Group #18071882 — subgroups

Subgroups — #18071882

Order 4864.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14565173	C₂	1	3	yes	maximal
2	#14561461	C₂	1	3	yes	maximal
3	C₁₉×#2811	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597264	—	2	3	no	—
5	C₂×#10597292	—	2	3	no	—
6	#11926414	C₂²	1	1	yes	characteristic
7	#11926299	C₂²	1	3	yes	—
8	C₁₉×#395	—	2	3	no	—
9	C₁₉×#391	—	2	3	no	—
10	C₁₉×#391	C₂²	1	3	yes	—
11	C₂²×Q₈×C₁₉	—	2	1	no	—
12	C₂²×Q₈×C₁₉	D₄	1	3	yes	—
13	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
14	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	—	2	3	no	—
18	C₂²×C₁₉⋊C₈	—	2	3	no	—
19	C₁₉×#95	—	2	3	no	—
20	C₁₉×#95	—	2	6	no	—
21	#10597292	—	4	6	no	—
22	#10597264	—	4	6	no	—
23	C₂×Q₈×C₁₉	—	2	3	no	—
24	C₂×Q₈×C₁₉	—	4	3	no	—
25	C₂×Q₈×C₁₉	—	4	3	no	—
26	C₂×Q₈×C₁₉	—	8	3	no	—
27	C₂×Q₈×C₁₉	Q₁₆	1	6	yes	—
28	C₂²×C₄×C₁₉	—	2	3	no	—
29	C₂²×C₄×C₁₉	—	2	3	no	—
30	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
31	C₂²×Dic₁₉	—	4	1	no	—
32	C₄⋊C₄×C₁₉	—	4	3	no	—
33	C₄⋊C₄×C₁₉	—	8	3	no	—
34	C₄²×C₁₉	—	4	1	no	—
35	C₄²×C₁₉	—	8	1	no	—
36	C₄⋊Dic₁₉	—	4	3	no	—
37	C₄⋊Dic₁₉	—	4	3	no	—
38	C₂×C₁₉⋊C₈	—	2	6	no	—
39	C₂×C₁₉⋊C₈	—	4	3	no	—
40	C₂×C₁₉⋊C₈	—	4	3	no	—
41	#7837	—	19	1	no	maximal, Sylow
42	C₂³×C₁₉	#120	1	1	yes	characteristic
43	Q₈×C₁₉	—	4	6	no	—
44	Q₈×C₁₉	—	8	3	no	—
45	Q₈×C₁₉	—	8	4	no	—
46	C₂×C₄×C₁₉	—	2	3	no	—
47	C₂×C₄×C₁₉	—	2	3	no	—
48	C₂×C₄×C₁₉	—	2	6	no	—
49	C₂×C₄×C₁₉	—	4	3	no	—
50	C₂×C₄×C₁₉	—	4	3	no	—
51	C₂×C₄×C₁₉	—	4	3	no	—
52	C₂×C₄×C₁₉	—	4	6	no	—
53	C₂×C₄×C₁₉	C₂×Q₁₆	1	3	yes	—
54	C₂×C₄×C₁₉	#137	1	3	yes	—
55	C₂×Dic₁₉	—	8	3	no	—
56	C₁₉⋊C₈	—	4	6	no	—
57	#2811	D₁₉	1	1	yes	characteristic
58	#2095	—	19	3	no	—
59	#1272	—	19	3	no	—
60	C₂²×C₁₉	#451	1	3	yes	—
61	C₂²×C₁₉	#453	1	3	yes	—
62	C₂²×C₁₉	#458	1	1	yes	characteristic
63	C₄×C₁₉	—	2	3	no	—
64	C₄×C₁₉	—	2	3	no	—
65	C₄×C₁₉	—	4	6	no	—
66	C₄×C₁₉	—	8	3	no	—
67	Dic₁₉	—	16	1	no	—
68	C₂×#107	—	38	3	no	—
69	C₂×#103	—	38	3	no	—
70	#395	—	2	3	no	—
71	#391	—	2	3	no	—
72	#391	C₂×D₁₉	1	3	yes	—
73	#384	—	19	1	no	—
74	#336	—	19	3	no	—
75	C₂×C₁₉	#1614	1	3	yes	—
76	C₂×C₁₉	#1633	1	3	yes	—
77	C₂×C₁₉	#1655	1	1	yes	characteristic
78	C₂²×Q₈	—	2	1	no	—
79	C₂²×Q₈	C₂²⋊D₁₉	1	3	yes	—
80	C₂²×C₈	—	38	3	no	—
81	C₂×C₄⋊C₄	—	2	3	no	—
82	C₂×C₄⋊C₄	—	38	3	no	—
83	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	3	yes	—
84	C₂×C₄²	—	2	1	no	—
85	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
86	#107	—	76	6	no	—
87	#103	—	76	6	no	—
88	#95	—	2	3	no	—
89	#95	—	2	6	no	—
90	C₁₉	#7837	1	1	yes	characteristic, complemented, Sylow
91	C₂×Q₈	—	2	3	no	—
92	C₂×Q₈	—	4	3	no	—
93	C₂×Q₈	—	4	3	no	—
94	C₂×Q₈	—	8	3	no	—
95	C₂×Q₈	#64528	1	6	yes	—
96	C₂²×C₄	—	2	3	no	—
97	C₂²×C₄	—	2	3	no	—
98	C₂²×C₄	—	76	1	no	—
99	C₂²×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
100	C₂×C₈	—	38	6	no	—
101	C₂×C₈	—	76	3	no	—
102	C₂×C₈	—	76	3	no	—
103	C₄⋊C₄	—	4	3	no	—
104	C₄⋊C₄	—	8	3	no	—
105	C₄⋊C₄	—	76	3	no	—
106	C₄⋊C₄	—	76	3	no	—
107	C₄²	—	4	1	no	—
108	C₄²	—	8	1	no	—
109	C₂³	#10597399	1	1	yes	characteristic
110	Q₈	—	4	6	no	—
111	Q₈	—	8	3	no	—
112	Q₈	—	8	4	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	2	6	no	—
116	C₂×C₄	—	4	3	no	—
117	C₂×C₄	—	4	3	no	—
118	C₂×C₄	—	4	3	no	—
119	C₂×C₄	—	4	6	no	—
120	C₂×C₄	—	152	3	no	—
121	C₂×C₄	#10597388	1	3	yes	—
122	C₂×C₄	C₂×#64528	1	3	yes	—
123	C₈	—	76	6	no	—
124	C₂²	#11926700	1	3	yes	—
125	C₂²	#11926712	1	3	yes	—
126	C₂²	#11926734	1	1	yes	characteristic
127	C₄	—	2	3	no	—
128	C₄	—	2	3	no	—
129	C₄	—	4	6	no	—
130	C₄	—	8	3	no	—
131	C₄	—	304	1	no	—
132	C₂	#14562660	1	3	yes	—
133	C₂	#14562775	1	3	yes	—
134	C₂	#14562924	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565173

