Group #18075107 — subgroups

Subgroups — #18075107

Order 4864.

656 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14564613	C₂	1	3	yes	maximal
2	#14562373	C₂	1	3	yes	maximal
3	C₁₉×#3556	C₂	1	1	yes	maximal, characteristic
4	#11926568	C₂²	1	3	yes	—
5	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
6	#11926303	—	2	6	no	—
7	#11926290	—	2	6	no	—
8	C₁₉×#564	C₄	1	4	yes	complemented
9	C₁₉×#557	—	2	6	no	—
10	C₁₉×#541	—	2	6	no	—
11	C₁₉×#533	C₂²	1	3	yes	—
12	C₁₉×C₄⋊Q₈	—	2	6	no	—
13	C₁₉×C₄⋊Q₈	D₄	1	6	yes	—
14	C₁₉×#126	—	2	8	no	—
15	C₁₉×#125	—	2	6	no	—
16	C₁₉×#125	—	2	24	no	—
17	C₁₉×#125	C₂×C₄	1	6	yes	—
18	C₁₉×C₂²⋊Q₈	—	2	6	no	—
19	C₄×Q₈×C₁₉	—	2	12	no	—
20	C₄×Q₈×C₁₉	—	2	6	no	—
21	C₁₉×#117	D₄	1	6	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄×Dic₁₉	—	2	3	no	—
24	C₂×#64520	—	2	3	no	—
25	C₄⋊(C₁₉⋊C₈)	—	2	6	no	—
26	C₂×Q₈×C₁₉	—	2	6	no	—
27	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
28	C₂²×Dic₁₉	—	4	1	no	—
29	C₄⋊C₄×C₁₉	—	2	24	no	—
30	C₄⋊C₄×C₁₉	—	2	12	no	—
31	C₄⋊C₄×C₁₉	—	2	6	no	—
32	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	12	yes	—
33	C₂²⋊C₄×C₁₉	—	2	6	no	—
34	C₄²×C₁₉	—	2	8	no	—
35	C₄²×C₁₉	—	2	6	no	—
36	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂×D₄	1	3	yes	—
38	C₄×Dic₁₉	—	2	6	no	—
39	C₄×Dic₁₉	—	4	3	no	—
40	#64520	—	4	6	no	—
41	C₂×C₁₉⋊C₈	—	4	3	no	—
42	#8533	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	#120	1	1	yes	characteristic
44	Q₈×C₁₉	—	4	6	no	—
45	Q₈×C₁₉	—	4	6	no	—
46	C₂×C₄×C₁₉	—	2	3	no	—
47	C₂×C₄×C₁₉	—	2	3	no	—
48	C₂×C₄×C₁₉	—	2	12	no	—
49	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
50	C₂×C₄×C₁₉	#120	1	3	yes	—
51	C₂×Dic₁₉	—	4	6	no	—
52	C₁₉⋊C₈	—	8	3	no	—
53	#3556	D₁₉	1	1	yes	characteristic
54	#1994	—	19	3	no	—
55	#1561	—	19	3	no	—
56	C₂²×C₁₉	—	2	3	no	—
57	C₂²×C₁₉	#379	1	1	yes	characteristic
58	C₄×C₁₉	—	2	3	no	—
59	C₄×C₁₉	—	4	12	no	—
60	C₄×C₁₉	#454	1	3	yes	—
61	C₄×C₁₉	#456	1	3	yes	—
62	Dic₁₉	—	4	4	no	—
63	#564	Dic₁₉	1	4	yes	complemented
64	#557	—	2	6	no	—
65	#541	—	2	6	no	—
66	#533	C₂×D₁₉	1	3	yes	—
67	#423	—	19	3	no	—
68	C₄³	—	19	1	no	—
69	#339	—	38	6	no	—
70	#332	—	38	6	no	—
71	C₂×C₁₉	—	4	1	no	—
72	C₂×C₁₉	#1793	1	3	yes	—
73	C₂×M₁₆	—	38	3	no	—
74	C₄⋊Q₈	—	2	6	no	—
75	C₄⋊Q₈	C₂²⋊D₁₉	1	6	yes	—
76	#126	—	2	8	no	—
77	#125	—	2	6	no	—
78	#125	—	2	24	no	—
79	#125	C₂×Dic₁₉	1	6	yes	—
80	C₂²⋊Q₈	—	2	6	no	—
81	C₄×Q₈	—	2	12	no	—
82	C₄×Q₈	—	2	6	no	—
83	#117	C₂²⋊D₁₉	1	6	yes	—
84	C₂×C₄²	—	38	3	no	—
85	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
86	C₄⋊C₈	—	38	6	no	—
87	C₁₉	#8533	1	1	yes	characteristic, complemented, Sylow
88	C₂×Q₈	—	2	6	no	—
89	C₂²×C₄	—	76	1	no	—
90	C₂²×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
91	M₁₆	—	76	6	no	—
92	C₂×C₈	—	76	3	no	—
93	C₄⋊C₄	—	2	24	no	—
94	C₄⋊C₄	—	2	12	no	—
95	C₄⋊C₄	—	2	6	no	—
96	C₄⋊C₄	C₂²⋊Dic₁₉	1	12	yes	—
97	C₂²⋊C₄	—	2	6	no	—
98	C₄²	—	2	8	no	—
99	C₄²	—	2	6	no	—
100	C₄²	—	38	6	no	—
101	C₄²	—	76	3	no	—
102	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
103	C₄²	C₂×C₂²⋊D₁₉	1	3	yes	—
104	C₂³	#10597399	1	1	yes	characteristic
105	Q₈	—	4	6	no	—
106	Q₈	—	4	6	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	2	12	no	—
110	C₂×C₄	—	76	6	no	—
111	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	3	yes	—
112	C₂×C₄	#10597399	1	3	yes	—
113	C₈	—	152	3	no	—
114	C₂²	—	2	3	no	—
115	C₂²	#11926400	1	1	yes	characteristic
116	C₄	—	2	3	no	—
117	C₄	—	4	12	no	—
118	C₄	—	76	4	no	—
119	C₄	#11926717	1	3	yes	—
120	C₄	#11926727	1	3	yes	—
121	C₂	—	4	1	no	—
122	C₂	#14563594	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564613

