Subgroups — #46834574

Order 34688.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₂₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂₇₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₄×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₂₇₁	C₄	1	1	yes	characteristic
5	C₂₇₁⋊C₃₂	C₄	1	1	yes	characteristic
6	C₃₂×C₂₇₁	C₂²	1	1	yes	characteristic
7	C₈×D₂₇₁	C₈	1	1	yes	characteristic
8	C₂₇₁⋊C₁₆	C₈	1	1	yes	characteristic
9	C₁₆×C₂₇₁	C₂×C₄	1	1	yes	characteristic
10	C₄×D₂₇₁	C₁₆	1	1	yes	characteristic
11	C₂₇₁⋊C₈	C₁₆	1	1	yes	characteristic
12	C₈×C₂₇₁	C₂×C₈	1	1	yes	characteristic
13	C₂×D₂₇₁	C₃₂	1	1	yes	characteristic
14	C₄×C₂₇₁	C₂×C₁₆	1	1	yes	characteristic
15	Dic₂₇₁	C₃₂	1	1	yes	characteristic
16	C₂×C₂₇₁	C₂×C₃₂	1	1	yes	characteristic
17	D₂₇₁	—	2	1	no	—
18	C₂₇₁	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	M₁₂₈	—	271	1	no	maximal, Sylow
20	C₂×C₃₂	—	271	1	no	—
21	C₆₄	—	271	1	no	—
22	C₆₄	D₂₇₁	1	1	yes	characteristic, complemented
23	C₂×C₁₆	—	271	1	no	—
24	C₃₂	—	271	1	no	—
25	C₃₂	C₂×D₂₇₁	1	1	yes	characteristic
26	C₂×C₈	—	271	1	no	—
27	C₁₆	—	271	1	no	—
28	C₁₆	C₄×D₂₇₁	1	1	yes	characteristic
29	C₂×C₄	—	271	1	no	—
30	C₈	—	271	1	no	—
31	C₈	C₈×D₂₇₁	1	1	yes	characteristic
32	C₂²	—	271	1	no	—
33	C₄	—	271	1	no	—
34	C₄	C₁₆×D₂₇₁	1	1	yes	characteristic
35	C₂	—	542	1	no	—
36	C₂	C₃₂×D₂₇₁	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.