Group #18069962 — subgroups

Subgroups — #18069962

Order 4864.

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

normal subgroups only

This group has 148 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	#14563809	C₂	1	1	yes	maximal, characteristic
2	#14561586	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1327	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597279	—	2	1	no	—
5	C₂×#10597279	—	2	1	no	—
6	#11926568	C₄	1	1	yes	characteristic
7	C₂×#10597260	C₄	1	1	yes	characteristic
8	#11926326	—	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	#10597279	—	4	2	no	—
19	#10597279	—	4	2	no	—
20	#10597269	—	4	1	no	—
21	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
22	#10597260	—	2	1	no	—
23	#10597260	C₈	1	2	yes	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	M₁₆×C₁₉	—	4	1	no	—
27	M₁₆×C₁₉	—	4	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	—	2	1	no	—
31	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
33	#64520	—	4	1	no	—
34	#64520	—	4	1	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	4	1	no	—
39	C₁₆×C₁₉	—	8	1	no	—
40	C₁₉⋊C₁₆	—	8	1	no	—
41	#7374	—	19	1	no	maximal, Sylow
42	C₂³×C₁₉	#101	1	1	yes	characteristic
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	8	1	no	—
48	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
50	C₈×C₁₉	—	4	1	no	—
51	C₈×C₁₉	—	4	1	no	—
52	C₁₉⋊C₈	—	2	4	no	—
53	C₁₉⋊C₈	—	8	1	no	—
54	#1849	—	19	1	no	—
55	#1327	—	19	1	no	—
56	#1327	D₁₉	1	1	yes	characteristic
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	#324	1	1	yes	characteristic
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	4	1	no	—
62	C₄×C₁₉	—	4	1	no	—
63	C₄×C₁₉	#353	1	1	yes	characteristic
64	C₄×C₁₉	#356	1	1	yes	characteristic
65	C₂×#108	—	38	1	no	—
66	C₂×#108	—	38	1	no	—
67	#423	—	19	1	no	—
68	#423	C₂×D₁₉	1	1	yes	characteristic
69	C₂×#97	—	19	1	no	—
70	#349	—	2	1	no	—
71	#349	—	38	1	no	—
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	—	4	1	no	—
74	C₂×C₁₉	#1325	1	1	yes	characteristic
75	C₂×M₁₆	—	38	1	no	—
76	C₂×M₁₆	D₇₆	1	1	yes	characteristic
77	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₂²×C₈	—	38	1	no	—
79	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
80	M₃₂	—	4	1	no	—
81	M₃₂	—	76	1	no	—
82	#108	—	76	2	no	—
83	#108	—	76	2	no	—
84	C₄⋊C₈	—	4	1	no	—
85	C₄⋊C₈	—	76	1	no	—
86	#97	—	19	2	no	—
87	#97	—	38	1	no	—
88	C₁₉	#7374	1	1	yes	characteristic, complemented, Sylow
89	C₂²×C₄	—	2	1	no	—
90	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
91	M₁₆	—	4	1	no	—
92	M₁₆	—	4	1	no	—
93	M₁₆	—	76	1	no	—
94	M₁₆	—	76	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	38	2	no	—
98	C₂×C₈	—	38	2	no	—
99	C₂×C₈	—	38	2	no	—
100	C₂×C₈	—	76	1	no	—
101	C₄²	—	2	1	no	—
102	C₄²	C₈×D₁₉	1	1	yes	characteristic
103	C₄²	#64515	1	1	yes	characteristic
104	C₁₆	—	8	1	no	—
105	C₁₆	—	152	1	no	—
106	C₂³	#10597281	1	1	yes	characteristic
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	8	1	no	—
112	C₂×C₄	#10597263	1	1	yes	characteristic
113	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	38	4	no	—
117	C₈	—	152	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	4	1	no	—
120	C₂²	#11926269	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	4	1	no	—
123	C₄	—	4	1	no	—
124	C₄	#11926336	1	1	yes	characteristic
125	C₄	#11926342	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	4	1	no	—
128	C₂	#14561580	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563809

C₂

yes

maximal, characteristic

#14561586

C₂

yes

maximal, characteristic

C₁₉×#1327

C₂

yes

maximal, characteristic

C₂×#10597279

—

C₂×#10597279

—

#11926568

C₄

yes

characteristic

C₂×#10597260

C₄

yes

characteristic

#11926326

—

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

—

#10597279

—

#10597279

—

#10597269

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

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

—

#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

—

#1849

—

#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×#97

—

#349

—

#349

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1325

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

—

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

#97

—

C₁₉

#7374

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

—

102

C₄²

C₈×D₁₉

yes

characteristic

103

C₄²

#64515

yes

characteristic

104

C₁₆

—

105

C₁₆

—

152

—

106

C₂³

#10597281

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

#10597263

yes

characteristic

113

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

152

—

118

C₂²

—

119

C₂²

—

120

C₂²

#11926269

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#11926336

yes

characteristic

125

C₄

#11926342

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#14561580

yes

characteristic

	subgroup	G/H
center	C₄	#11926336
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1327	C₂
socle	C₂×C₁₉	#1325
prime radical	C₂³×C₁₉	#101
cosocle	C₁₉×#423	C₂²
hypercenter	#1327	D₁₉
hypocenter	C₁₉	#7374
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

#11926336

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
88. C₁₉	#7374	semidirect

H ≅ G/N

type

88. C₁₉

#7374

semidirect

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

subgroup	index
#14563809	2
#14561586	2
C₁₉×#1327	2
#7374	19

subgroup

index

#14563809

#14561586

C₁₉×#1327

#7374

Subgroups — #18069962

Conjugacy classes of subgroups

Complements

Maximal subgroups