C₂

yes

maximal

#14562373

C₂

yes

maximal

C₁₉×#3556

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926303

—

#11926290

—

C₁₉×#564

C₄

yes

complemented

C₁₉×#557

—

C₁₉×#541

—

C₁₉×#533

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#126

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#3556

D₁₉

yes

characteristic

#1994

—

#1561

—

C₂²×C₁₉

—

C₂²×C₁₉

#379

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#454

yes

—

C₄×C₁₉

#456

yes

—

Dic₁₉

—

#564

Dic₁₉

yes

—

—

C₂×D₁₉

yes

—

#423

—

C₄³

—

#339

—

#332

—

C₂×C₁₉

—

C₂×C₁₉

#1793

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

—

—

—

C₂×Dic₁₉

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

C₂²⋊D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₁₉

#8533

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂²×Dic₁₉

yes

characteristic

103

C₄²

C₂×C₂²⋊D₁₉

yes

—

104

C₂³

#10597399

yes

characteristic

105

Q₈

—

106

Q₈

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

112

C₂×C₄

#10597399

yes

—

113

C₈

—

152

—

114

C₂²

—

115

C₂²

#11926400

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

#11926717

yes

—

120

C₄

#11926727

yes

—

121

C₂

—

122

C₂

#14563594

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3556	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3556	D₁₉
hypocenter	C₁₉	#8533
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3556

subgroup

G/H

center

C₂²

#11926400

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3556

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3556

N	H ≅ G/N	type
8. C₁₉×#564	C₄	semidirect
63. #564	Dic₁₉	semidirect
87. C₁₉	#8533	semidirect

H ≅ G/N

type

8. C₁₉×#564

C₄

semidirect

63. #564

Dic₁₉

semidirect

87. C₁₉

#8533

semidirect

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

subgroup	index
#14564613	2
#14562373	2
C₁₉×#3556	2
#8533	19

subgroup

index

#14564613

#14562373

C₁₉×#3556

#8533

Subgroups — #18075107

Conjugacy classes of subgroups

Complements

Maximal subgroups