Subgroups — C₈²×Dic₄₃ #24985942

Order 11008.

750 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×Dic₄₃	C₂	1	3	yes	maximal
2	C₂×C₈×C₄₃⋊C₈	C₂	1	3	yes	maximal
3	C₂×C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄₃⋊C₈	C₂²	1	3	yes	—
5	C₂×C₈×Dic₄₃	C₄	1	12	yes	—
6	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
7	C₈×C₄₃⋊C₈	C₄	1	12	yes	complemented
8	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	—
9	C₈²×C₄₃	C₄	1	4	yes	complemented
10	C₂²×C₄₃⋊C₈	C₂×C₄	1	6	yes	—
11	C₂×C₄×Dic₄₃	C₂×C₄	1	6	yes	—
12	C₄×C₄₃⋊C₈	C₂×C₄	1	12	yes	—
13	C₈×Dic₄₃	C₈	1	48	yes	direct product factor
14	C₂²×C₈×C₄₃	C₂×C₄	1	6	yes	—
15	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₄₃	C₂×C₄	1	6	yes	—
17	C₄×C₈×C₄₃	C₂×C₄	1	6	yes	—
18	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
19	C₂²×Dic₄₃	C₄²	1	4	yes	—
20	C₂×C₈×C₄₃	C₄²	1	12	yes	—
21	C₂×C₈×C₄₃	C₂×C₈	1	24	yes	—
22	C₄²×C₄₃	C₂²×C₄	1	3	yes	—
23	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×Dic₄₃	C₂×C₈	1	24	yes	—
25	C₂×C₄₃⋊C₈	C₄²	1	12	yes	—
26	C₂×C₄₃⋊C₈	C₂×C₈	1	24	yes	—
27	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×C₄²	1	3	yes	—
29	C₂×C₄×C₄₃	C₂×C₄²	1	3	yes	—
30	C₂×C₄×C₄₃	C₂²×C₈	1	12	yes	—
31	C₂×Dic₄₃	C₄×C₈	1	24	yes	—
32	C₈×C₄₃	C₄×C₈	1	24	yes	complemented
33	C₄₃⋊C₈	C₄×C₈	1	24	yes	complemented
34	C₄×C₈²	—	43	1	no	maximal, Sylow
35	C₂²×C₄₃	C₄³	1	1	yes	characteristic
36	C₂²×C₄₃	C₂×C₄×C₈	1	6	yes	—
37	C₄×C₄₃	C₂×C₄×C₈	1	6	yes	—
38	C₄×C₄₃	C₂×C₄×C₈	1	6	yes	—
39	Dic₄₃	C₈²	1	16	yes	direct product factor
40	C₄²×C₈	—	43	3	no	—
41	C₂×C₈²	—	43	3	no	—
42	C₂×C₈²	D₄₃	1	1	yes	characteristic
43	C₂×C₄₃	C₂×C₈²	1	4	yes	—
44	C₂×C₄₃	C₄²×C₈	1	3	yes	—
45	C₂×C₄×C₈	—	43	12	no	—
46	C₂×C₄×C₈	—	43	3	no	—
47	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
48	C₄³	—	43	1	no	—
49	C₈²	—	43	12	no	—
50	C₈²	Dic₄₃	1	4	yes	direct product factor
51	C₄₃	C₄×C₈²	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₈	—	43	6	no	—
53	C₂²×C₈	C₄×D₄₃	1	6	yes	—
54	C₂×C₄²	—	43	6	no	—
55	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
56	C₄×C₈	—	43	48	no	—
57	C₄×C₈	—	43	12	no	—
58	C₄×C₈	C₄×D₄₃	1	6	yes	—
59	C₄×C₈	C₂×Dic₄₃	1	6	yes	—
60	C₂²×C₄	—	43	4	no	—
61	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
62	C₂×C₈	—	43	12	no	—
63	C₂×C₈	—	43	24	no	—
64	C₂×C₈	C₈×D₄₃	1	24	yes	—
65	C₂×C₈	C₄×Dic₄₃	1	12	yes	—
66	C₄²	—	43	24	no	—
67	C₄²	C₂×C₄×D₄₃	1	3	yes	—
68	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
69	C₂³	C₄²×D₄₃	1	1	yes	characteristic
70	C₂×C₄	—	43	24	no	—
71	C₂×C₄	C₄²×D₄₃	1	3	yes	—
72	C₂×C₄	C₂×C₄×Dic₄₃	1	3	yes	—
73	C₂×C₄	C₂×C₈×D₄₃	1	12	yes	—
74	C₈	—	43	24	no	—
75	C₈	C₈×Dic₄₃	1	24	yes	direct product factor
76	C₂²	C₄²×Dic₄₃	1	1	yes	characteristic
77	C₂²	C₄×C₈×D₄₃	1	6	yes	—
78	C₄	—	43	16	no	—
79	C₄	C₄×C₈×D₄₃	1	6	yes	—
80	C₄	C₂×C₈×Dic₄₃	1	6	yes	—
81	C₂	C₈²×D₄₃	1	4	yes	—
82	C₂	C₄×C₈×Dic₄₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₈²	D₄₃
commutator, hypocenter	C₄₃	C₄×C₈²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₈²×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₈²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. C₈×C₄₃⋊C₈	C₄	semidirect
9. C₈²×C₄₃	C₄	semidirect
13. C₈×Dic₄₃	C₈	direct (N × H)
32. C₈×C₄₃	C₄×C₈	semidirect
33. C₄₃⋊C₈	C₄×C₈	semidirect
39. Dic₄₃	C₈²	direct (N × H)
50. C₈²	Dic₄₃	direct (N × H)
51. C₄₃	C₄×C₈²	semidirect
75. C₈	C₈×Dic₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₈×Dic₄₃	2
C₂×C₈×C₄₃⋊C₈	2
C₂×C₈²×C₄₃	2
C₄×C₈²	43

Subgroups — C82×Dic43 #24985942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈²×Dic₄₃ #24985942