Group #18085305 — subgroups

Subgroups — #18085305

Order 4864.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14575029	C₂	1	3	yes	maximal
2	#14564611	C₂	1	3	yes	maximal
3	C₁₉×#1309	C₂	1	1	yes	maximal, characteristic
4	#11927101	C₂²	1	3	yes	—
5	#11926830	—	2	6	no	—
6	#11926802	—	2	6	no	—
7	#11926755	—	2	6	no	—
8	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
9	#11926305	—	2	6	no	—
10	C₁₉×#423	C₂²	1	3	yes	—
11	C₂×M₁₆×C₁₉	D₄	1	6	yes	—
12	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	#10597372	—	2	3	no	—
14	#10597370	—	2	6	no	—
15	C₂×C₄×Dic₁₉	—	2	3	no	—
16	C₂×Dic₇₆	—	2	6	no	—
17	#10597316	—	2	3	no	—
18	#10597315	D₄	1	6	yes	—
19	C₄×Dic₃₈	—	2	6	no	—
20	C₁₉×C₄⋊C₈	—	2	6	no	—
21	#10597274	—	2	6	no	—
22	#10597273	—	2	12	no	—
23	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
24	C₂²×Dic₁₉	—	4	1	no	—
25	C₂×Dic₃₈	—	2	6	no	—
26	M₁₆×C₁₉	—	4	6	no	—
27	C₂×C₈×C₁₉	—	2	6	no	—
28	C₄²×C₁₉	C₂×D₄	1	3	yes	—
29	C₄²×C₁₉	#41	1	1	yes	characteristic
30	C₂²⋊Dic₁₉	—	4	3	no	—
31	C₄⋊Dic₁₉	—	2	6	no	—
32	C₄⋊Dic₁₉	—	2	6	no	—
33	Dic₁₉⋊C₄	—	4	6	no	—
34	C₄×Dic₁₉	—	2	6	no	—
35	C₄×Dic₁₉	—	4	3	no	—
36	C₄×Dic₁₉	—	4	3	no	—
37	Dic₇₆	—	8	6	no	—
38	#10303	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#127	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	3	no	—
41	C₂×C₄×C₁₉	—	2	3	no	—
42	C₂×C₄×C₁₉	#120	1	3	yes	—
43	C₂×C₄×C₁₉	#121	1	3	yes	—
44	C₂×Dic₁₉	—	4	6	no	—
45	C₂×Dic₁₉	—	4	6	no	—
46	Dic₃₈	—	4	6	no	—
47	Dic₃₈	—	4	6	no	—
48	C₈×C₁₉	—	4	6	no	—
49	#3255	—	19	3	no	—
50	#1994	—	19	3	no	—
51	#1309	D₁₉	1	1	yes	characteristic
52	C₂²×C₁₉	—	2	3	no	—
53	C₂²×C₁₉	#392	1	1	yes	characteristic
54	C₄×C₁₉	—	2	3	no	—
55	C₄×C₁₉	#455	1	3	yes	—
56	C₄×C₁₉	#456	1	3	yes	—
57	Dic₁₉	—	4	4	no	—
58	Dic₁₉	—	8	6	no	—
59	#533	—	19	3	no	—
60	#475	—	38	6	no	—
61	#470	—	38	6	no	—
62	#462	—	38	6	no	—
63	#423	C₂×D₁₉	1	3	yes	—
64	C₄³	—	19	1	no	—
65	#339	—	38	6	no	—
66	C₂×C₁₉	—	4	1	no	—
67	C₂×C₁₉	#2007	1	3	yes	—
68	C₂×Q₁₆	—	38	6	no	—
69	C₂×M₁₆	D₇₆	1	6	yes	—
70	C₄⋊Q₈	—	19	6	no	—
71	#125	—	38	3	no	—
72	C₂²⋊Q₈	—	38	6	no	—
73	C₄×Q₈	—	38	6	no	—
74	#117	—	38	3	no	—
75	C₂×C₄²	—	38	3	no	—
76	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
77	#106	—	38	6	no	—
78	C₄⋊C₈	—	2	6	no	—
79	#103	—	38	12	no	—
80	C₁₉	#10303	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₈	—	38	6	no	—
82	C₂²×C₄	—	76	1	no	—
83	C₂²×C₄	C₂×D₇₆	1	3	yes	—
84	Q₁₆	—	152	6	no	—
85	M₁₆	—	4	6	no	—
86	C₂×C₈	—	2	6	no	—
87	C₄⋊C₄	—	38	6	no	—
88	C₄⋊C₄	—	38	6	no	—
89	C₄⋊C₄	—	76	6	no	—
90	C₂²⋊C₄	—	76	3	no	—
91	C₄²	—	38	6	no	—
92	C₄²	—	76	3	no	—
93	C₄²	—	76	3	no	—
94	C₄²	D₄×D₁₉	1	3	yes	—
95	C₄²	#64545	1	1	yes	characteristic
96	C₂³	#10597320	1	1	yes	characteristic
97	Q₈	—	76	6	no	—
98	Q₈	—	76	6	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	76	6	no	—
102	C₂×C₄	—	76	6	no	—
103	C₂×C₄	#10597328	1	3	yes	—
104	C₂×C₄	#10597341	1	3	yes	—
105	C₈	—	4	6	no	—
106	C₂²	—	2	3	no	—
107	C₂²	#11926454	1	1	yes	characteristic
108	C₄	—	2	3	no	—
109	C₄	—	76	4	no	—
110	C₄	—	152	6	no	—
111	C₄	#11926724	1	3	yes	—
112	C₄	#11926729	1	3	yes	—
113	C₂	—	4	1	no	—
114	C₂	#14564684	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14575029

C₂

yes

maximal

#14564611

C₂

yes

maximal

C₁₉×#1309

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926830

—

#11926802

—

#11926755

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926305

—

C₁₉×#423

C₂²

yes

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

#10597370

—

C₂×C₄×Dic₁₉

—

C₂×Dic₇₆

—

#10597316

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

#10597274

—

#10597273

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#3255

—

#1994

—

#1309

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#392

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#455

yes

—

C₄×C₁₉

#456

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

C₂×D₁₉

yes

—

C₄³

—

#339

—

C₂×C₁₉

—

C₂×C₁₉

#2007

yes

—

C₂×Q₁₆

—

C₂×M₁₆

D₇₆

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#106

—

C₄⋊C₈

—

#103

—

C₁₉

#10303

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

—

Q₁₆

—

152

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

D₄×D₁₉

yes

—

C₄²

yes

C₂³

yes

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#10597328

yes

—

104

C₂×C₄

#10597341

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

#11926454

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

152

—

111

C₄

#11926724

yes

—

112

C₄

#11926729

yes

—

113

C₂

—

114

C₂

#14564684

yes

—

	subgroup	G/H
center	C₂²	#11926454
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1309	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂³×C₁₉	#127
hypercenter	#1309	D₁₉
hypocenter	C₁₉	#10303
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#11926454

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1309

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
80. C₁₉	#10303	semidirect

H ≅ G/N

type

80. C₁₉

#10303

semidirect

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

subgroup	index
#14575029	2
#14564611	2
C₁₉×#1309	2
#10303	19

subgroup

index

#14575029

#14564611

C₁₉×#1309

#10303

Subgroups — #18085305

Conjugacy classes of subgroups

Complements

Maximal subgroups