Subgroups — C₂×Dic₃₀₅₆ #37574825

Order 24448.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₂₈	C₂	1	2	yes	maximal
2	Dic₃₀₅₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₆₄	—	2	2	no	—
5	Dic₁₅₂₈	—	2	2	no	—
6	Dic₁₅₂₈	C₂²	1	4	yes	—
7	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₉₁	C₂²	1	2	yes	—
9	C₂×Dic₃₈₂	—	4	2	no	—
10	Dic₇₆₄	—	2	4	no	—
11	Dic₇₆₄	—	4	2	no	—
12	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
13	C₁₆×C₁₉₁	D₄	1	1	yes	characteristic
14	C₁₆×C₁₉₁	C₂³	1	1	yes	characteristic
15	Dic₃₈₂	—	4	4	no	—
16	Dic₃₈₂	—	8	2	no	—
17	C₂×Dic₁₉₁	—	8	2	no	—
18	C₂×C₄×C₁₉₁	D₈	1	1	yes	characteristic
19	C₈×C₁₉₁	D₈	1	1	yes	characteristic
20	C₈×C₁₉₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₉₁	D₁₆	1	1	yes	characteristic
22	C₄×C₁₉₁	D₁₆	1	1	yes	characteristic
23	C₄×C₁₉₁	C₂×D₈	1	1	yes	characteristic
24	Dic₁₉₁	—	8	4	no	—
25	C₂×C₁₉₁	Q₆₄	1	2	yes	complemented
26	C₂×C₁₉₁	C₂×D₁₆	1	1	yes	characteristic
27	C₁₉₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₆₄	—	191	1	no	maximal, Sylow
29	C₂×Q₃₂	—	191	2	no	—
30	Q₆₄	—	191	4	no	—
31	C₂×C₃₂	D₁₉₁	1	1	yes	characteristic
32	C₂×Q₁₆	—	382	2	no	—
33	Q₃₂	—	382	2	no	—
34	Q₃₂	—	191	4	no	—
35	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
36	C₃₂	C₂×D₁₉₁	1	2	yes	—
37	C₂×Q₈	—	764	2	no	—
38	Q₁₆	—	382	4	no	—
39	Q₁₆	—	764	2	no	—
40	C₂×C₈	D₇₆₄	1	1	yes	characteristic
41	C₁₆	D₇₆₄	1	1	yes	characteristic
42	C₁₆	C₂²×D₁₉₁	1	1	yes	characteristic
43	Q₈	—	1528	2	no	—
44	Q₈	—	764	4	no	—
45	C₂×C₄	—	1528	2	no	—
46	C₂×C₄	D₁₅₂₈	1	1	yes	characteristic
47	C₈	D₁₅₂₈	1	1	yes	characteristic
48	C₈	C₂×D₇₆₄	1	1	yes	characteristic
49	C₂²	D₃₀₅₆	1	1	yes	characteristic
50	C₄	—	1528	4	no	—
51	C₄	D₃₀₅₆	1	1	yes	characteristic
52	C₄	C₂×D₁₅₂₈	1	1	yes	characteristic
53	C₂	Dic₃₀₅₆	1	2	yes	direct product factor
54	C₂	C₂×D₃₀₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₀₅₆
commutator, cosocle	C₁₆×C₁₉₁	C₂³
Frattini	C₁₆	C₂²×D₁₉₁
Fitting	C₂×C₃₂×C₁₉₁	C₂
socle, prime radical	C₂²×C₁₉₁	D₁₆
hypercenter	C₂×C₃₂	D₁₉₁
hypocenter	C₁₉₁	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₉₁ ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
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. Dic₃₀₅₆	C₂	direct (N × H)
25. C₂×C₁₉₁	Q₆₄	semidirect
27. C₁₉₁	C₂×Q₆₄	semidirect
53. C₂	Dic₃₀₅₆	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×Dic₁₅₂₈	2
Dic₃₀₅₆	2
C₂×C₃₂×C₁₉₁	2
C₂×Q₆₄	191

Subgroups — C2×Dic3056 #37574825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃₀₅₆ #37574825