Group #18069272 — subgroups

Subgroups — #18069272

Order 4864.

142 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14561705	C₂	1	1	yes	maximal, characteristic
2	#14561705	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1713	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
5	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
6	C₁₉×#500	—	2	1	no	—
7	C₁₉×#500	C₄	1	2	yes	—
8	C₁₉×#494	—	2	1	no	—
9	C₈²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₉	—	4	1	no	—
11	C₂×Q₁₆×C₁₉	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	—	2	2	no	—
13	C₁₉×#107	—	4	1	no	—
14	C₁₉×#107	—	4	1	no	—
15	C₁₉×#107	—	4	2	no	—
16	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₁₉⋊C₁₆	—	4	1	no	—
20	C₂×C₁₉⋊C₁₆	—	4	1	no	—
21	C₂×Q₈×C₁₉	—	4	2	no	—
22	Q₁₆×C₁₉	—	8	2	no	—
23	Q₁₆×C₁₉	—	8	1	no	—
24	Q₁₆×C₁₉	—	8	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₄⋊C₄×C₁₉	—	4	2	no	—
31	C₄⋊C₄×C₁₉	—	4	2	no	—
32	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₁₉⋊C₁₆	—	8	1	no	—
34	C₁₉⋊C₁₆	—	8	1	no	—
35	#7097	—	19	1	no	maximal, Sylow
36	Q₈×C₁₉	—	8	2	no	—
37	Q₈×C₁₉	—	8	2	no	—
38	C₂×C₄×C₁₉	—	8	2	no	—
39	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
42	C₈×C₁₉	—	2	2	no	—
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	—	2	1	no	—
45	C₈×C₁₉	D₁₆	1	1	yes	characteristic
46	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
47	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
48	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
49	#1713	D₁₉	1	1	yes	characteristic
50	#1370	—	19	1	no	—
51	#1370	—	19	1	no	—
52	C₂²×C₁₉	#331	1	1	yes	characteristic
53	C₄×C₁₉	—	2	1	no	—
54	C₄×C₁₉	—	16	2	no	—
55	C₄×C₁₉	#357	1	1	yes	characteristic
56	C₄×C₁₉	#358	1	1	yes	characteristic
57	C₄×C₁₉	#361	1	1	yes	characteristic
58	C₄×C₁₉	#362	1	1	yes	characteristic
59	#500	—	2	1	no	—
60	#500	Dic₁₉	1	2	yes	—
61	#494	—	2	1	no	—
62	C₄⋊C₁₆	—	38	1	no	—
63	C₄⋊C₁₆	—	38	1	no	—
64	C₈²	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₁₉	#1358	1	1	yes	characteristic
66	C₂×C₁₉	#1361	1	1	yes	characteristic
67	C₂×C₁₉	#1362	1	1	yes	characteristic
68	C₂×Q₁₆	—	4	1	no	—
69	C₂×Q₁₆	—	4	1	no	—
70	C₄⋊Q₈	—	2	2	no	—
71	C₂×C₁₆	—	76	1	no	—
72	C₂×C₁₆	—	76	1	no	—
73	#107	—	4	1	no	—
74	#107	—	4	1	no	—
75	#107	—	4	2	no	—
76	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
77	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
79	C₁₉	#7097	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₈	—	4	2	no	—
81	Q₁₆	—	8	2	no	—
82	Q₁₆	—	8	1	no	—
83	Q₁₆	—	8	1	no	—
84	C₂×C₈	—	2	1	no	—
85	C₂×C₈	#64525	1	1	yes	characteristic
86	C₂×C₈	#64525	1	1	yes	characteristic
87	C₂×C₈	#64526	1	1	yes	characteristic
88	C₂×C₈	#64526	1	1	yes	characteristic
89	C₄⋊C₄	—	4	2	no	—
90	C₄⋊C₄	—	4	2	no	—
91	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
92	C₁₆	—	152	1	no	—
93	C₁₆	—	152	1	no	—
94	Q₈	—	8	2	no	—
95	Q₈	—	8	2	no	—
96	C₂×C₄	—	8	2	no	—
97	C₂×C₄	#10597289	1	1	yes	characteristic
98	C₂×C₄	#10597289	1	1	yes	characteristic
99	C₂×C₄	#10597290	1	1	yes	characteristic
100	C₈	—	2	2	no	—
101	C₈	—	2	1	no	—
102	C₈	—	2	1	no	—
103	C₈	#10597283	1	1	yes	characteristic
104	C₈	#10597284	1	1	yes	characteristic
105	C₈	#10597285	1	1	yes	characteristic
106	C₈	#10597286	1	1	yes	characteristic
107	C₂²	#11926288	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	16	2	no	—
110	C₄	#11926345	1	1	yes	characteristic
111	C₄	#11926348	1	1	yes	characteristic
112	C₄	#11926357	1	1	yes	characteristic
113	C₄	#11926360	1	1	yes	characteristic
114	C₂	#14561674	1	1	yes	characteristic
115	C₂	#14561681	1	1	yes	characteristic
116	C₂	#14561684	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561705

C₂

yes

maximal, characteristic

#14561705

C₂

yes

maximal, characteristic

C₁₉×#1713

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₄⋊(C₁₉⋊C₁₆)

—

C₁₉×#500

—

C₁₉×#500

C₄

yes

—

C₁₉×#494

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

#7097

—

maximal, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

Q₃₂

yes

characteristic

#1713

D₁₉

yes

characteristic

#1370

—

#1370

—

C₂²×C₁₉

#331

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

yes

—

#494

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

—

#107

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7097

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊Dic₁₉

yes

characteristic

C₁₆

—

152

—

C₁₆

—

152

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

#10597283

yes

characteristic

104

C₈

#10597284

yes

characteristic

105

C₈

#10597285

yes

characteristic

106

C₈

#10597286

yes

characteristic

107

C₂²

#11926288

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

#11926345

yes

characteristic

111

C₄

#11926348

yes

characteristic

112

C₄

#11926357

yes

characteristic

113

C₄

#11926360

yes

characteristic

114

C₂

#14561674

yes

characteristic

115

C₂

#14561681

yes

characteristic

116

C₂

#14561684

yes

characteristic

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1713	C₂
socle, prime radical	C₂²×C₁₉	#331
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1713	D₁₉
hypocenter	C₁₉	#7097
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

subgroup

G/H

center

C₂²

#11926288

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1713

C₂

socle, prime radical

C₂²×C₁₉

#331

cosocle

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

N	H ≅ G/N	type
79. C₁₉	#7097	semidirect

H ≅ G/N

type

79. C₁₉

#7097

semidirect

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

subgroup	index
#14561705	2
C₁₉×#1713	2
#7097	19

subgroup

index

#14561705

C₁₉×#1713

#7097

Subgroups — #18069272

Conjugacy classes of subgroups

Complements

Maximal subgroups