Group #14565229 — subgroups

Subgroups — C₄×#10597269 #14565229

Order 2432.

196 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597269	C₂	1	2	yes	maximal
2	#11926320	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₉	C₄	1	1	yes	characteristic
8	C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597269	C₄	1	8	yes	direct product factor
13	C₂×C₁₉⋊C₁₆	C₂²	1	4	yes	—
14	C₂²×C₄×C₁₉	C₈	1	2	yes	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₈	1	4	yes	—
17	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄²×C₁₉	C₈	1	2	yes	—
23	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₁₉⋊C₁₆	C₂×C₄	1	8	yes	complemented
26	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₉	—	2	4	no	—
28	C₂×C₄×C₁₉	C₄²	1	2	yes	—
29	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₉	C₄²	1	2	yes	—
35	C₈×C₁₉	C₂×C₈	1	2	yes	—
36	C₈×C₁₉	C₂×C₈	1	2	yes	—
37	C₈×C₁₉	C₂²×C₄	1	2	yes	—
38	C₄×M₃₂	—	19	1	no	maximal, Sylow
39	C₂²×C₁₉	—	2	2	no	—
40	C₂²×C₁₉	C₄×C₈	1	2	yes	—
41	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₁₉	—	2	2	no	—
43	C₄×C₁₉	C₄×C₈	1	2	yes	—
44	C₄×C₁₉	M₃₂	1	4	yes	complemented
45	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
46	C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
47	C₂×M₃₂	—	19	2	no	—
48	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
49	#346	—	19	2	no	—
50	C₄×C₁₆	—	19	2	no	—
51	C₂×C₁₉	—	2	2	no	—
52	C₂×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
53	C₂×C₁₉	C₂×M₃₂	1	2	yes	—
54	C₂²×C₈	Dic₁₉	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
56	C₂×C₄²	Dic₁₉	1	1	yes	characteristic
57	M₃₂	—	19	8	no	—
58	C₂×C₁₆	—	19	4	no	—
59	C₄×C₈	Dic₁₉	1	1	yes	characteristic
60	C₄×C₈	Dic₁₉	1	1	yes	characteristic
61	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
62	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
63	C₁₉	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	C₁₉⋊C₈	1	2	yes	—
65	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
66	C₂×C₈	C₁₉⋊C₈	1	4	yes	—
67	C₂×C₈	C₄×D₁₉	1	4	yes	—
68	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
69	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
70	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
72	C₄²	C₁₉⋊C₈	1	2	yes	—
73	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
74	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
75	C₁₆	—	19	8	no	—
76	C₂³	C₂×C₁₉⋊C₈	1	1	yes	characteristic
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
79	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
80	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
81	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
82	C₂×C₄	C₄×Dic₁₉	1	2	yes	—
83	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
84	C₈	C₂×C₁₉⋊C₈	1	2	yes	—
85	C₈	C₂×C₁₉⋊C₈	1	2	yes	—
86	C₈	C₄×Dic₁₉	1	2	yes	—
87	C₈	C₂×C₄×D₁₉	1	2	yes	—
88	C₂²	—	2	2	no	—
89	C₂²	C₄×C₁₉⋊C₈	1	2	yes	—
90	C₂²	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	C₄×C₁₉⋊C₈	1	2	yes	—
93	C₄	#10597269	1	4	yes	direct product factor
94	C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
95	C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
98	C₂	C₂×#10597269	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597269

C₂

yes

maximal

#11926320

C₂

yes

maximal, complemented

C₄×C₁₉⋊C₁₆

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₄

yes

characteristic

C₄×C₈×C₁₉

C₄

yes

characteristic

C₄×C₈×C₁₉

C₄

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597269

C₄

yes

direct product factor

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂²×C₄×C₁₉

C₈

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₈

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₈

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉⋊C₁₆

C₂×C₄

yes

complemented

C₂³×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

C₄²

yes

—

C₈×C₁₉

C₂×C₈

yes

—

C₈×C₁₉

C₂×C₈

yes

—

C₈×C₁₉

C₂²×C₄

yes

—

C₄×M₃₂

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₈

yes

—

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₄×C₈

yes

—

C₄×C₁₉

M₃₂

yes

complemented

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×M₃₂

—

C₂×C₄×C₈

D₁₉

yes

characteristic

#346

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄×C₈

yes

characteristic

C₂×C₁₉

C₂×M₃₂

yes

—

C₂²×C₈

Dic₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄²

Dic₁₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄×C₈

Dic₁₉

yes

characteristic

C₄×C₈

Dic₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

C₄×M₃₂

yes

characteristic, complemented, Sylow

C₂²×C₄

C₁₉⋊C₈

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₁₉⋊C₈

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

C₁₉⋊C₈

yes

—

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₁₆

—

C₂³

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

C₄×Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₈

C₂×C₁₉⋊C₈

yes

—

C₈

C₂×C₁₉⋊C₈

yes

—

C₈

C₄×Dic₁₉

yes

—

C₈

C₂×C₄×D₁₉

yes

—

C₂²

—

C₂²

C₄×C₁₉⋊C₈

yes

—

C₂²

C₂²×C₁₉⋊C₈

yes

characteristic

C₄

—

C₄

C₄×C₁₉⋊C₈

yes

—

C₄

#10597269

yes

direct product factor

C₄

C₂²×C₁₉⋊C₈

yes

characteristic

C₄

C₂×C₄×Dic₁₉

yes

characteristic

C₂

—

C₂

C₂×C₄×C₁₉⋊C₈

yes

characteristic

C₂

C₂×#10597269

yes

—

	subgroup	G/H
center	C₄×C₈	C₂×D₁₉
commutator	C₂×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×C₈
prime radical	C₂³×C₁₉	C₂×C₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	C₄×M₃₂
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₄×C₈

C₂×D₁₉

commutator

C₂×C₁₉

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂²×C₈

prime radical

C₂³×C₁₉

C₂×C₈

cosocle

C₂×C₈×C₁₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₉

hypocenter

C₁₉

C₄×M₃₂

LCS

G ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #11926320	C₂	semidirect
3. C₄×C₁₉⋊C₁₆	C₂	semidirect
12. #10597269	C₄	direct (N × H)
25. C₁₉⋊C₁₆	C₂×C₄	semidirect
44. C₄×C₁₉	M₃₂	semidirect
63. C₁₉	C₄×M₃₂	semidirect
93. C₄	#10597269	direct (N × H)

H ≅ G/N

type

2. #11926320

C₂

semidirect

3. C₄×C₁₉⋊C₁₆

C₂

semidirect

12. #10597269

C₄

direct (N × H)

25. C₁₉⋊C₁₆

C₂×C₄

semidirect

44. C₄×C₁₉

M₃₂

semidirect

63. C₁₉

C₄×M₃₂

semidirect

93. C₄

#10597269

direct (N × H)

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

subgroup	index
C₂×#10597269	2
#11926320	2
C₄×C₁₉⋊C₁₆	2
C₂×C₄×C₈×C₁₉	2
C₄×M₃₂	19

subgroup

index

C₂×#10597269

#11926320

C₄×C₁₉⋊C₁₆

C₂×C₄×C₈×C₁₉

C₄×M₃₂

Subgroups — C₄×#10597269 #14565229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#10597269 #14565229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597269 #14565229