Subgroups — #31774314

Order 17344.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22576100	C₂	1	3	yes	maximal, complemented
2	C₂×C₂₇₁⋊C₁₆	C₂	1	3	yes	maximal, complemented
3	#131×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
5	C₂₇₁⋊C₁₆	C₂²	1	3	yes	—
6	#41×C₂₇₁	C₄	1	1	yes	characteristic
7	M₁₆×C₂₇₁	C₄	1	3	yes	—
8	C₂×C₈×C₂₇₁	C₂²	1	3	yes	—
9	Q₈×C₂₇₁	C₈	1	1	yes	characteristic
10	D₄×C₂₇₁	C₈	1	3	yes	—
11	C₂×C₄×C₂₇₁	C₂×C₄	1	3	yes	—
12	C₈×C₂₇₁	C₂×C₄	1	3	yes	—
13	C₈×C₂₇₁	C₂³	1	1	yes	characteristic
14	C₂²×C₂₇₁	C₂×C₈	1	3	yes	—
15	C₄×C₂₇₁	C₂×C₈	1	3	yes	—
16	C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₂₇₁	—	2	3	no	—
18	C₂×C₂₇₁	C₂²×C₈	1	1	yes	characteristic
19	C₂₇₁	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	271	1	no	maximal, Sylow
21	#131	D₂₇₁	1	1	yes	characteristic
22	M₃₂	—	271	3	no	—
23	C₂×C₁₆	—	271	3	no	—
24	#41	Dic₂₇₁	1	1	yes	characteristic
25	M₁₆	Dic₂₇₁	1	3	yes	—
26	C₂×C₈	C₂×D₂₇₁	1	3	yes	—
27	C₁₆	—	271	1	no	—
28	C₁₆	—	271	3	no	—
29	Q₈	C₂₇₁⋊C₈	1	1	yes	characteristic
30	D₄	C₂₇₁⋊C₈	1	3	yes	—
31	C₂×C₄	C₂×Dic₂₇₁	1	3	yes	—
32	C₈	C₂×Dic₂₇₁	1	3	yes	—
33	C₈	C₂²×D₂₇₁	1	1	yes	characteristic
34	C₂²	C₂×C₂₇₁⋊C₈	1	3	yes	—
35	C₄	C₂×C₂₇₁⋊C₈	1	3	yes	—
36	C₄	C₂²×Dic₂₇₁	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×C₂₇₁⋊C₈	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.