Subgroups — #42117888

Order 27488.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28351702	C₂	1	4	yes	maximal, complemented
2	#28351701	C₂	1	6	yes	maximal, complemented
3	Q₈×D₈₅₉	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×C₈₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₇₁₈	C₂²	1	6	yes	—
6	D₃₄₃₆	C₂²	1	6	yes	—
7	C₂²⋊D₈₅₉	C₂²	1	4	yes	—
8	C₄×D₈₅₉	C₂²	1	12	yes	—
9	Q₈×C₈₅₉	C₂²	1	4	yes	—
10	C₂×C₄×C₈₅₉	C₂²	1	3	yes	—
11	C₂²×C₈₅₉	C₂³	1	1	yes	characteristic
12	C₂×D₈₅₉	C₂³	1	4	yes	—
13	C₄×C₈₅₉	C₂³	1	6	yes	—
14	Dic₈₅₉	C₂³	1	4	yes	—
15	C₂×C₈₅₉	—	2	1	no	—
16	C₂×C₈₅₉	C₂⁴	1	1	yes	characteristic
17	D₈₅₉	—	2	4	no	—
18	C₈₅₉	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
19	2₋¹⁺⁴	—	859	1	no	maximal, Sylow
20	#41	—	859	4	no	—
21	#41	—	859	6	no	—
22	C₂×Q₈	—	859	4	no	—
23	C₂×Q₈	D₈₅₉	1	1	yes	characteristic, complemented
24	Q₈	—	859	6	no	—
25	Q₈	C₂×D₈₅₉	1	4	yes	—
26	D₄	—	859	4	no	—
27	D₄	—	859	6	no	—
28	C₂×C₄	—	859	12	no	—
29	C₂×C₄	C₂×D₈₅₉	1	3	yes	—
30	C₂²	—	859	4	no	—
31	C₂²	C₂²×D₈₅₉	1	1	yes	characteristic
32	C₄	—	859	4	no	—
33	C₄	C₂²×D₈₅₉	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	1718	4	no	—
36	C₂	C₂³×D₈₅₉	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.