Subgroups — #15688900

Order 3008.

46 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	#13093934	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
5	C₄×Dic₄₇	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₁₆×C₄₇	C₄	1	2	yes	complemented
8	C₄₇⋊C₁₆	C₄	1	2	yes	complemented
9	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₄₇	—	2	1	no	—
11	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₄₇⋊C₈	—	2	1	no	—
14	C₂²×C₄₇	M₁₆	1	1	yes	characteristic
15	C₄×C₄₇	C₄²	1	1	yes	characteristic
16	C₄×C₄₇	M₁₆	1	1	yes	characteristic
17	Dic₄₇	—	4	1	no	—
18	C₂×C₄₇	—	2	1	no	—
19	C₂×C₄₇	#97	1	1	yes	characteristic
20	#347	—	47	1	no	maximal, Sylow
21	C₄₇	#347	1	1	yes	characteristic, complemented, Sylow
22	M₃₂	—	47	1	no	—
23	M₃₂	D₄₇	1	1	yes	characteristic
24	#97	—	47	1	no	—
25	C₂×C₈	—	47	1	no	—
26	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
27	C₄²	—	47	1	no	—
28	C₁₆	—	47	2	no	—
29	C₁₆	Dic₄₇	1	2	yes	complemented
30	C₂×C₄	—	94	1	no	—
31	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
32	C₈	—	94	1	no	—
33	C₈	C₄×D₄₇	1	1	yes	characteristic
34	C₈	C₂×Dic₄₇	1	1	yes	characteristic
35	C₂²	#10625324	1	1	yes	characteristic
36	C₄	—	188	1	no	—
37	C₄	#10625324	1	1	yes	characteristic
38	C₄	C₄×Dic₄₇	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#13093934	1	1	yes	characteristic

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

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