Group #14269696 — subgroups

Subgroups — C₁₉×#942 #14269696

Order 1824.

120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#235	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#216	C₂	1	2	yes	maximal, complemented
4	C₁₉×#215	C₂	1	2	yes	maximal, complemented
5	C₁₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#137	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₉	—	2	1	no	—
8	C₃×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₁₉	—	2	1	no	—
10	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#67	—	2	1	no	—
12	C₁₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₄×D₃×C₁₉	—	2	1	no	—
14	C₁₉×Dic₆	C₂²	1	1	yes	characteristic
15	C₁₉×C₃⋊C₈	C₂²	1	2	yes	—
16	#41×C₁₉	—	3	1	no	—
17	C₂×Q₈×C₁₉	D₃	1	1	yes	characteristic, complemented
18	Q₁₆×C₁₉	—	3	2	no	—
19	SD₁₆×C₁₉	—	3	2	no	—
20	M₁₆×C₁₉	—	3	1	no	—
21	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
22	C₂×D₃×C₁₉	—	2	1	no	—
23	C₃×C₄×C₁₉	—	2	2	no	—
24	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	Dic₃×C₁₉	—	2	1	no	—
27	Q₈×C₁₉	—	2	1	no	—
28	Q₈×C₁₉	—	3	1	no	—
29	Q₈×C₁₉	C₂×D₃	1	2	yes	—
30	D₄×C₁₉	—	3	1	no	—
31	D₄×C₁₉	—	6	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	6	1	no	—
34	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
35	C₈×C₁₉	—	3	2	no	—
36	C₂×C₃×C₁₉	—	2	1	no	—
37	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
38	D₃×C₁₉	—	4	1	no	—
39	#942	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂²×C₁₉	—	6	1	no	—
41	C₂²×C₁₉	#67	1	1	yes	characteristic
42	C₄×C₁₉	—	2	2	no	—
43	C₄×C₁₉	—	6	1	no	—
44	C₄×C₁₉	#67	1	1	yes	characteristic
45	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
46	C₃×C₁₉	#137	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
48	#235	C₂×C₁₉	1	1	yes	characteristic
49	#216	C₂×C₁₉	1	2	yes	complemented
50	#215	C₂×C₁₉	1	2	yes	complemented
51	#208	C₂×C₁₉	1	1	yes	characteristic, complemented
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	12	1	no	—
54	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
55	#137	—	3	1	no	Sylow
56	C₃×Q₈	—	2	1	no	—
57	C₃×Q₈	C₂²×C₁₉	1	2	yes	—
58	C₂×C₃×C₄	—	2	1	no	—
59	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
60	#67	—	2	1	no	—
61	D₁₂	C₂²×C₁₉	1	1	yes	characteristic
62	C₄×D₃	—	2	1	no	—
63	Dic₆	C₂²×C₁₉	1	1	yes	characteristic
64	C₃⋊C₈	C₂²×C₁₉	1	2	yes	—
65	C₁₉	#942	1	1	yes	characteristic, direct product factor, Sylow
66	#41	—	3	1	no	—
67	C₂×Q₈	D₃×C₁₉	1	1	yes	characteristic, complemented
68	Q₁₆	—	3	2	no	—
69	SD₁₆	—	3	2	no	—
70	M₁₆	—	3	1	no	—
71	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
72	C₂×D₃	—	2	1	no	—
73	C₃×C₄	—	2	2	no	—
74	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
75	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
76	Dic₃	—	2	1	no	—
77	Q₈	—	2	1	no	—
78	Q₈	—	3	1	no	—
79	Q₈	C₂×D₃×C₁₉	1	2	yes	—
80	D₄	—	3	1	no	—
81	D₄	—	6	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	6	1	no	—
84	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
85	C₈	—	3	2	no	—
86	C₂×C₃	—	2	1	no	—
87	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
88	D₃	—	4	1	no	—
89	C₂²	—	6	1	no	—
90	C₂²	C₁₉×#67	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	6	1	no	—
93	C₄	C₁₉×#67	1	1	yes	characteristic
94	C₄	C₂²×D₃×C₁₉	1	1	yes	characteristic
95	C₃	C₁₉×#137	1	1	yes	characteristic, complemented, Sylow
96	C₂	—	2	1	no	—
97	C₂	—	12	1	no	—
98	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×Q₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×#235

