Subgroups — #19142990

Order 5504.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063322	C₂	1	14	yes	maximal, complemented
2	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₇₂	C₂²	1	28	yes	—
4	#13063322	—	2	56	no	—
5	C₂×C₄²×C₄₃	C₂²	1	7	yes	—
6	C₂³×D₄₃	C₂³	1	8	yes	—
7	C₂²×C₄×C₄₃	C₂³	1	7	yes	—
8	C₂×D₁₇₂	—	2	168	no	—
9	C₄²×C₄₃	D₄	1	28	yes	complemented
10	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
11	C₂²×D₄₃	—	2	56	no	—
12	C₂×C₄×C₄₃	C₂×D₄	1	42	yes	—
13	D₁₇₂	—	4	112	no	—
14	C₂²×C₄₃	C₂²×D₄	1	7	yes	—
15	C₂×D₄₃	—	4	56	no	—
16	C₄×C₄₃	#127	1	28	yes	complemented
17	#2867	—	43	1	no	maximal, Sylow
18	C₂×C₄₃	C₂×#127	1	7	yes	—
19	D₄₃	—	8	8	no	—
20	C₂×#127	—	43	14	no	—
21	C₄³	D₄₃	1	1	yes	characteristic, complemented
22	C₄₃	#2867	1	1	yes	characteristic, complemented, Sylow
23	C₂²×D₄	—	43	28	no	—
24	#127	—	86	56	no	—
25	C₂×C₄²	C₂×D₄₃	1	7	yes	—
26	C₂⁴	—	43	8	no	—
27	C₂×D₄	—	86	168	no	—
28	C₂²×C₄	C₂²×D₄₃	1	7	yes	—
29	C₄²	D₁₇₂	1	28	yes	complemented
30	C₂³	—	86	56	no	—
31	C₂³	C₂³×D₄₃	1	1	yes	characteristic
32	D₄	—	172	112	no	—
33	C₂×C₄	C₂×D₁₇₂	1	42	yes	—
34	C₂²	—	172	56	no	—
35	C₂²	C₂²×D₁₇₂	1	7	yes	—
36	C₄	#13063322	1	28	yes	complemented
37	C₂	—	344	8	no	—
38	C₂	C₂×#13063322	1	7	yes	—

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