Subgroups — #22586544

Order 9088.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985829	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
3	#14556064	—	2	2	no	—
4	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₇₁	C₄	1	2	yes	—
6	#11765849	—	4	2	no	—
7	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
8	C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₇₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
11	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₇₁	Q₁₆	1	1	yes	characteristic
13	C₇₁⋊C₈	—	8	2	no	—
14	C₂²×C₇₁	Q₃₂	1	1	yes	characteristic
15	C₄×C₇₁	#107	1	1	yes	characteristic
16	C₄×C₇₁	D₁₆	1	1	yes	characteristic
17	C₂×C₇₁	—	2	1	no	—
18	C₂×C₇₁	#366	1	1	yes	characteristic
19	#1425	—	71	1	no	maximal, Sylow
20	C₇₁	#1425	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₂	D₇₁	1	1	yes	characteristic
22	#368	—	71	2	no	—
23	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
24	#108	—	142	2	no	—
25	C₃₂	Dic₇₁	1	2	yes	—
26	M₁₆	—	284	2	no	—
27	C₂×C₈	D₂₈₄	1	1	yes	characteristic
28	C₁₆	Dic₁₄₂	1	1	yes	characteristic
29	C₁₆	C₂×Dic₇₁	1	1	yes	characteristic
30	C₂×C₄	D₅₆₈	1	1	yes	characteristic
31	C₈	—	568	2	no	—
32	C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
33	C₈	Dic₂₈₄	1	1	yes	characteristic
34	C₂²	Dic₅₆₈	1	1	yes	characteristic
35	C₄	#14556062	1	1	yes	characteristic
36	C₄	D₁₁₃₆	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#17985825	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₇₁	#1425	semidirect