Group #18069963 — subgroups

Subgroups — #18069963

Order 4864.

148 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561586	C₂	1	2	yes	maximal
2	C₁₉×#1849	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₂×C₁₉×#108	—	2	2	no	—
5	C₁₉×#423	C₄	1	1	yes	characteristic
6	C₁₉×#423	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	—	2	1	no	—
9	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₁₉×#108	—	4	4	no	—
13	C₁₉×C₄⋊C₈	—	4	1	no	—
14	C₁₉×C₄⋊C₈	—	4	1	no	—
15	C₁₉×#97	—	2	1	no	—
16	C₁₉×#97	C₈	1	2	yes	—
17	#10597269	—	4	2	no	—
18	C₂²×C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
20	M₁₆×C₁₉	—	4	2	no	—
21	M₁₆×C₁₉	—	4	2	no	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	4	1	no	—
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
29	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
30	C₁₉⋊C₁₆	—	8	2	no	—
31	#7374	—	19	1	no	maximal, Sylow
32	C₂³×C₁₉	#101	1	1	yes	characteristic
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	8	1	no	—
38	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
40	C₈×C₁₉	—	2	4	no	—
41	C₈×C₁₉	—	4	2	no	—
42	C₈×C₁₉	—	8	1	no	—
43	#1849	D₁₉	1	1	yes	characteristic
44	#1327	—	19	2	no	—
45	C₂²×C₁₉	—	2	1	no	—
46	C₂²×C₁₉	—	4	1	no	—
47	C₂²×C₁₉	#324	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	4	1	no	—
50	C₄×C₁₉	—	4	1	no	—
51	C₄×C₁₉	#353	1	1	yes	characteristic
52	C₄×C₁₉	#356	1	1	yes	characteristic
53	C₂×#108	—	2	2	no	—
54	#423	Dic₁₉	1	1	yes	characteristic
55	#423	C₂×D₁₉	1	1	yes	characteristic
56	C₂×#97	Dic₁₉	1	1	yes	characteristic
57	#349	—	38	2	no	—
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	—	4	1	no	—
60	C₂×C₁₉	#1325	1	1	yes	characteristic
61	C₂×M₁₆	—	2	1	no	—
62	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
63	C₂²×C₈	—	2	1	no	—
64	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
65	M₃₂	—	76	2	no	—
66	#108	—	4	4	no	—
67	C₄⋊C₈	—	4	1	no	—
68	C₄⋊C₈	—	4	1	no	—
69	#97	—	2	1	no	—
70	#97	C₁₉⋊C₈	1	2	yes	—
71	C₁₉	#7374	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	2	1	no	—
73	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
74	M₁₆	—	4	2	no	—
75	M₁₆	—	4	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	4	1	no	—
81	C₄²	—	2	1	no	—
82	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
83	C₄²	#64520	1	1	yes	characteristic
84	C₁₆	—	152	2	no	—
85	C₂³	#10597293	1	1	yes	characteristic
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	8	1	no	—
91	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
92	C₂×C₄	#10597291	1	1	yes	characteristic
93	C₈	—	2	4	no	—
94	C₈	—	4	2	no	—
95	C₈	—	8	1	no	—
96	C₂²	—	2	1	no	—
97	C₂²	—	4	1	no	—
98	C₂²	#11926270	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	#11926337	1	1	yes	characteristic
103	C₄	#11926343	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	4	1	no	—
106	C₂	#14561581	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561586

C₂

yes

maximal

C₁₉×#1849

C₂

yes

maximal, characteristic

#11926326

—

C₂×C₁₉×#108

—

C₁₉×#423

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#97

C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉×#97

C₈

yes

—

#10597269

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1849

D₁₉

yes

characteristic

#1327

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#324

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

yes

characteristic

#423

C₂×D₁₉

yes

characteristic

C₂×#97

Dic₁₉

yes

characteristic

#349

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1325

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂²⋊D₁₉

yes

—

C₂²×C₈

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

#97

C₁₉⋊C₈

yes

—

C₁₉

#7374

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

C₄²

#64520

yes

characteristic

C₁₆

—

152

—

C₂³

#10597293

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

C₂×C₄

#10597291

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

#11926270

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

#11926337

yes

characteristic

103

C₄

#11926343

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#14561581

yes

characteristic

	subgroup	G/H
center	C₄	#11926337
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1849	C₂
socle	C₂×C₁₉	#1325
prime radical	C₂³×C₁₉	#101
cosocle	C₁₉×#423	C₂²
hypercenter	#1849	D₁₉
hypocenter	C₁₉	#7374
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1849

subgroup

G/H

center

C₄

#11926337

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1849

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 ◁ #1849

N	H ≅ G/N	type
71. C₁₉	#7374	semidirect

H ≅ G/N

type

71. C₁₉

#7374

semidirect

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

subgroup	index
#14561586	2
C₁₉×#1849	2
#7374	19

subgroup

index

#14561586

C₁₉×#1849

#7374

Subgroups — #18069963

Conjugacy classes of subgroups

Complements

Maximal subgroups