Subgroups — C₂×Dic₁₀₇₂ #22562514

Order 8576.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₃₆	C₂	1	2	yes	maximal
2	Dic₁₀₇₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₆₈	—	2	2	no	—
5	Dic₅₃₆	—	2	2	no	—
6	Dic₅₃₆	C₂²	1	4	yes	—
7	C₂×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₆₇	C₂²	1	2	yes	—
9	C₂×Dic₁₃₄	—	4	2	no	—
10	Dic₂₆₈	—	2	4	no	—
11	Dic₂₆₈	—	4	2	no	—
12	C₂×C₈×C₆₇	D₄	1	1	yes	characteristic
13	C₁₆×C₆₇	D₄	1	1	yes	characteristic
14	C₁₆×C₆₇	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₆₇	D₈	1	1	yes	characteristic
16	C₂×Dic₆₇	—	8	2	no	—
17	Dic₁₃₄	—	4	4	no	—
18	Dic₁₃₄	—	8	2	no	—
19	C₈×C₆₇	D₈	1	1	yes	characteristic
20	C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₆₇	D₁₆	1	1	yes	characteristic
22	C₄×C₆₇	D₁₆	1	1	yes	characteristic
23	C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
24	Dic₆₇	—	8	4	no	—
25	C₂×C₆₇	Q₆₄	1	2	yes	complemented
26	C₂×C₆₇	C₂×D₁₆	1	1	yes	characteristic
27	C₂×Q₆₄	—	67	1	no	maximal, Sylow
28	C₆₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₃₂	—	67	2	no	—
30	Q₆₄	—	67	4	no	—
31	C₂×C₃₂	D₆₇	1	1	yes	characteristic
32	C₂×Q₁₆	—	134	2	no	—
33	Q₃₂	—	67	4	no	—
34	Q₃₂	—	134	2	no	—
35	C₂×C₁₆	C₂×D₆₇	1	1	yes	characteristic
36	C₃₂	C₂×D₆₇	1	2	yes	—
37	C₂×Q₈	—	268	2	no	—
38	Q₁₆	—	268	2	no	—
39	Q₁₆	—	134	4	no	—
40	C₂×C₈	D₂₆₈	1	1	yes	characteristic
41	C₁₆	D₂₆₈	1	1	yes	characteristic
42	C₁₆	C₂²×D₆₇	1	1	yes	characteristic
43	Q₈	—	268	4	no	—
44	Q₈	—	536	2	no	—
45	C₂×C₄	—	536	2	no	—
46	C₂×C₄	D₅₃₆	1	1	yes	characteristic
47	C₈	D₅₃₆	1	1	yes	characteristic
48	C₈	C₂×D₂₆₈	1	1	yes	characteristic
49	C₂²	D₁₀₇₂	1	1	yes	characteristic
50	C₄	—	536	4	no	—
51	C₄	D₁₀₇₂	1	1	yes	characteristic
52	C₄	C₂×D₅₃₆	1	1	yes	characteristic
53	C₂	Dic₁₀₇₂	1	2	yes	direct product factor
54	C₂	C₂×D₁₀₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₀₇₂
commutator	C₁₆×C₆₇	C₂³
Frattini	C₁₆	C₂²×D₆₇
Fitting	C₂×C₃₂×C₆₇	C₂
socle	C₂²×C₆₇	D₁₆
hypercenter	C₂×C₃₂	D₆₇
hypocenter	C₆₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₆₇ ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
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. Dic₁₀₇₂	C₂	direct (N × H)
25. C₂×C₆₇	Q₆₄	semidirect
28. C₆₇	C₂×Q₆₄	semidirect
53. C₂	Dic₁₀₇₂	direct (N × H)

Subgroups — C2×Dic1072 #22562514

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₁₀₇₂ #22562514