Subgroups — #15688944

Order 3008.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093964	C₂	1	2	yes	maximal
2	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₄₇	C₄	1	1	yes	characteristic
4	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
5	C₄²×C₄₇	C₄	1	1	yes	characteristic
6	C₄₇⋊C₁₆	—	2	2	no	—
7	C₂×C₄×C₄₇	—	2	1	no	—
8	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₄₇	C₈	1	2	yes	—
10	C₈×C₄₇	D₄	1	1	yes	characteristic
11	C₈×C₄₇	Q₈	1	1	yes	characteristic
12	C₂²×C₄₇	M₁₆	1	1	yes	characteristic
13	C₄×C₄₇	—	2	2	no	—
14	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄₇	—	2	1	no	—
17	C₂×C₄₇	C₄⋊C₈	1	1	yes	characteristic
18	#364	—	47	1	no	maximal, Sylow
19	C₄₇	#364	1	1	yes	characteristic, complemented, Sylow
20	M₃₂	—	47	2	no	—
21	C₄×C₈	D₄₇	1	1	yes	characteristic
22	C₂×C₈	Dic₄₇	1	1	yes	characteristic
23	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
24	C₄²	Dic₄₇	1	1	yes	characteristic
25	C₁₆	—	94	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
28	C₈	C₄₇⋊C₈	1	2	yes	—
29	C₈	Dic₉₄	1	1	yes	characteristic
30	C₈	D₁₈₈	1	1	yes	characteristic
31	C₂²	#10625329	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
34	C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₄₇	#364	semidirect

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