C₂

yes

maximal

#14561461

C₂

yes

maximal

C₁₉×#2811

C₂

yes

maximal, characteristic

C₂×#10597264

—

C₂×#10597292

—

#11926414

C₂²

yes

characteristic

#11926299

C₂²

yes

—

C₁₉×#395

—

C₁₉×#391

—

C₁₉×#391

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

#10597292

—

#10597264

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2811

D₁₉

yes

characteristic

#2095

—

#1272

—

C₂²×C₁₉

#451

yes

—

C₂²×C₁₉

#453

yes

—

C₂²×C₁₉

#458

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

—

C₂×D₁₉

yes

—

#384

—

#336

—

C₂×C₁₉

#1614

yes

—

C₂×C₁₉

#1633

yes

—

C₂×C₁₉

#1655

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

C₂²⋊D₁₉

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

—

—

—

—

C₁₉

#7837

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

#64528

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

—

109

C₂³

#10597399

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

152

—

121

C₂×C₄

#10597388

yes

—

122

C₂×C₄

C₂×#64528

yes

—

123

C₈

—

124

C₂²

#11926700

yes

—

125

C₂²

#11926712

yes

—

126

C₂²

#11926734

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

304

—

132

C₂

#14562660

yes

—

133

C₂

#14562775

yes

—

134

C₂

#14562924

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2811	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#2811	D₁₉
hypocenter	C₁₉	#7837
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2811

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2811

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2811

N	H ≅ G/N	type
90. C₁₉	#7837	semidirect

H ≅ G/N

type

90. C₁₉

#7837

semidirect

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

subgroup	index
#14565173	2
#14561461	2
C₁₉×#2811	2
#7837	19

subgroup

index

#14565173

#14561461

C₁₉×#2811

#7837

Subgroups — #18071882

Conjugacy classes of subgroups

Complements

Maximal subgroups