Group #18070397 — subgroups

Subgroups — #18070397

Order 4864.

186 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 27 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	#14561798	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1712	C₂	1	1	yes	maximal, characteristic
3	#11926337	—	2	2	no	—
4	C₁₉×#493	—	2	2	no	—
5	C₁₉×#493	C₄	1	1	yes	characteristic, complemented
6	C₁₉×#493	C₂²	1	1	yes	characteristic
7	C₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂×D₈×C₁₉	—	4	1	no	—
9	C₂×D₈×C₁₉	—	4	4	no	—
10	C₂×D₈×C₁₉	—	4	1	no	—
11	C₁₉×#127	—	2	1	no	—
12	C₁₉×#127	D₄	1	2	yes	—
13	C₄×C₈×C₁₉	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	#10597291	—	4	2	no	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×D₄×C₁₉	—	4	2	no	—
18	C₂×D₄×C₁₉	—	4	2	no	—
19	C₂×D₄×C₁₉	—	4	1	no	—
20	D₈×C₁₉	—	8	2	no	—
21	D₈×C₁₉	—	8	8	no	—
22	D₈×C₁₉	—	8	2	no	—
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²⋊Dic₁₉	—	8	2	no	—
27	#7529	—	19	1	no	maximal, Sylow
28	C₂³×C₁₉	—	4	2	no	—
29	C₂³×C₁₉	—	8	1	no	—
30	D₄×C₁₉	—	8	2	no	—
31	D₄×C₁₉	—	8	4	no	—
32	D₄×C₁₉	—	8	4	no	—
33	D₄×C₁₉	—	8	2	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
36	C₂×Dic₁₉	—	16	2	no	—
37	C₈×C₁₉	—	2	4	no	—
38	C₈×C₁₉	—	2	2	no	—
39	#1712	D₁₉	1	1	yes	characteristic
40	#1408	—	19	2	no	—
41	C₂²×C₁₉	—	8	2	no	—
42	C₂²×C₁₉	—	16	2	no	—
43	C₂²×C₁₉	—	16	2	no	—
44	C₂²×C₁₉	—	16	1	no	—
45	C₂²×C₁₉	#353	1	1	yes	characteristic
46	C₄×C₁₉	—	2	2	no	—
47	C₄×C₁₉	—	2	1	no	—
48	Dic₁₉	—	32	2	no	—
49	#493	—	2	2	no	—
50	#493	Dic₁₉	1	1	yes	characteristic, complemented
51	#493	C₂×D₁₉	1	1	yes	characteristic
52	#353	—	38	2	no	—
53	C₈²	Dic₁₉	1	1	yes	characteristic, complemented
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	—	16	2	no	—
56	C₂×C₁₉	—	32	1	no	—
57	C₂×C₁₉	#1408	1	1	yes	characteristic
58	C₂×D₈	—	4	1	no	—
59	C₂×D₈	—	4	1	no	—
60	C₂×D₈	—	4	4	no	—
61	#127	—	2	1	no	—
62	#127	C₂²⋊D₁₉	1	2	yes	—
63	#99	—	76	2	no	—
64	C₄×C₈	—	2	1	no	—
65	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
66	C₁₉	#7529	1	1	yes	characteristic, complemented, Sylow
67	C₂×D₄	—	2	2	no	—
68	C₂×D₄	—	4	2	no	—
69	C₂×D₄	—	4	2	no	—
70	C₂×D₄	—	4	1	no	—
71	D₈	—	8	2	no	—
72	D₈	—	8	2	no	—
73	D₈	—	8	8	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	2	1	no	—
76	C₂²⋊C₄	—	152	2	no	—
77	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
78	C₂³	—	4	2	no	—
79	C₂³	—	8	1	no	—
80	D₄	—	8	2	no	—
81	D₄	—	8	4	no	—
82	D₄	—	8	4	no	—
83	D₄	—	8	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	304	2	no	—
86	C₂×C₄	#10597291	1	1	yes	characteristic
87	C₈	—	2	4	no	—
88	C₈	—	2	2	no	—
89	C₂²	—	8	2	no	—
90	C₂²	—	16	2	no	—
91	C₂²	—	16	2	no	—
92	C₂²	—	16	1	no	—
93	C₂²	#11926337	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	2	1	no	—
96	C₄	—	608	2	no	—
97	C₂	—	2	1	no	—
98	C₂	—	16	2	no	—
99	C₂	—	32	1	no	—
100	C₂	#14561798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561798

C₂

yes

maximal, complemented

C₁₉×#1712

C₂

yes

maximal, characteristic

#11926337

—

C₁₉×#493

—

C₁₉×#493

C₄

yes

characteristic, complemented

C₁₉×#493

C₂²

yes

characteristic

C₈²×C₁₉

C₄

yes

characteristic, complemented

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×#127

—

C₁₉×#127

D₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

#10597291

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

#7529

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1712

D₁₉

yes

characteristic

#1408

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#353

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#493

—

#493

Dic₁₉

yes

characteristic, complemented

#493

C₂×D₁₉

yes

characteristic

#353

—

C₈²

Dic₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1408

yes

characteristic

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

#127

—

#127

C₂²⋊D₁₉

yes

—

#99

—

C₄×C₈

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₁₉

#7529

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂²⋊C₄

—

152

—

C₄²

C₂²⋊Dic₁₉

yes

characteristic

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

304

—

C₂×C₄

#10597291

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#11926337

yes

characteristic

C₄

—

C₄

—

C₄

—

608

—

C₂

—

C₂

—

C₂

—

100

C₂

#14561798

yes

characteristic

	subgroup	G/H
center	C₂	#14561798
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#493	C₂×D₁₉
Fitting, prime radical	C₁₉×#1712	C₂
socle	C₂×C₁₉	#1408
cosocle	C₁₉×#493	C₂²
hypercenter	#1712	D₁₉
hypocenter	C₁₉	#7529
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1712

subgroup

G/H

center

C₂

#14561798

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

#493

C₂×D₁₉

Fitting, prime radical

C₁₉×#1712

C₂

socle

C₂×C₁₉

#1408

cosocle

C₁₉×#493

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1712

N	H ≅ G/N	type
1. #14561798	C₂	semidirect
5. C₁₉×#493	C₄	semidirect
7. C₈²×C₁₉	C₄	semidirect
50. #493	Dic₁₉	semidirect
53. C₈²	Dic₁₉	semidirect
66. C₁₉	#7529	semidirect

H ≅ G/N

type

1. #14561798

C₂

semidirect

5. C₁₉×#493

C₄

semidirect

7. C₈²×C₁₉

C₄

semidirect

50. #493

Dic₁₉

semidirect

53. C₈²

Dic₁₉

semidirect

66. C₁₉

#7529

semidirect

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

subgroup	index
#14561798	2
C₁₉×#1712	2
#7529	19

subgroup

index

#14561798

C₁₉×#1712

#7529

Subgroups — #18070397

Conjugacy classes of subgroups

Complements

Maximal subgroups