Subgroups — #15688947

Order 3008.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093964	C₂	1	1	yes	maximal, characteristic
2	#13093956	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	C₄⋊Dic₄₇	—	2	1	no	—
7	C₄₇⋊C₁₆	C₄	1	2	yes	complemented
8	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
9	C₂×Dic₄₇	—	4	1	no	—
10	C₈×C₄₇	—	4	1	no	—
11	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₇	Q₈	1	1	yes	characteristic
13	C₂²×C₄₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₄₇	SD₁₆	1	1	yes	characteristic
16	Dic₄₇	—	8	1	no	—
17	C₂×C₄₇	—	2	1	no	—
18	C₂×C₄₇	#106	1	1	yes	characteristic
19	#365	—	47	1	no	maximal, Sylow
20	C₄₇	#365	1	1	yes	characteristic, complemented, Sylow
21	M₃₂	—	47	1	no	—
22	#108	D₄₇	1	1	yes	characteristic
23	#106	—	47	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
26	C₄⋊C₄	—	94	1	no	—
27	C₁₆	—	47	2	no	—
28	C₂×C₄	—	188	1	no	—
29	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	Dic₉₄	1	1	yes	characteristic
32	C₈	C₄×D₄₇	1	1	yes	characteristic
33	C₂²	#10625336	1	1	yes	characteristic
34	C₄	—	376	1	no	—
35	C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
36	C₄	#10625335	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#13093955	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₄₇⋊C₁₆	C₄	semidirect
20. C₄₇	#365	semidirect

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