Subgroups — #46834568

Order 34688.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31773727	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₇₁	C₂	1	1	yes	maximal, characteristic
3	#22576096	—	2	2	no	—
4	C₂×C₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₇₁	C₄	1	2	yes	—
6	#16864638	—	4	2	no	—
7	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
8	C₁₆×C₂₇₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₇₁	Q₈	1	1	yes	characteristic
10	C₂₇₁⋊C₈	—	8	2	no	—
11	C₂×C₄×C₂₇₁	D₈	1	1	yes	characteristic
12	C₈×C₂₇₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₇₁	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₇₁	Q₃₂	1	1	yes	characteristic
15	C₄×C₂₇₁	#107	1	1	yes	characteristic
16	C₄×C₂₇₁	D₁₆	1	1	yes	characteristic
17	C₂×C₂₇₁	—	2	1	no	—
18	C₂×C₂₇₁	#366	1	1	yes	characteristic
19	C₂₇₁	#1425	1	1	yes	characteristic, complemented, Sylow
20	#1425	—	271	1	no	maximal, Sylow
21	C₂×C₃₂	D₂₇₁	1	1	yes	characteristic
22	#368	—	271	2	no	—
23	C₂×C₁₆	C₂×D₂₇₁	1	1	yes	characteristic
24	#108	—	542	2	no	—
25	C₃₂	Dic₂₇₁	1	2	yes	—
26	M₁₆	—	1084	2	no	—
27	C₂×C₈	D₁₀₈₄	1	1	yes	characteristic
28	C₁₆	C₂×Dic₂₇₁	1	1	yes	characteristic
29	C₁₆	Dic₅₄₂	1	1	yes	characteristic
30	C₂×C₄	D₂₁₆₈	1	1	yes	characteristic
31	C₈	—	2168	2	no	—
32	C₈	C₄⋊Dic₂₇₁	1	1	yes	characteristic
33	C₈	Dic₁₀₈₄	1	1	yes	characteristic
34	C₂²	Dic₂₁₆₈	1	1	yes	characteristic
35	C₄	#22576094	1	1	yes	characteristic
36	C₄	D₄₃₃₆	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#31773723	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₂₇₁	#1425	semidirect

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