Subgroups — C₂×Dic₂₈₄₈ #36475478

Order 22784.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₂₄	C₂	1	2	yes	maximal
2	Dic₂₈₄₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₁₂	—	2	2	no	—
5	Dic₁₄₂₄	—	2	2	no	—
6	Dic₁₄₂₄	C₂²	1	4	yes	—
7	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
8	C₆₄×C₈₉	C₂²	1	2	yes	—
9	C₂×Dic₃₅₆	—	4	2	no	—
10	Dic₇₁₂	—	2	4	no	—
11	Dic₇₁₂	—	4	2	no	—
12	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
13	C₃₂×C₈₉	D₄	1	1	yes	characteristic
14	C₃₂×C₈₉	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₇₈	—	8	2	no	—
16	Dic₃₅₆	—	4	4	no	—
17	Dic₃₅₆	—	8	2	no	—
18	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
19	C₁₆×C₈₉	D₈	1	1	yes	characteristic
20	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
22	C₂×Dic₈₉	—	16	2	no	—
23	Dic₁₇₈	—	8	4	no	—
24	Dic₁₇₈	—	16	2	no	—
25	C₈×C₈₉	D₁₆	1	1	yes	characteristic
26	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
27	C₂²×C₈₉	D₃₂	1	1	yes	characteristic
28	C₄×C₈₉	D₃₂	1	1	yes	characteristic
29	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
30	Dic₈₉	—	16	4	no	—
31	C₂×Q₁₂₈	—	89	1	no	maximal, Sylow
32	C₂×C₈₉	Q₁₂₈	1	2	yes	complemented
33	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
34	C₂×Q₆₄	—	89	2	no	—
35	Q₁₂₈	—	89	4	no	—
36	C₂×C₆₄	D₈₉	1	1	yes	characteristic
37	C₈₉	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₃₂	—	178	2	no	—
39	Q₆₄	—	89	4	no	—
40	Q₆₄	—	178	2	no	—
41	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
42	C₆₄	C₂×D₈₉	1	2	yes	—
43	C₂×Q₁₆	—	356	2	no	—
44	Q₃₂	—	356	2	no	—
45	Q₃₂	—	178	4	no	—
46	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
47	C₃₂	D₃₅₆	1	1	yes	characteristic
48	C₃₂	C₂²×D₈₉	1	1	yes	characteristic
49	C₂×Q₈	—	712	2	no	—
50	Q₁₆	—	356	4	no	—
51	Q₁₆	—	712	2	no	—
52	C₂×C₈	D₇₁₂	1	1	yes	characteristic
53	C₁₆	D₇₁₂	1	1	yes	characteristic
54	C₁₆	C₂×D₃₅₆	1	1	yes	characteristic
55	Q₈	—	1424	2	no	—
56	Q₈	—	712	4	no	—
57	C₂×C₄	—	1424	2	no	—
58	C₂×C₄	D₁₄₂₄	1	1	yes	characteristic
59	C₈	D₁₄₂₄	1	1	yes	characteristic
60	C₈	C₂×D₇₁₂	1	1	yes	characteristic
61	C₂²	D₂₈₄₈	1	1	yes	characteristic
62	C₄	—	1424	4	no	—
63	C₄	D₂₈₄₈	1	1	yes	characteristic
64	C₄	C₂×D₁₄₂₄	1	1	yes	characteristic
65	C₂	Dic₂₈₄₈	1	2	yes	direct product factor
66	C₂	C₂×D₂₈₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₈₄₈
commutator, cosocle	C₃₂×C₈₉	C₂³
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₂×C₆₄×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	D₃₂
hypercenter	C₂×C₆₄	D₈₉
hypocenter	C₈₉	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₂₈₄₈	C₂	direct (N × H)
32. C₂×C₈₉	Q₁₂₈	semidirect
37. C₈₉	C₂×Q₁₂₈	semidirect
65. C₂	Dic₂₈₄₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₂₄	2
Dic₂₈₄₈	2
C₂×C₆₄×C₈₉	2
C₂×Q₁₂₈	89

Subgroups — C2×Dic2848 #36475478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₈₄₈ #36475478