Subgroups — C₂×Dic₁₂₆₄ #23765705

Order 10112.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₃₂	C₂	1	2	yes	maximal
2	Dic₁₂₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁₆	—	2	2	no	—
5	Dic₆₃₂	—	2	2	no	—
6	Dic₆₃₂	C₂²	1	4	yes	—
7	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
8	C₃₂×C₇₉	C₂²	1	2	yes	—
9	C₂×Dic₁₅₈	—	4	2	no	—
10	Dic₃₁₆	—	2	4	no	—
11	Dic₃₁₆	—	4	2	no	—
12	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
13	C₁₆×C₇₉	D₄	1	1	yes	characteristic
14	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
16	C₂×Dic₇₉	—	8	2	no	—
17	Dic₁₅₈	—	4	4	no	—
18	Dic₁₅₈	—	8	2	no	—
19	C₈×C₇₉	D₈	1	1	yes	characteristic
20	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
22	C₄×C₇₉	D₁₆	1	1	yes	characteristic
23	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
24	Dic₇₉	—	8	4	no	—
25	C₂×C₇₉	Q₆₄	1	2	yes	complemented
26	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
27	C₂×Q₆₄	—	79	1	no	maximal, Sylow
28	C₇₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₃₂	—	79	2	no	—
30	Q₆₄	—	79	4	no	—
31	C₂×C₃₂	D₇₉	1	1	yes	characteristic
32	C₂×Q₁₆	—	158	2	no	—
33	Q₃₂	—	79	4	no	—
34	Q₃₂	—	158	2	no	—
35	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
36	C₃₂	C₂×D₇₉	1	2	yes	—
37	C₂×Q₈	—	316	2	no	—
38	Q₁₆	—	316	2	no	—
39	Q₁₆	—	158	4	no	—
40	C₂×C₈	D₃₁₆	1	1	yes	characteristic
41	C₁₆	D₃₁₆	1	1	yes	characteristic
42	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
43	Q₈	—	316	4	no	—
44	Q₈	—	632	2	no	—
45	C₂×C₄	—	632	2	no	—
46	C₂×C₄	D₆₃₂	1	1	yes	characteristic
47	C₈	D₆₃₂	1	1	yes	characteristic
48	C₈	C₂×D₃₁₆	1	1	yes	characteristic
49	C₂²	D₁₂₆₄	1	1	yes	characteristic
50	C₄	—	632	4	no	—
51	C₄	D₁₂₆₄	1	1	yes	characteristic
52	C₄	C₂×D₆₃₂	1	1	yes	characteristic
53	C₂	Dic₁₂₆₄	1	2	yes	direct product factor
54	C₂	C₂×D₁₂₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₂₆₄
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	C₂×C₃₂×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	D₁₆
hypercenter	C₂×C₃₂	D₇₉
hypocenter	C₇₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
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. Dic₁₂₆₄	C₂	direct (N × H)
25. C₂×C₇₉	Q₆₄	semidirect
28. C₇₉	C₂×Q₆₄	semidirect
53. C₂	Dic₁₂₆₄	direct (N × H)

Subgroups — C2×Dic1264 #23765705

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₁₂₆₄ #23765705