Subgroups — Q₁₆×D₆₁₇ #34089718

Order 19744.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₆₁₇	C₂	1	2	yes	maximal
2	Dic₂₄₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#23754590	C₂	1	2	yes	maximal, complemented
4	C₈×D₆₁₇	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×C₆₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₂₃₄	—	2	2	no	—
7	Dic₁₂₃₄	C₂²	1	2	yes	—
8	C₄×D₆₁₇	—	2	2	no	—
9	C₄×D₆₁₇	C₂²	1	1	yes	characteristic
10	#19096921	C₂²	1	1	yes	characteristic
11	Q₈×C₆₁₇	C₂²	1	2	yes	—
12	C₈×C₆₁₇	C₂²	1	1	yes	characteristic
13	C₂×D₆₁₇	D₄	1	1	yes	characteristic
14	C₄×C₆₁₇	—	2	2	no	—
15	C₄×C₆₁₇	C₂³	1	1	yes	characteristic
16	Dic₆₁₇	—	2	2	no	—
17	Dic₆₁₇	D₄	1	1	yes	characteristic
18	C₂×C₆₁₇	C₂×D₄	1	1	yes	characteristic
19	D₆₁₇	Q₁₆	1	2	yes	direct product factor
20	C₆₁₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	617	1	no	maximal, Sylow
22	C₂×Q₈	—	617	2	no	—
23	Q₁₆	—	617	2	no	—
24	Q₁₆	—	617	1	no	—
25	Q₁₆	D₆₁₇	1	1	yes	characteristic, direct product factor
26	C₂×C₈	—	617	1	no	—
27	Q₈	—	617	2	no	—
28	Q₈	—	1234	2	no	—
29	Q₈	C₂×D₆₁₇	1	2	yes	—
30	C₂×C₄	—	617	1	no	—
31	C₂×C₄	—	1234	2	no	—
32	C₈	—	617	1	no	—
33	C₈	C₂×D₆₁₇	1	1	yes	characteristic
34	C₂²	—	617	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	617	1	no	—
37	C₄	—	1234	2	no	—
38	C₄	C₂²×D₆₁₇	1	1	yes	characteristic
39	C₂	—	617	2	no	—
40	C₂	D₄×D₆₁₇	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.