Subgroups — #15688953

Order 3008.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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

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