Group #18069267 — subgroups

Subgroups — #18069267

Order 4864.

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

normal subgroups only

This group has 136 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	#14561705	C₂	1	1	yes	maximal, characteristic
2	#14561699	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1707	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
5	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
6	C₁₉×#500	C₄	1	1	yes	characteristic
7	C₁₉×#498	—	2	1	no	—
8	C₁₉×#494	C₄	1	1	yes	characteristic
9	C₁₉×#487	—	2	1	no	—
10	C₈²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₁₉	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	—	2	1	no	—
13	C₁₉×C₄⋊Q₈	—	2	1	no	—
14	C₁₉×#107	—	4	1	no	—
15	C₁₉×#106	—	4	1	no	—
16	C₁₉×#106	—	4	1	no	—
17	C₁₉×#103	—	4	1	no	—
18	C₁₉×#103	—	4	1	no	—
19	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₁₉⋊C₁₆	—	4	1	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	C₂×Q₈×C₁₉	—	4	1	no	—
25	C₂×Q₈×C₁₉	—	4	1	no	—
26	Q₁₆×C₁₉	—	8	2	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
31	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₄⋊C₄×C₁₉	—	4	1	no	—
36	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₁₉⋊C₁₆	—	8	1	no	—
38	C₁₉⋊C₁₆	—	8	1	no	—
39	#7095	—	19	1	no	maximal, Sylow
40	Q₈×C₁₉	—	8	2	no	—
41	Q₈×C₁₉	—	8	1	no	—
42	Q₈×C₁₉	—	8	1	no	—
43	C₂×C₄×C₁₉	—	8	1	no	—
44	C₂×C₄×C₁₉	—	8	1	no	—
45	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
48	C₈×C₁₉	—	2	2	no	—
49	C₈×C₁₉	—	2	1	no	—
50	C₈×C₁₉	—	2	1	no	—
51	C₈×C₁₉	—	2	1	no	—
52	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
53	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
54	#1707	D₁₉	1	1	yes	characteristic
55	#1370	—	19	1	no	—
56	#1367	—	19	1	no	—
57	C₂²×C₁₉	#331	1	1	yes	characteristic
58	C₄×C₁₉	—	2	1	no	—
59	C₄×C₁₉	—	16	1	no	—
60	C₄×C₁₉	—	16	1	no	—
61	C₄×C₁₉	#358	1	1	yes	characteristic
62	C₄×C₁₉	#359	1	1	yes	characteristic
63	C₄×C₁₉	#360	1	1	yes	characteristic
64	C₄×C₁₉	#362	1	1	yes	characteristic
65	#500	Dic₁₉	1	1	yes	characteristic
66	#498	—	2	1	no	—
67	#494	Dic₁₉	1	1	yes	characteristic
68	#487	—	2	1	no	—
69	C₄⋊C₁₆	—	38	1	no	—
70	C₄⋊C₁₆	—	38	1	no	—
71	C₈²	C₂×D₁₉	1	1	yes	characteristic
72	C₂×C₁₉	#1359	1	1	yes	characteristic
73	C₂×C₁₉	#1360	1	1	yes	characteristic
74	C₂×C₁₉	#1362	1	1	yes	characteristic
75	C₂×Q₁₆	—	4	1	no	—
76	C₄⋊Q₈	—	2	1	no	—
77	C₄⋊Q₈	—	2	1	no	—
78	C₂×C₁₆	—	76	1	no	—
79	C₂×C₁₆	—	76	1	no	—
80	#107	—	4	1	no	—
81	#106	—	4	1	no	—
82	#106	—	4	1	no	—
83	#103	—	4	1	no	—
84	#103	—	4	1	no	—
85	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
86	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
87	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₁₉	#7095	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	4	1	no	—
90	C₂×Q₈	—	4	1	no	—
91	Q₁₆	—	8	2	no	—
92	C₂×C₈	—	2	1	no	—
93	C₂×C₈	#64525	1	1	yes	characteristic
94	C₂×C₈	#64525	1	1	yes	characteristic
95	C₂×C₈	#64526	1	1	yes	characteristic
96	C₂×C₈	#64526	1	1	yes	characteristic
97	C₄⋊C₄	—	4	1	no	—
98	C₄⋊C₄	—	4	1	no	—
99	C₄⋊C₄	—	4	1	no	—
100	C₄⋊C₄	—	4	1	no	—
101	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
102	C₁₆	—	152	1	no	—
103	C₁₆	—	152	1	no	—
104	Q₈	—	8	2	no	—
105	Q₈	—	8	1	no	—
106	Q₈	—	8	1	no	—
107	C₂×C₄	—	8	1	no	—
108	C₂×C₄	—	8	1	no	—
109	C₂×C₄	#10597289	1	1	yes	characteristic
110	C₂×C₄	#10597289	1	1	yes	characteristic
111	C₂×C₄	#10597290	1	1	yes	characteristic
112	C₈	—	2	2	no	—
113	C₈	—	2	1	no	—
114	C₈	—	2	1	no	—
115	C₈	—	2	1	no	—
116	C₈	#10597285	1	1	yes	characteristic
117	C₈	#10597286	1	1	yes	characteristic
118	C₂²	#11926288	1	1	yes	characteristic
119	C₄	—	2	1	no	—
120	C₄	—	16	1	no	—
121	C₄	—	16	1	no	—
122	C₄	#11926348	1	1	yes	characteristic
123	C₄	#11926351	1	1	yes	characteristic
124	C₄	#11926354	1	1	yes	characteristic
125	C₄	#11926360	1	1	yes	characteristic
126	C₂	#14561676	1	1	yes	characteristic
127	C₂	#14561678	1	1	yes	characteristic
128	C₂	#14561684	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561705

