Subgroups — #15688952

Order 3008.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#13093960	C₂	1	1	yes	maximal, characteristic
3	#108×C₄₇	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₄₇	—	2	1	no	—
5	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	#10625329	—	2	1	no	—
7	C₄₇⋊C₁₆	C₄	1	2	yes	—
8	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
9	C₈×C₄₇	—	4	1	no	—
10	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₄₇	Q₈	1	1	yes	characteristic
12	C₄₇⋊C₈	—	4	1	no	—
13	C₂²×C₄₇	Q₁₆	1	1	yes	characteristic
14	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₄₇	D₈	1	1	yes	characteristic
16	C₂×C₄₇	—	2	1	no	—
17	C₂×C₄₇	#107	1	1	yes	characteristic
18	#368	—	47	1	no	maximal, Sylow
19	C₄₇	#368	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₆	—	47	1	no	—
21	#108	—	47	1	no	—
22	#108	D₄₇	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	94	1	no	—
25	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
26	C₁₆	—	47	2	no	—
27	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	188	1	no	—
30	C₈	Dic₉₄	1	1	yes	characteristic
31	C₈	C₄×D₄₇	1	1	yes	characteristic
32	C₂²	#10625337	1	1	yes	characteristic
33	C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
34	C₄	#10625334	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#13093957	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₄₇	#368	semidirect

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