Group #14565884 — subgroups

Subgroups — #14565884

Order 2432.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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×#10597283	C₂	1	4	yes	maximal, complemented
2	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₁₉	—	2	1	no	—
6	C₂×D₈×C₁₉	C₂²	1	2	yes	—
7	C₁₉×#127	—	2	1	no	—
8	C₂×D₁₅₂	—	2	1	no	—
9	C₂×D₁₅₂	C₂²	1	2	yes	—
10	#10597320	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597283	—	2	8	no	—
13	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
14	C₂×D₄×C₁₉	—	2	2	no	—
15	C₂×D₄×C₁₉	—	4	2	no	—
16	C₂×D₇₆	—	2	2	no	—
17	C₂×D₇₆	—	4	2	no	—
18	D₈×C₁₉	—	2	4	no	—
19	D₈×C₁₉	—	4	2	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄²×C₁₉	D₄	1	1	yes	characteristic
23	D₁₅₂	—	2	4	no	—
24	D₁₅₂	—	4	2	no	—
25	C₁₉⋊C₁₆	D₄	1	4	yes	complemented
26	C₂³×C₁₉	—	4	2	no	—
27	C₂²×D₁₉	—	4	2	no	—
28	D₄×C₁₉	—	4	2	no	—
29	D₄×C₁₉	—	4	2	no	—
30	D₄×C₁₉	—	8	4	no	—
31	C₂×C₄×C₁₉	D₈	1	2	yes	—
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	D₇₆	—	4	2	no	—
34	D₇₆	—	4	2	no	—
35	D₇₆	—	8	4	no	—
36	C₈×C₁₉	D₈	1	2	yes	—
37	C₈×C₁₉	C₂×D₄	1	2	yes	—
38	#2246	—	19	1	no	maximal, Sylow
39	C₂²×C₁₉	—	8	2	no	—
40	C₂²×C₁₉	—	8	4	no	—
41	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
42	C₂×D₁₉	—	8	2	no	—
43	C₂×D₁₉	—	8	4	no	—
44	C₄×C₁₉	D₁₆	1	4	yes	complemented
45	C₄×C₁₉	#127	1	1	yes	characteristic
46	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
47	C₂×D₁₆	—	19	4	no	—
48	#493	—	19	1	no	—
49	#493	D₁₉	1	1	yes	characteristic, complemented
50	C₄×C₁₆	—	19	1	no	—
51	C₂×C₁₉	—	16	2	no	—
52	C₂×C₁₉	#493	1	1	yes	characteristic
53	C₂×C₁₉	C₂×D₁₆	1	2	yes	—
54	D₁₉	—	16	2	no	—
55	C₂×D₈	—	2	1	no	—
56	C₂×D₈	—	19	2	no	—
57	C₂×D₈	—	38	1	no	—
58	C₂×D₈	C₂×D₁₉	1	2	yes	—
59	#127	—	2	1	no	—
60	#127	—	38	1	no	—
61	D₁₆	—	38	8	no	—
62	C₂×C₁₆	—	19	2	no	—
63	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
64	C₁₉	#2246	1	1	yes	characteristic, complemented, Sylow
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	4	2	no	—
67	C₂×D₄	—	38	2	no	—
68	C₂×D₄	—	76	2	no	—
69	D₈	—	2	4	no	—
70	D₈	—	4	2	no	—
71	D₈	—	38	4	no	—
72	D₈	—	76	2	no	—
73	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
76	C₁₆	—	19	4	no	—
77	C₂³	—	4	2	no	—
78	C₂³	—	76	2	no	—
79	D₄	—	4	2	no	—
80	D₄	—	4	2	no	—
81	D₄	—	8	4	no	—
82	D₄	—	76	2	no	—
83	D₄	—	76	2	no	—
84	D₄	—	152	4	no	—
85	C₂×C₄	#64525	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
87	C₈	#64525	1	2	yes	—
88	C₈	D₄×D₁₉	1	2	yes	—
89	C₂²	—	8	2	no	—
90	C₂²	—	8	4	no	—
91	C₂²	—	152	2	no	—
92	C₂²	—	152	4	no	—
93	C₂²	C₂×#64525	1	1	yes	characteristic
94	C₄	#10597283	1	4	yes	complemented
95	C₄	C₂×#64525	1	1	yes	characteristic
96	C₄	#10597386	1	1	yes	characteristic
97	C₂	—	16	2	no	—
98	C₂	—	304	2	no	—
99	C₂	#11926920	1	1	yes	characteristic
100	C₂	C₂×#10597283	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597283

C₂

yes

maximal, complemented

#11926921

C₂

yes

maximal, characteristic, complemented

C₄×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#493

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

—

C₁₉×#127

—

C₂×D₁₅₂

—

C₂×D₁₅₂

C₂²

yes

—

#10597320

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597283

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

D₁₅₂

—

D₁₅₂

—

C₁₉⋊C₁₆

D₄

yes

complemented

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

D₈

yes

—

C₈×C₁₉

C₂×D₄

yes

—

#2246

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

D₁₆

yes

complemented

C₄×C₁₉

#127

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₆

—

#493

—

#493

D₁₉

yes

characteristic, complemented

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

C₂×D₁₆

yes

—

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

—

#127

—

#127

—

D₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2246

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

D₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

152

—

C₂×C₄

#64525

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

#64525

yes

—

C₈

D₄×D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

—

152

—

C₂²

—

152

—

C₂²

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

—

304

—

C₂

#11926920

yes

characteristic

100

C₂

C₂×#10597283

yes

—

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#493	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	#493	D₁₉
hypocenter	C₁₉	#2246
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#493

C₂

socle

C₂²×C₁₉

C₂×D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. C₂×#10597283	C₂	semidirect
2. #11926921	C₂	semidirect
3. C₄×C₁₉⋊C₁₆	C₂	semidirect
4. C₁₉×#493	C₂	semidirect
25. C₁₉⋊C₁₆	D₄	semidirect
44. C₄×C₁₉	D₁₆	semidirect
49. #493	D₁₉	semidirect
64. C₁₉	#2246	semidirect
94. C₄	#10597283	semidirect

H ≅ G/N

type

1. C₂×#10597283

C₂

semidirect

2. #11926921

C₂

semidirect

3. C₄×C₁₉⋊C₁₆

C₂

semidirect

4. C₁₉×#493

C₂

semidirect

25. C₁₉⋊C₁₆

D₄

semidirect

44. C₄×C₁₉

D₁₆

semidirect

49. #493

D₁₉

semidirect

64. C₁₉

#2246

semidirect

94. C₄

#10597283

semidirect

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

subgroup	index
C₂×#10597283	2
#11926921	2
C₄×C₁₉⋊C₁₆	2
C₁₉×#493	2
#2246	19

subgroup

index

C₂×#10597283

#11926921

C₄×C₁₉⋊C₁₆

C₁₉×#493

#2246

Subgroups — #14565884

Conjugacy classes of subgroups

Complements

Maximal subgroups