Subgroups — C₂×Dic₆₈₈ #19136900

Order 5504.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₄₄	C₂	1	2	yes	maximal
2	Dic₆₈₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₂	—	2	2	no	—
5	Dic₃₄₄	—	2	2	no	—
6	Dic₃₄₄	C₂²	1	4	yes	—
7	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₄₃	C₂²	1	2	yes	—
9	C₂×Dic₈₆	—	4	2	no	—
10	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
11	Dic₁₇₂	—	2	4	no	—
12	Dic₁₇₂	—	4	2	no	—
13	C₁₆×C₄₃	D₄	1	1	yes	characteristic
14	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
16	C₂×Dic₄₃	—	8	2	no	—
17	Dic₈₆	—	4	4	no	—
18	Dic₈₆	—	8	2	no	—
19	C₈×C₄₃	D₈	1	1	yes	characteristic
20	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
22	C₄×C₄₃	D₁₆	1	1	yes	characteristic
23	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
24	Dic₄₃	—	8	4	no	—
25	C₂×Q₆₄	—	43	1	no	maximal, Sylow
26	C₂×C₄₃	Q₆₄	1	2	yes	complemented
27	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
28	C₂×Q₃₂	—	43	2	no	—
29	Q₆₄	—	43	4	no	—
30	C₂×C₃₂	D₄₃	1	1	yes	characteristic
31	C₄₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	86	2	no	—
33	Q₃₂	—	43	4	no	—
34	Q₃₂	—	86	2	no	—
35	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
36	C₃₂	C₂×D₄₃	1	2	yes	—
37	C₂×Q₈	—	172	2	no	—
38	Q₁₆	—	86	4	no	—
39	Q₁₆	—	172	2	no	—
40	C₂×C₈	D₁₇₂	1	1	yes	characteristic
41	C₁₆	D₁₇₂	1	1	yes	characteristic
42	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
43	Q₈	—	344	2	no	—
44	Q₈	—	172	4	no	—
45	C₂×C₄	—	344	2	no	—
46	C₂×C₄	D₃₄₄	1	1	yes	characteristic
47	C₈	D₃₄₄	1	1	yes	characteristic
48	C₈	C₂×D₁₇₂	1	1	yes	characteristic
49	C₂²	D₆₈₈	1	1	yes	characteristic
50	C₄	—	344	4	no	—
51	C₄	D₆₈₈	1	1	yes	characteristic
52	C₄	C₂×D₃₄₄	1	1	yes	characteristic
53	C₂	Dic₆₈₈	1	2	yes	direct product factor
54	C₂	C₂×D₆₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₆₈₈
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	C₂×Q₆₄
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
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. Dic₆₈₈	C₂	direct (N × H)
26. C₂×C₄₃	Q₆₄	semidirect
31. C₄₃	C₂×Q₆₄	semidirect
53. C₂	Dic₆₈₈	direct (N × H)

Subgroups — C2×Dic688 #19136900

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₆₈₈ #19136900