Group #18069949 — subgroups

Subgroups — #18069949

Order 4864.

136 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14563772	C₂	1	1	yes	maximal, characteristic
2	#14561586	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1327	C₂	1	1	yes	maximal, characteristic
4	#11926568	C₄	1	1	yes	characteristic
5	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
6	#11926326	—	2	1	no	—
7	#11926308	—	2	1	no	—
8	#11926308	—	2	1	no	—
9	C₁₉×#423	C₂²	1	1	yes	characteristic
10	C₁₉×#349	—	2	1	no	—
11	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×#64520	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	—	2	1	no	—
16	C₁₉×M₃₂	—	4	1	no	—
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	#10597269	—	4	1	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
20	C₄×C₁₉⋊C₈	—	2	1	no	—
21	C₄×C₁₉⋊C₈	C₈	1	2	yes	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆×C₁₉	—	4	1	no	—
25	M₁₆×C₁₉	—	4	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
31	#64520	—	4	2	no	—
32	C₂×C₁₉⋊C₈	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	4	1	no	—
34	C₂×C₁₉⋊C₈	—	4	1	no	—
35	C₂×C₁₉⋊C₈	—	4	1	no	—
36	C₁₆×C₁₉	—	8	1	no	—
37	C₁₉⋊C₁₆	—	8	1	no	—
38	#7368	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#101	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
47	C₈×C₁₉	—	4	1	no	—
48	C₈×C₁₉	—	4	1	no	—
49	C₁₉⋊C₈	—	4	2	no	—
50	C₁₉⋊C₈	—	8	1	no	—
51	#1837	—	19	1	no	—
52	#1327	—	19	1	no	—
53	#1327	D₁₉	1	1	yes	characteristic
54	C₂²×C₁₉	—	2	1	no	—
55	C₂²×C₁₉	—	4	1	no	—
56	C₂²×C₁₉	#324	1	1	yes	characteristic
57	C₄×C₁₉	—	2	2	no	—
58	C₄×C₁₉	—	2	1	no	—
59	C₄×C₁₉	—	4	1	no	—
60	C₄×C₁₉	#354	1	1	yes	characteristic
61	C₄×C₁₉	#355	1	1	yes	characteristic
62	#423	—	19	1	no	—
63	#423	C₂×D₁₉	1	1	yes	characteristic
64	C₂×C₄×C₈	—	19	1	no	—
65	#349	—	2	1	no	—
66	#349	—	38	1	no	—
67	#341	—	38	1	no	—
68	#341	—	38	1	no	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	—	4	1	no	—
71	C₂×C₁₉	#1324	1	1	yes	characteristic
72	C₂×M₁₆	—	38	1	no	—
73	C₂×M₁₆	D₇₆	1	1	yes	characteristic
74	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
75	C₂²×C₈	—	38	1	no	—
76	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
77	M₃₂	—	4	1	no	—
78	M₃₂	—	76	1	no	—
79	C₄⋊C₈	—	4	1	no	—
80	C₄⋊C₈	—	76	1	no	—
81	C₄×C₈	—	19	2	no	—
82	C₄×C₈	—	38	1	no	—
83	C₁₉	#7368	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	—	2	1	no	—
85	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
86	M₁₆	—	4	1	no	—
87	M₁₆	—	4	1	no	—
88	M₁₆	—	76	2	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	—	38	2	no	—
92	C₂×C₈	—	76	1	no	—
93	C₂×C₈	—	76	1	no	—
94	C₂×C₈	—	76	1	no	—
95	C₄²	—	2	1	no	—
96	C₄²	C₈×D₁₉	1	1	yes	characteristic
97	C₄²	#64515	1	1	yes	characteristic
98	C₁₆	—	8	1	no	—
99	C₁₆	—	152	1	no	—
100	C₂³	#10597281	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	#10597263	1	1	yes	characteristic
107	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
108	C₈	—	4	1	no	—
109	C₈	—	4	1	no	—
110	C₈	—	76	2	no	—
111	C₈	—	152	1	no	—
112	C₂²	—	2	1	no	—
113	C₂²	—	4	1	no	—
114	C₂²	#11926269	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	2	1	no	—
117	C₄	—	4	1	no	—
118	C₄	#11926338	1	1	yes	characteristic
119	C₄	#11926340	1	1	yes	characteristic
120	C₂	—	2	1	no	—
121	C₂	—	4	1	no	—
122	C₂	#14561578	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563772

C₂

yes

maximal, characteristic

#14561586

C₂

yes

maximal, characteristic

C₁₉×#1327

C₂

yes

maximal, characteristic

#11926568

C₄

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

—

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#349

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×M₃₂

—

C₁₉×C₄⋊C₈

—

#10597269

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1837

—

#1327

—

#1327

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#324

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1324

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

D₇₆

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄²

C₄×D₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#7368

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

C₈×D₁₉

yes

characteristic

C₄²

#64515

yes

characteristic

C₁₆

—

C₁₆

—

152

—

100

C₂³

#10597281

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#10597263

yes

characteristic

107

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

152

—

112

C₂²

—

113

C₂²

—

114

C₂²

#11926269

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#11926338

yes

characteristic

119

C₄

#11926340

yes

characteristic

120

C₂

—

121

C₂

—

122

C₂

#14561578

yes

characteristic

	subgroup	G/H
center	C₄	#11926338
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1327	C₂
socle	C₂×C₁₉	#1324
prime radical	C₂³×C₁₉	#101
cosocle	C₁₉×#423	C₂²
hypercenter	#1327	D₁₉
hypocenter	C₁₉	#7368
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

subgroup

G/H

center

C₄

#11926338

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1327

C₂

C₂×C₁₉

C₂³×C₁₉

C₁₉×#423

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

N	H ≅ G/N	type
83. C₁₉	#7368	semidirect

H ≅ G/N

type

83. C₁₉

#7368

semidirect

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

subgroup	index
#14563772	2
#14561586	2
C₁₉×#1327	2
#7368	19

subgroup

index

#14563772

#14561586

C₁₉×#1327

#7368

Subgroups — #18069949

Conjugacy classes of subgroups

Complements

Maximal subgroups