Group #19136189 — subgroups

Subgroups — C₄×#13063265 #19136189

Order 5504.

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×#13063265	C₂	1	2	yes	maximal
2	#14582675	C₂	1	2	yes	maximal, complemented
3	C₄×C₄₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	#13063265	C₄	1	8	yes	direct product factor
6	C₂×C₄₃⋊C₁₆	C₂²	1	4	yes	—
7	C₂²×C₈×C₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₄₃	C₄	1	1	yes	characteristic
10	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
11	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
12	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	C₈	1	2	yes	—
15	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₈	1	4	yes	—
17	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₄²×C₄₃	C₈	1	2	yes	—
23	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₄₃⋊C₁₆	C₂×C₄	1	8	yes	complemented
26	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₄₃	—	2	4	no	—
28	C₂×C₄×C₄₃	C₄²	1	2	yes	—
29	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₄₃	C₄²	1	2	yes	—
35	C₈×C₄₃	C₂×C₈	1	2	yes	—
36	C₈×C₄₃	C₂×C₈	1	2	yes	—
37	C₈×C₄₃	C₂²×C₄	1	2	yes	—
38	C₂²×C₄₃	—	2	2	no	—
39	C₂²×C₄₃	C₄×C₈	1	2	yes	—
40	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₄₃	—	2	2	no	—
42	C₄×C₄₃	C₄×C₈	1	2	yes	—
43	C₄×C₄₃	M₃₂	1	4	yes	complemented
44	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
46	C₄×M₃₂	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	—	2	2	no	—
48	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₄₃	C₂×M₃₂	1	2	yes	—
50	C₂×M₃₂	—	43	2	no	—
51	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
52	#346	—	43	2	no	—
53	C₄×C₁₆	—	43	2	no	—
54	C₄₃	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	Dic₄₃	1	1	yes	characteristic
56	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
57	C₂×C₄²	Dic₄₃	1	1	yes	characteristic
58	M₃₂	—	43	8	no	—
59	C₂×C₁₆	—	43	4	no	—
60	C₄×C₈	Dic₄₃	1	1	yes	characteristic
61	C₄×C₈	Dic₄₃	1	1	yes	characteristic
62	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
63	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
64	C₂²×C₄	C₄₃⋊C₈	1	2	yes	—
65	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
66	C₂×C₈	C₄₃⋊C₈	1	4	yes	—
67	C₂×C₈	C₄×D₄₃	1	4	yes	—
68	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
69	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
70	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
72	C₄²	C₄₃⋊C₈	1	2	yes	—
73	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
74	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
75	C₁₆	—	43	8	no	—
76	C₂³	C₂×C₄₃⋊C₈	1	1	yes	characteristic
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
79	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
81	C₂×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
82	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
83	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
84	C₈	C₂×C₄₃⋊C₈	1	2	yes	—
85	C₈	C₂×C₄₃⋊C₈	1	2	yes	—
86	C₈	C₄×Dic₄₃	1	2	yes	—
87	C₈	C₂×C₄×D₄₃	1	2	yes	—
88	C₂²	—	2	2	no	—
89	C₂²	C₄×C₄₃⋊C₈	1	2	yes	—
90	C₂²	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	C₄×C₄₃⋊C₈	1	2	yes	—
93	C₄	#13063265	1	4	yes	direct product factor
94	C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
95	C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
98	C₂	C₂×#13063265	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063265

C₂

yes

maximal

#14582675

C₂

yes

maximal, complemented

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

#13063265

C₄

yes

direct product factor

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₂²×C₈×C₄₃

C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₈

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₈

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₈

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄₃⋊C₁₆

C₂×C₄

yes

complemented

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₄²

yes

—

C₈×C₄₃

C₂×C₈

yes

—

C₈×C₄₃

C₂×C₈

yes

—

C₈×C₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×C₈

yes

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×C₈

yes

—

C₄×C₄₃

M₃₂

yes

complemented

C₄×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

C₂²×C₈

yes

characteristic

C₄×M₃₂

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×C₄₃

C₂×M₃₂

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

D₄₃

yes

characteristic

#346

—

C₄×C₁₆

—

C₄₃

C₄×M₃₂

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄²

Dic₄₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄×C₈

Dic₄₃

yes

characteristic

C₄×C₈

Dic₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

C₄₃⋊C₈

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₄₃⋊C₈

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

C₄₃⋊C₈

yes

—

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₁₆

—

C₂³

C₂×C₄₃⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

characteristic

C₂×C₄

C₂×C₄₃⋊C₈

yes

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

—

C₂×C₄

C₄×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

C₂×C₄₃⋊C₈

yes

—

C₈

C₂×C₄₃⋊C₈

yes

—

C₈

C₄×Dic₄₃

yes

—

C₈

C₂×C₄×D₄₃

yes

—

C₂²

—

C₂²

C₄×C₄₃⋊C₈

yes

—

C₂²

C₂²×C₄₃⋊C₈

yes

characteristic

C₄

—

C₄

C₄×C₄₃⋊C₈

yes

—

C₄

#13063265

yes

direct product factor

C₄

C₂×C₄×Dic₄₃

yes

characteristic

C₄

C₂²×C₄₃⋊C₈

yes

characteristic

C₂

—

C₂

C₂×C₄×C₄₃⋊C₈

yes

characteristic

C₂

C₂×#13063265

yes

—

	subgroup	G/H
center	C₄×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×C₈
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	C₄×M₃₂
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₄×C₈

C₂×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂²×C₄₃

C₂²×C₈

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

C₄×M₃₂

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14582675	C₂	semidirect
3. C₄×C₄₃⋊C₁₆	C₂	semidirect
5. #13063265	C₄	direct (N × H)
25. C₄₃⋊C₁₆	C₂×C₄	semidirect
43. C₄×C₄₃	M₃₂	semidirect
54. C₄₃	C₄×M₃₂	semidirect
93. C₄	#13063265	direct (N × H)

H ≅ G/N

type

2. #14582675

C₂

semidirect

3. C₄×C₄₃⋊C₁₆

C₂

semidirect

5. #13063265

C₄

direct (N × H)

25. C₄₃⋊C₁₆

C₂×C₄

semidirect

43. C₄×C₄₃

M₃₂

semidirect

54. C₄₃

C₄×M₃₂

semidirect

93. C₄

#13063265

direct (N × H)

Subgroups — C₄×#13063265 #19136189

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13063265 #19136189

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063265 #19136189