Group #18069948 — subgroups

Subgroups — #18069948

Order 4864.

162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561581	C₂	1	2	yes	maximal
2	C₁₉×#1836	C₂	1	1	yes	maximal, characteristic
3	#11926270	—	2	2	no	—
4	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
5	C₁₉×#384	C₂²	1	1	yes	characteristic
6	C₁₉×#382	C₄	1	1	yes	characteristic
7	C₁₉×#340	—	2	2	no	—
8	C₂²×C₈×C₁₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
11	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₁₉×#97	—	2	1	no	—
14	C₁₉×#97	C₈	1	2	yes	complemented
15	C₁₉×#95	—	4	1	no	—
16	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	4	1	no	—
20	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	—	2	2	no	—
22	C₂×C₈×C₁₉	—	4	1	no	—
23	C₂×C₈×C₁₉	—	4	1	no	—
24	C₄⋊C₄×C₁₉	—	4	2	no	—
25	C₄⋊C₄×C₁₉	—	4	2	no	—
26	C₄⋊C₄×C₁₉	—	8	2	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	C₂×C₁₉⋊C₈	—	8	2	no	—
31	#7367	—	19	1	no	maximal, Sylow
32	C₂³×C₁₉	#99	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	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	8	2	no	—
41	C₂×C₄×C₁₉	—	8	1	no	—
42	C₂×C₄×C₁₉	—	8	1	no	—
43	C₂×C₄×C₁₉	—	8	1	no	—
44	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
46	C₈×C₁₉	—	4	2	no	—
47	C₁₉⋊C₈	—	16	2	no	—
48	#1836	D₁₉	1	1	yes	characteristic
49	#1325	—	19	2	no	—
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	2	1	no	—
52	C₂²×C₁₉	#324	1	1	yes	characteristic
53	C₂²×C₁₉	#354	1	1	yes	characteristic
54	C₂²×C₁₉	#355	1	1	yes	characteristic
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	—	4	1	no	—
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	—	8	2	no	—
60	C₄×C₁₉	—	16	1	no	—
61	C₂×#97	Dic₁₉	1	1	yes	characteristic
62	#384	C₂×D₁₉	1	1	yes	characteristic
63	#382	Dic₁₉	1	1	yes	characteristic
64	#340	—	2	2	no	—
65	#324	—	38	2	no	—
66	C₂×C₁₉	—	2	1	no	—
67	C₂×C₁₉	—	2	1	no	—
68	C₂×C₁₉	#1324	1	1	yes	characteristic
69	C₂×C₁₉	#1412	1	1	yes	characteristic
70	C₂×C₁₉	#1413	1	1	yes	characteristic
71	C₂²×C₈	—	2	1	no	—
72	C₂×C₄⋊C₄	—	2	1	no	—
73	C₂×C₄⋊C₄	—	4	1	no	—
74	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
75	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
76	C₂²⋊C₈	—	76	2	no	—
77	#97	—	2	1	no	—
78	#97	C₁₉⋊C₈	1	2	yes	complemented
79	#95	—	4	1	no	—
80	C₁₉	#7367	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	2	1	no	—
82	C₂²×C₄	—	2	2	no	—
83	C₂²×C₄	—	4	1	no	—
84	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	4	1	no	—
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	—	152	2	no	—
89	C₄⋊C₄	—	4	2	no	—
90	C₄⋊C₄	—	4	2	no	—
91	C₄⋊C₄	—	8	2	no	—
92	C₄²	—	2	1	no	—
93	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
94	C₄²	#64520	1	1	yes	characteristic
95	C₂³	#10597291	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	—	8	2	no	—
104	C₂×C₄	—	8	1	no	—
105	C₂×C₄	—	8	1	no	—
106	C₂×C₄	—	8	1	no	—
107	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
108	C₂×C₄	#10597293	1	1	yes	characteristic
109	C₈	—	4	2	no	—
110	C₈	—	304	2	no	—
111	C₂²	—	2	1	no	—
112	C₂²	—	2	1	no	—
113	C₂²	#11926270	1	1	yes	characteristic
114	C₂²	#11926339	1	1	yes	characteristic
115	C₂²	#11926341	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	2	1	no	—
118	C₄	—	4	1	no	—
119	C₄	—	4	1	no	—
120	C₄	—	8	2	no	—
121	C₄	—	16	1	no	—
122	C₂	—	2	1	no	—
123	C₂	—	2	1	no	—
124	C₂	#14561579	1	1	yes	characteristic
125	C₂	#14561806	1	1	yes	characteristic
126	C₂	#14561808	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561581

C₂

yes

maximal

C₁₉×#1836

C₂

yes

maximal, characteristic

#11926270

—

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#382

C₄

yes

characteristic

C₁₉×#340

—

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#97

—

C₁₉×#97

C₈

yes

complemented

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#101

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1836

D₁₉

yes

characteristic

#1325

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#97

Dic₁₉

yes

characteristic

#384

C₂×D₁₉

yes

characteristic

#382

Dic₁₉

yes

characteristic

#340

—

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂²⋊C₈

—

#97

—

#97

C₁₉⋊C₈

yes

complemented

#95

—

C₁₉

#7367

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

152

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×C₁₉⋊C₈

yes

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

108

C₂×C₄

#10597293

yes

characteristic

109

C₈

—

110

C₈

—

304

—

111

C₂²

—

112

C₂²

—

113

C₂²

#11926270

yes

characteristic

114

C₂²

#11926339

yes

characteristic

115

C₂²

#11926341

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₂

—

123

C₂

—

124

C₂

#14561579

yes

characteristic

125

C₂

#14561806

yes

characteristic

126

C₂

#14561808

yes

characteristic

	subgroup	G/H
center	C₂²	#11926339
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#384	C₂×D₁₉
Fitting	C₁₉×#1836	C₂
socle	C₂²×C₁₉	#354
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#384	C₂²
hypercenter	#1836	D₁₉
hypocenter	C₁₉	#7367
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1836

subgroup

G/H

center

C₂²

#11926339

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#384

C₂×D₁₉

Fitting

C₁₉×#1836

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#384

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1836

N	H ≅ G/N	type
14. C₁₉×#97	C₈	semidirect
78. #97	C₁₉⋊C₈	semidirect
80. C₁₉	#7367	semidirect

H ≅ G/N

type

14. C₁₉×#97

C₈

semidirect

78. #97

C₁₉⋊C₈

semidirect

80. C₁₉

#7367

semidirect

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

subgroup	index
#14561581	2
C₁₉×#1836	2
#7367	19

subgroup

index

#14561581

C₁₉×#1836

#7367

Subgroups — #18069948

Conjugacy classes of subgroups

Complements

Maximal subgroups