Subgroups — #19132807

Order 5504.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₆₈₈	—	2	1	no	—
5	D₁₆×C₄₃	—	2	1	no	—
6	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	D₈×C₄₃	—	4	1	no	—
8	D₃₄₄	—	4	1	no	—
9	C₁₆×C₄₃	D₄	1	1	yes	characteristic
10	D₄×C₄₃	—	8	1	no	—
11	D₁₇₂	—	8	1	no	—
12	C₈×C₄₃	D₈	1	1	yes	characteristic
13	C₂²×C₄₃	—	16	1	no	—
14	C₂×D₄₃	—	16	1	no	—
15	C₄×C₄₃	D₁₆	1	1	yes	characteristic
16	D₆₄	—	43	1	no	maximal, Sylow
17	C₂×C₄₃	—	32	1	no	—
18	C₂×C₄₃	D₃₂	1	1	yes	characteristic
19	D₄₃	—	32	1	no	—
20	D₃₂	—	43	1	no	—
21	D₃₂	D₄₃	1	1	yes	characteristic, complemented
22	C₆₄	—	43	1	no	—
23	C₄₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
24	D₁₆	—	2	1	no	—
25	D₁₆	—	86	1	no	—
26	C₃₂	C₂×D₄₃	1	1	yes	characteristic
27	D₈	—	4	1	no	—
28	D₈	—	172	1	no	—
29	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
30	D₄	—	8	1	no	—
31	D₄	—	344	1	no	—
32	C₈	#10621882	1	1	yes	characteristic
33	C₂²	—	16	1	no	—
34	C₂²	—	688	1	no	—
35	C₄	#13063266	1	1	yes	characteristic
36	C₂	—	32	1	no	—
37	C₂	—	1376	1	no	—
38	C₂	#14582734	1	1	yes	characteristic

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