Subgroups — #21432491

Order 7552.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273724	C₂	1	14	yes	maximal, complemented
2	C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₂₃₆	C₂²	1	28	yes	—
4	#14273724	—	2	56	no	—
5	C₂×C₄²×C₅₉	C₂²	1	7	yes	—
6	C₂³×D₅₉	C₂³	1	8	yes	—
7	C₂²×C₄×C₅₉	C₂³	1	7	yes	—
8	C₂×D₂₃₆	—	2	168	no	—
9	C₄²×C₅₉	D₄	1	28	yes	complemented
10	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
11	C₂²×D₅₉	—	2	56	no	—
12	C₂×C₄×C₅₉	C₂×D₄	1	42	yes	—
13	D₂₃₆	—	4	112	no	—
14	C₂²×C₅₉	C₂²×D₄	1	7	yes	—
15	C₂×D₅₉	—	4	56	no	—
16	C₄×C₅₉	#127	1	28	yes	complemented
17	#2867	—	59	1	no	maximal, Sylow
18	C₂×C₅₉	C₂×#127	1	7	yes	—
19	D₅₉	—	8	8	no	—
20	C₂×#127	—	59	14	no	—
21	C₄³	D₅₉	1	1	yes	characteristic, complemented
22	C₅₉	#2867	1	1	yes	characteristic, complemented, Sylow
23	C₂²×D₄	—	59	28	no	—
24	#127	—	118	56	no	—
25	C₂×C₄²	C₂×D₅₉	1	7	yes	—
26	C₂⁴	—	59	8	no	—
27	C₂×D₄	—	118	168	no	—
28	C₂²×C₄	C₂²×D₅₉	1	7	yes	—
29	C₄²	D₂₃₆	1	28	yes	complemented
30	C₂³	—	118	56	no	—
31	C₂³	C₂³×D₅₉	1	1	yes	characteristic
32	D₄	—	236	112	no	—
33	C₂×C₄	C₂×D₂₃₆	1	42	yes	—
34	C₂²	—	236	56	no	—
35	C₂²	C₂²×D₂₃₆	1	7	yes	—
36	C₄	#14273724	1	28	yes	complemented
37	C₂	—	472	8	no	—
38	C₂	C₂×#14273724	1	7	yes	—

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