Subgroups — Q₁₆×D₄₇ #13094040

Order 1504.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₄₇	C₂	1	2	yes	maximal
2	Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625337	C₂	1	2	yes	maximal, complemented
4	Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₄₇	C₂²	1	2	yes	—
7	C₄×D₄₇	—	2	2	no	—
8	C₄×D₄₇	C₂²	1	1	yes	characteristic
9	Dic₉₄	—	2	2	no	—
10	Dic₉₄	C₂²	1	2	yes	—
11	C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×D₄₇	D₄	1	1	yes	characteristic
14	C₄×C₄₇	—	2	2	no	—
15	C₄×C₄₇	C₂³	1	1	yes	characteristic
16	Dic₄₇	—	2	2	no	—
17	Dic₄₇	D₄	1	1	yes	characteristic
18	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
19	D₄₇	Q₁₆	1	2	yes	direct product factor
20	C₄₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	47	1	no	maximal, Sylow
22	C₂×Q₈	—	47	2	no	—
23	Q₁₆	—	47	2	no	—
24	Q₁₆	—	47	1	no	—
25	Q₁₆	D₄₇	1	1	yes	characteristic, direct product factor
26	C₂×C₈	—	47	1	no	—
27	Q₈	—	47	2	no	—
28	Q₈	—	94	2	no	—
29	Q₈	C₂×D₄₇	1	2	yes	—
30	C₂×C₄	—	47	1	no	—
31	C₂×C₄	—	94	2	no	—
32	C₈	—	47	1	no	—
33	C₈	C₂×D₄₇	1	1	yes	characteristic
34	C₂²	—	47	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	47	1	no	—
37	C₄	—	94	2	no	—
38	C₄	C₂²×D₄₇	1	1	yes	characteristic
39	C₂	—	47	2	no	—
40	C₂	D₄×D₄₇	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.