Subgroups — #20241305

Order 6016.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄₇⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₄₇	C₄	1	2	yes	—
5	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₇	C₈	1	4	yes	—
7	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
8	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₄₇⋊C₁₆	C₈	1	8	yes	complemented
10	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
12	C₈×C₄₇	—	2	4	no	—
13	C₈×C₄₇	C₂×C₈	1	4	yes	—
14	C₂²×C₄₇	C₄×C₈	1	1	yes	characteristic
15	C₄×C₄₇	C₄×C₈	1	2	yes	—
16	C₄×C₄₇	M₃₂	1	4	yes	—
17	#1311	—	47	1	no	maximal, Sylow
18	C₂×C₄₇	C₈²	1	1	yes	characteristic
19	C₂×C₄₇	#346	1	2	yes	—
20	C₄×C₁₆	—	47	2	no	—
21	C₈²	D₄₇	1	1	yes	characteristic
22	C₄₇	#1311	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	47	4	no	—
24	C₄×C₈	Dic₄₇	1	2	yes	—
25	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
26	C₂×C₈	C₄₇⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₄₇	1	2	yes	—
28	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
29	C₁₆	—	47	8	no	—
30	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
31	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
32	C₈	—	2	4	no	—
33	C₈	C₈×D₄₇	1	4	yes	—
34	C₂²	C₄×C₄₇⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₄₇	1	2	yes	—
36	C₄	#13093964	1	4	yes	—
37	C₂	C₈×C₄₇⋊C₈	1	1	yes	characteristic
38	C₂	#15688899	1	2	yes	—

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

N	H ≅ G/N	type
9. C₄₇⋊C₁₆	C₈	semidirect
22. C₄₇	#1311	semidirect