Subgroups — #20241592

Order 6016.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688953	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093960	—	2	2	no	—
4	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₄₇	C₄	1	2	yes	—
6	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
7	#10625329	—	4	2	no	—
8	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₄₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
11	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
13	C₄₇⋊C₈	—	8	2	no	—
14	C₂²×C₄₇	Q₃₂	1	1	yes	characteristic
15	C₄×C₄₇	#107	1	1	yes	characteristic
16	C₄×C₄₇	D₁₆	1	1	yes	characteristic
17	#1425	—	47	1	no	maximal, Sylow
18	C₂×C₄₇	—	2	1	no	—
19	C₂×C₄₇	#366	1	1	yes	characteristic
20	C₂×C₃₂	D₄₇	1	1	yes	characteristic
21	#368	—	47	2	no	—
22	C₄₇	#1425	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
24	#108	—	94	2	no	—
25	C₃₂	Dic₄₇	1	2	yes	—
26	M₁₆	—	188	2	no	—
27	C₂×C₈	D₁₈₈	1	1	yes	characteristic
28	C₁₆	Dic₉₄	1	1	yes	characteristic
29	C₁₆	C₂×Dic₄₇	1	1	yes	characteristic
30	C₂×C₄	D₃₇₆	1	1	yes	characteristic
31	C₈	—	376	2	no	—
32	C₈	Dic₁₈₈	1	1	yes	characteristic
33	C₈	C₄⋊Dic₄₇	1	1	yes	characteristic
34	C₂²	Dic₃₇₆	1	1	yes	characteristic
35	C₄	#13093958	1	1	yes	characteristic
36	C₄	D₇₅₂	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#15688949	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₄₇	#1425	semidirect