Subgroups — #19132812

Order 5504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₈₈	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₄₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	Dic₃₄₄	—	2	1	no	—
5	Q₃₂×C₄₃	—	2	1	no	—
6	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	Q₁₆×C₄₃	—	4	1	no	—
8	Dic₁₇₂	—	4	1	no	—
9	C₁₆×C₄₃	D₄	1	1	yes	characteristic
10	Q₈×C₄₃	—	8	1	no	—
11	Dic₈₆	—	8	1	no	—
12	C₈×C₄₃	D₈	1	1	yes	characteristic
13	C₄×C₄₃	—	16	1	no	—
14	C₄×C₄₃	D₁₆	1	1	yes	characteristic
15	Dic₄₃	—	16	1	no	—
16	Q₁₂₈	—	43	1	no	maximal, Sylow
17	C₂×C₄₃	D₃₂	1	1	yes	characteristic
18	Q₆₄	—	43	1	no	—
19	Q₆₄	D₄₃	1	1	yes	characteristic
20	C₆₄	—	43	1	no	—
21	C₄₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	86	1	no	—
24	C₃₂	C₂×D₄₃	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	172	1	no	—
27	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	344	1	no	—
30	C₈	#10621882	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	688	1	no	—
33	C₄	#13063266	1	1	yes	characteristic
34	C₂	#14582734	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₄₃	Q₁₂₈	semidirect