Group #18072992 — subgroups

Subgroups — #18072992

Order 4864.

330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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	#14561927	C₂	1	2	yes	maximal
2	#14561466	C₂	1	2	yes	maximal
3	#14561464	C₂	1	2	yes	maximal
4	C₁₉×#1726	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926266	C₄	1	8	yes	complemented
7	C₂×C₁₉×#97	C₄	1	2	yes	—
8	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#376	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₁₉×#97	—	2	4	no	—
18	C₁₉×#97	—	2	2	no	—
19	C₄×C₈×C₁₉	—	2	4	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
21	C₁₉×#95	—	2	2	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
24	C₄×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
25	C₂²×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	#41	1	2	yes	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	2	2	no	—
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	C₄²	1	2	yes	—
33	C₂×C₈×C₁₉	C₄²	1	2	yes	—
34	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
35	C₄²×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	M₁₆	1	4	yes	—
37	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
38	C₄²×C₁₉	#41	1	2	yes	—
39	C₂×C₁₉⋊C₈	—	2	8	no	—
40	#8140	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	#117	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	4	no	—
45	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#117	1	4	yes	—
47	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
50	C₈×C₁₉	—	2	2	no	—
51	C₈×C₁₉	—	2	2	no	—
52	C₈×C₁₉	—	2	4	no	—
53	C₁₉⋊C₈	—	4	8	no	—
54	#1726	D₁₉	1	1	yes	characteristic
55	#1452	—	19	2	no	—
56	#1275	—	19	2	no	—
57	#1274	—	19	2	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	#376	1	1	yes	characteristic
60	C₂²×C₁₉	#432	1	2	yes	—
61	C₄×C₁₉	—	2	4	no	—
62	C₄×C₁₉	—	4	4	no	—
63	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
64	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
65	C₄×C₁₉	#432	1	2	yes	—
66	#431	—	19	4	no	—
67	C₂×#97	Dic₁₉	1	2	yes	—
68	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
69	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
70	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
71	#376	C₂×D₁₉	1	1	yes	characteristic
72	#322	—	19	8	no	—
73	C₂×C₁₉	—	2	2	no	—
74	C₂×C₁₉	#1745	1	1	yes	characteristic
75	C₂×C₁₉	#1747	1	2	yes	—
76	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
77	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
78	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
79	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
80	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
81	C₄⋊C₈	—	38	4	no	—
82	C₂²⋊C₈	—	38	4	no	—
83	#97	—	2	4	no	—
84	#97	—	2	2	no	—
85	C₄×C₈	—	2	4	no	—
86	C₄×C₈	—	19	8	no	—
87	C₄×C₈	C₄×D₁₉	1	4	yes	—
88	#95	—	2	2	no	—
89	C₁₉	#8140	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	#64541	1	2	yes	—
92	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	38	8	no	—
98	C₂×C₈	#64520	1	4	yes	—
99	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
100	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
101	C₄²	—	2	2	no	—
102	C₄²	#64520	1	4	yes	—
103	C₄²	C₂×C₄×D₁₉	1	2	yes	—
104	C₄²	#64541	1	2	yes	—
105	C₂³	#10597372	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	4	no	—
109	C₂×C₄	#10597318	1	4	yes	—
110	C₂×C₄	C₂×#64520	1	2	yes	—
111	C₂×C₄	C₂×#64520	1	2	yes	—
112	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
113	C₂×C₄	#10597372	1	1	yes	characteristic
114	C₈	—	2	4	no	—
115	C₈	—	2	2	no	—
116	C₈	—	2	2	no	—
117	C₈	—	76	8	no	—
118	C₂²	—	2	2	no	—
119	C₂²	#11926390	1	1	yes	characteristic
120	C₂²	#11926601	1	2	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₄×#64520	1	1	yes	characteristic
124	C₄	C₄×#64520	1	1	yes	characteristic
125	C₄	#11926601	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	#14563384	1	1	yes	characteristic
128	C₂	#14563390	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561927

C₂

yes

maximal

#14561466

C₂

yes

maximal

#14561464

C₂

yes

maximal

C₁₉×#1726

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926266

C₄

yes

complemented

C₂×C₁₉×#97

C₄

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#97

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1726

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

#432

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

#432

yes

—

#431

—

C₂×#97

Dic₁₉

yes

—

C₂×#97

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#376

C₂×D₁₉

yes

characteristic

#322

—

C₂×C₁₉

—

C₂×C₁₉

#1745

yes

characteristic

C₂×C₁₉

#1747

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

—

#95

—

C₁₉

#8140

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

#64541

yes

—

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64520

yes

—

C₂×C₈

C₄×Dic₁₉

yes

—

100

C₂×C₈

C₄×Dic₁₉

yes

—

101

C₄²

—

102

C₄²

#64520

yes

—

103

C₄²

C₂×C₄×D₁₉

yes

—

104

C₄²

#64541

yes

—

105

C₂³

#10597372

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#10597318

yes

—

110

C₂×C₄

C₂×#64520

yes

—

111

C₂×C₄

C₂×#64520

yes

—

112

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

113

C₂×C₄

#10597372

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₂²

—

119

C₂²

#11926390

yes

characteristic

120

C₂²

#11926601

yes

—

121

C₄

—

122

C₄

—

123

C₄

C₄×#64520

yes

characteristic

124

C₄

C₄×#64520

yes

characteristic

125

C₄

#11926601

yes

—

126

C₂

—

127

C₂

#14563384

yes

characteristic

128

C₂

#14563390

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1726	C₂
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1726	D₁₉
hypocenter	C₁₉	#8140
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #1726

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1726

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #1726

N	H ≅ G/N	type
6. #11926266	C₄	semidirect
89. C₁₉	#8140	semidirect

H ≅ G/N

type

6. #11926266

C₄

semidirect

89. C₁₉

#8140

semidirect

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

subgroup	index
#14561927	2
#14561466	2
#14561464	2
C₁₉×#1726	2
#8140	19

subgroup

index

C₁₉×#1726

Subgroups — #18072992

Conjugacy classes of subgroups

Complements

Maximal subgroups