Subgroups — C₂×Dic₄₄₉₆ #49097608

Order 35968.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂₄₈	C₂	1	2	yes	maximal
2	Dic₄₄₉₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₂₄	—	2	2	no	—
5	Dic₂₂₄₈	—	2	2	no	—
6	Dic₂₂₄₈	C₂²	1	4	yes	—
7	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₈₁	C₂²	1	2	yes	—
9	C₂×Dic₅₆₂	—	4	2	no	—
10	Dic₁₁₂₄	—	2	4	no	—
11	Dic₁₁₂₄	—	4	2	no	—
12	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
13	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
14	C₁₆×C₂₈₁	C₂³	1	1	yes	characteristic
15	Dic₅₆₂	—	4	4	no	—
16	Dic₅₆₂	—	8	2	no	—
17	C₂×Dic₂₈₁	—	8	2	no	—
18	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
19	C₈×C₂₈₁	D₈	1	1	yes	characteristic
20	C₈×C₂₈₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₂₈₁	D₁₆	1	1	yes	characteristic
22	C₄×C₂₈₁	D₁₆	1	1	yes	characteristic
23	C₄×C₂₈₁	C₂×D₈	1	1	yes	characteristic
24	Dic₂₈₁	—	8	4	no	—
25	C₂×C₂₈₁	Q₆₄	1	2	yes	complemented
26	C₂×C₂₈₁	C₂×D₁₆	1	1	yes	characteristic
27	C₂₈₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₆₄	—	281	1	no	maximal, Sylow
29	C₂×Q₃₂	—	281	2	no	—
30	Q₆₄	—	281	4	no	—
31	C₂×C₃₂	D₂₈₁	1	1	yes	characteristic
32	C₂×Q₁₆	—	562	2	no	—
33	Q₃₂	—	281	4	no	—
34	Q₃₂	—	562	2	no	—
35	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
36	C₃₂	C₂×D₂₈₁	1	2	yes	—
37	C₂×Q₈	—	1124	2	no	—
38	Q₁₆	—	562	4	no	—
39	Q₁₆	—	1124	2	no	—
40	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
41	C₁₆	D₁₁₂₄	1	1	yes	characteristic
42	C₁₆	C₂²×D₂₈₁	1	1	yes	characteristic
43	Q₈	—	1124	4	no	—
44	Q₈	—	2248	2	no	—
45	C₂×C₄	—	2248	2	no	—
46	C₂×C₄	D₂₂₄₈	1	1	yes	characteristic
47	C₈	D₂₂₄₈	1	1	yes	characteristic
48	C₈	C₂×D₁₁₂₄	1	1	yes	characteristic
49	C₂²	D₄₄₉₆	1	1	yes	characteristic
50	C₄	—	2248	4	no	—
51	C₄	D₄₄₉₆	1	1	yes	characteristic
52	C₄	C₂×D₂₂₄₈	1	1	yes	characteristic
53	C₂	Dic₄₄₉₆	1	2	yes	direct product factor
54	C₂	C₂×D₄₄₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₄₉₆
commutator, cosocle	C₁₆×C₂₈₁	C₂³
Frattini	C₁₆	C₂²×D₂₈₁
Fitting	C₂×C₃₂×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	D₁₆
hypercenter	C₂×C₃₂	D₂₈₁
hypocenter	C₂₈₁	C₂×Q₆₄
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₄₄₉₆	C₂	direct (N × H)
25. C₂×C₂₈₁	Q₆₄	semidirect
27. C₂₈₁	C₂×Q₆₄	semidirect
53. C₂	Dic₄₄₉₆	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×Dic₂₂₄₈	2
Dic₄₄₉₆	2
C₂×C₃₂×C₂₈₁	2
C₂×Q₆₄	281

Subgroups — C2×Dic4496 #49097608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₄₄₉₆ #49097608