C₂

yes

maximal, characteristic

#14561699

C₂

yes

maximal, characteristic

C₁₉×#1707

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₄⋊(C₁₉⋊C₁₆)

—

C₁₉×#500

C₄

yes

characteristic

C₁₉×#498

—

C₁₉×#494

C₄

yes

characteristic

C₁₉×#487

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#106

—

C₁₉×#103

—

C₁₉×#103

—

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

—

C₂×Q₈×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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

#7095

—

maximal, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

Q₃₂

yes

characteristic

#1707

D₁₉

yes

characteristic

#1370

—

#1367

—

C₂²×C₁₉

#331

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

yes

characteristic

#498

—

#494

Dic₁₉

yes

characteristic

#487

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

—

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7095

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

C₂²⋊Dic₁₉

yes

characteristic

102

C₁₆

—

152

—

103

C₁₆

—

152

—

104

Q₈

—

105

Q₈

—

106

Q₈

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#10597289

yes

characteristic

110

C₂×C₄

#10597289

yes

characteristic

111

C₂×C₄

#10597290

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

#10597285

yes

characteristic

117

C₈

#10597286

yes

characteristic

118

C₂²

#11926288

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11926348

yes

characteristic

123

C₄

#11926351

yes

characteristic

124

C₄

#11926354

yes

characteristic

125

C₄

#11926360

yes

characteristic

126

C₂

#14561676

yes

characteristic

127

C₂

#14561678

yes

characteristic

128

C₂

#14561684

yes

characteristic

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1707	C₂
socle, prime radical	C₂²×C₁₉	#331
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1707	D₁₉
hypocenter	C₁₉	#7095
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1707

subgroup

G/H

center

C₂²

#11926288

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1707

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 ◁ #1707

N	H ≅ G/N	type
88. C₁₉	#7095	semidirect

H ≅ G/N

type

88. C₁₉

#7095

semidirect

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

subgroup	index
#14561705	2
#14561699	2
C₁₉×#1707	2
#7095	19

subgroup

index

#14561705

#14561699

C₁₉×#1707

#7095

Subgroups — #18069267

Conjugacy classes of subgroups

Complements

Maximal subgroups