Subgroups — #22580790

Order 8896.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₂₂₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₃₂×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁₁₂	—	2	1	no	—
5	Q₁₆×C₁₃₉	—	2	1	no	—
6	C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
7	D₅₅₆	—	4	1	no	—
8	Q₈×C₁₃₉	—	4	1	no	—
9	C₈×C₁₃₉	D₄	1	1	yes	characteristic
10	C₂×D₁₃₉	—	8	1	no	—
11	C₄×C₁₃₉	—	8	1	no	—
12	C₄×C₁₃₉	D₈	1	1	yes	characteristic
13	C₂×C₁₃₉	D₁₆	1	1	yes	characteristic
14	D₁₃₉	—	16	1	no	—
15	C₁₃₉	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	139	1	no	maximal, Sylow
17	Q₃₂	D₁₃₉	1	1	yes	characteristic, complemented
18	D₁₆	—	139	1	no	—
19	C₃₂	—	139	1	no	—
20	Q₁₆	—	2	1	no	—
21	D₈	—	278	1	no	—
22	C₁₆	C₂×D₁₃₉	1	1	yes	characteristic
23	Q₈	—	4	1	no	—
24	D₄	—	556	1	no	—
25	C₈	C₂²⋊D₁₃₉	1	1	yes	characteristic
26	C₂²	—	1112	1	no	—
27	C₄	—	8	1	no	—
28	C₄	#14555770	1	1	yes	characteristic
29	C₂	—	2224	1	no	—
30	C₂	#17984783	1	1	yes	characteristic

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