2	no	—
81	C₄×C₈	Dic₃₈	1	1	yes	characteristic
82	C₄×C₈	C₄×D₁₉	1	2	yes	—
83	C₄×C₈	D₇₆	1	1	yes	characteristic
84	C₁₉	#7268	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	—	4	2	no	—
87	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
88	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
89	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
90	C₂×C₈	#64525	1	2	yes	—
91	C₂×C₈	#64526	1	2	yes	—
92	C₂×C₈	#64527	1	2	yes	—
93	C₂×C₈	#64528	1	2	yes	—
94	C₄⋊C₄	—	4	4	no	—
95	C₄⋊C₄	—	8	4	no	—
96	C₄²	—	2	1	no	—
97	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
98	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
99	C₁₆	—	76	4	no	—
100	C₂³	#10597290	1	1	yes	characteristic
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	8	4	no	—
105	C₂×C₄	—	8	2	no	—
106	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
107	C₂×C₄	#10597289	1	2	yes	—
108	C₂×C₄	#10597292	1	2	yes	—
109	C₂×C₄	#10597293	1	1	yes	characteristic
110	C₈	#10597264	1	2	yes	—
111	C₈	#10597265	1	2	yes	—
112	C₈	#10597266	1	2	yes	—
113	C₈	#10597267	1	2	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	#11926288	1	1	yes	characteristic
116	C₂²	#11926293	1	1	yes	characteristic
117	C₂²	#11926313	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	—	16	2	no	—
121	C₄	#11926290	1	2	yes	—
122	C₄	#11926306	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	#14561518	1	1	yes	characteristic
126	C₂	#14561676	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926365

C₂

yes

maximal

C₁₉×#1844

C₂

yes

maximal, characteristic

C₂×#10597269

—

#11926365

—

#11926365

C₄

yes

complemented

C₂×C₁₉×#106

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#106

—

C₁₉×#106

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₈×C₁₉

#102

yes

—

C₈×C₁₉

#103

yes

—

C₈×C₁₉

#106

yes

—

C₈×C₁₉

#107

yes

—

C₂×#364

—

#1844

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#332

yes

—

C₄×C₁₉

#340

yes

—

C₂×M₃₂

—

C₂×#106

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

Dic₁₉

yes

—

#364

—

#364

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1296

yes

characteristic

C₂×C₁₉

#1359

yes

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#106

—

#106

—

C₄×C₈

Dic₃₈

yes

characteristic

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

D₇₆

yes

characteristic

C₁₉

#7268

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

C₂×C₈

#64525

yes

—

C₂×C₈

#64526

yes

—

C₂×C₈

#64527

yes

—

C₂×C₈

#64528

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₄×Dic₁₉

yes

characteristic

C₄²

C₄⋊Dic₁₉

yes

characteristic

C₁₆

—

100

C₂³

#10597290

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₁₉⋊#95

yes

characteristic

107

C₂×C₄

#10597289

yes

—

108

C₂×C₄

#10597292

yes

—

109

C₂×C₄

#10597293

yes

characteristic

110

C₈

#10597264

yes

—

111

C₈

#10597265

yes

—

112

C₈

#10597266

yes

—

113

C₈

#10597267

yes

—

114

C₂²

—

115

C₂²

#11926288

yes

characteristic

116

C₂²

#11926293

yes

characteristic

117

C₂²

#11926313

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

#11926290

yes

—

122

C₄

#11926306

yes

—

123

C₂

—

124

C₂

—

125

C₂

#14561518

yes

characteristic

126

C₂

#14561676

yes

—

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄²×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1844	C₂
socle	C₂²×C₁₉	#331
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#7268
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1844

subgroup

G/H

center

C₂²

#11926288

commutator

C₄²×C₁₉

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1844

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1844

N	H ≅ G/N	type
5. #11926365	C₄	semidirect
84. C₁₉	#7268	semidirect

H ≅ G/N

type

5. #11926365

C₄

semidirect

84. C₁₉

#7268

semidirect

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

subgroup	index
C₂×#11926365	2
C₁₉×#1844	2
#7268	19

subgroup

index

C₂×#11926365

C₁₉×#1844

#7268

Subgroups — #18069710

Conjugacy classes of subgroups

Complements

Maximal subgroups