C₂

yes

maximal, characteristic

C₁₉×#216

C₂

yes

maximal, complemented

C₁₉×#215

C₂

yes

maximal, complemented

C₁₉×#208

C₂

yes

maximal, characteristic, complemented

C₁₉×#137

—

maximal, Hall

C₃×Q₈×C₁₉

—

C₃×Q₈×C₁₉

C₂²

yes

—

C₂×C₃×C₄×C₁₉

—

C₂×C₃×C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#67

—

C₁₉×D₁₂

C₂²

yes

characteristic

C₄×D₃×C₁₉

—

C₁₉×Dic₆

C₂²

yes

characteristic

C₁₉×C₃⋊C₈

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₃

yes

characteristic, complemented

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂²×C₃×C₁₉

D₄

yes

characteristic

C₂×D₃×C₁₉

—

C₃×C₄×C₁₉

—

C₃×C₄×C₁₉

D₄

yes

characteristic

C₃×C₄×C₁₉

C₂³

yes

characteristic

Dic₃×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₂×D₃

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₃

yes

characteristic

C₈×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

D₃×C₁₉

—

#942

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₁₉

—

C₂²×C₁₉

#67

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#67

yes

characteristic

C₄×C₁₉

C₂²×D₃

yes

characteristic

C₃×C₁₉

#137

yes

characteristic, complemented, Hall

C₂×C₃×Q₈

C₂×C₁₉

yes

characteristic, complemented

#235

C₂×C₁₉

yes

characteristic

#216

C₂×C₁₉

yes

complemented

#215

C₂×C₁₉

yes

complemented

#208

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#67

yes

characteristic

#137

—

Sylow

C₃×Q₈

—

C₃×Q₈

C₂²×C₁₉

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×C₁₉

yes

characteristic

#67

—

D₁₂

C₂²×C₁₉

yes

characteristic

C₄×D₃

—

Dic₆

C₂²×C₁₉

yes

characteristic

C₃⋊C₈

C₂²×C₁₉

yes

—

C₁₉

#942

yes

characteristic, direct product factor, Sylow

#41

—

C₂×Q₈

D₃×C₁₉

yes

characteristic, complemented

Q₁₆

—

SD₁₆

—

M₁₆

—

C₂²×C₃

D₄×C₁₉

yes

characteristic

C₂×D₃

—

C₃×C₄

—

C₃×C₄

D₄×C₁₉

yes

characteristic

C₃×C₄

C₂³×C₁₉

yes

characteristic

Dic₃

—

Q₈

—

Q₈

—

Q₈

C₂×D₃×C₁₉

yes

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₃×C₁₉

yes

characteristic

C₈

—

C₂×C₃

—

C₂×C₃

C₂×D₄×C₁₉

yes

characteristic

D₃

—

C₂²

—

C₂²

C₁₉×#67

yes

characteristic

C₄

—

C₄

—

C₄

C₁₉×#67

yes

characteristic

C₄

C₂²×D₃×C₁₉

yes

characteristic

C₃

C₁₉×#137

yes

characteristic, complemented, Sylow

C₂

—

C₂

—

C₂

C₂×C₁₉×#67

yes

characteristic

	subgroup	G/H
center	C₂×C₁₉	C₂×#67
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂×D₄
prime radical	C₁₉×#235	C₂
hypercenter	C₂×Q₈×C₁₉	D₃
hypocenter	C₃	C₁₉×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×Q₈×C₁₉

subgroup

G/H

center

C₂×C₁₉

C₂×#67

commutator, cosocle

C₃×C₄

C₂³×C₁₉

Frattini

C₄

C₂²×D₃×C₁₉

Fitting

C₂×C₃×Q₈×C₁₉

C₂

socle

C₂×C₃×C₁₉

C₂×D₄

prime radical

C₁₉×#235

C₂

hypercenter

C₂×Q₈×C₁₉

D₃

hypocenter

C₃

C₁₉×#137

LCS

G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×Q₈×C₁₉

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₉	C₂	semidirect
3. C₁₉×#216	C₂	semidirect
4. C₁₉×#215	C₂	semidirect
5. C₁₉×#208	C₂	semidirect
17. C₂×Q₈×C₁₉	D₃	semidirect
39. #942	C₁₉	direct (N × H)
46. C₃×C₁₉	#137	semidirect
47. C₂×C₃×Q₈	C₂×C₁₉	semidirect
49. #216	C₂×C₁₉	semidirect
50. #215	C₂×C₁₉	semidirect
51. #208	C₂×C₁₉	semidirect
65. C₁₉	#942	direct (N × H)
67. C₂×Q₈	D₃×C₁₉	semidirect
95. C₃	C₁₉×#137	semidirect

H ≅ G/N

type

1. C₂×C₃×Q₈×C₁₉

C₂

semidirect

3. C₁₉×#216

C₂

semidirect

4. C₁₉×#215

C₂

semidirect

5. C₁₉×#208

C₂

semidirect

17. C₂×Q₈×C₁₉

D₃

semidirect

39. #942

C₁₉

direct (N × H)

46. C₃×C₁₉

#137

semidirect

47. C₂×C₃×Q₈

C₂×C₁₉

semidirect

49. #216

C₂×C₁₉

semidirect

50. #215

C₂×C₁₉

semidirect

51. #208

C₂×C₁₉

semidirect

65. C₁₉

#942

direct (N × H)

67. C₂×Q₈

D₃×C₁₉

semidirect

95. C₃

C₁₉×#137

semidirect

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

subgroup	index
C₂×C₃×Q₈×C₁₉	2
C₁₉×#235	2
C₁₉×#216	2
C₁₉×#215	2
C₁₉×#208	2
C₁₉×#137	3
#942	19

subgroup

index

C₂×C₃×Q₈×C₁₉

C₁₉×#235

C₁₉×#216

C₁₉×#215

C₁₉×#208

C₁₉×#137

#942

Subgroups — C₁₉×#942 #14269696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#942 #14269696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#942 #14269696