Subgroups — #11763730

Order 1088.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63216	C₂	1	2	yes	maximal
2	C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
4	C₄×Dic₁₇	C₄	1	1	yes	characteristic
5	C₂×#3622	C₂²	1	1	yes	characteristic
6	#63216	—	2	2	no	—
7	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₇	C₈	1	1	yes	characteristic
9	C₂×Dic₁₇	C₈	1	1	yes	characteristic
10	C₈×C₁₇	—	2	1	no	—
11	#3622	D₄	1	1	yes	characteristic
12	#3622	Q₈	1	1	yes	characteristic
13	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₇	M₁₆	1	1	yes	characteristic
16	Dic₁₇	—	2	1	no	—
17	Dic₁₇	C₁₆	1	2	yes	complemented
18	C₄⋊C₁₆	—	17	1	no	maximal, Sylow
19	C₂×C₁₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₇	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₁₇	M₃₂	1	1	yes	characteristic
22	C₂×C₁₆	—	17	2	no	—
23	C₄×C₈	—	17	1	no	—
24	C₁₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₈	—	17	1	no	—
26	C₂×C₈	#595	1	1	yes	characteristic
27	C₄²	—	17	1	no	—
28	C₁₆	—	34	2	no	—
29	C₂×C₄	—	17	1	no	—
30	C₂×C₄	—	17	1	no	—
31	C₂×C₄	C₂×#595	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	17	1	no	—
34	C₈	—	17	1	no	—
35	C₂²	#63242	1	1	yes	characteristic
36	C₄	—	17	2	no	—
37	C₄	—	34	1	no	—
38	C₄	C₄⋊#595	1	1	yes	characteristic
39	C₄	#63247	1	1	yes	characteristic
40	C₂	#10587529	1	1	yes	characteristic
41	C₂	#10587530	1	1	yes	characteristic
42	C₂	#10587544	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. Dic₁₇	C₁₆	semidirect
24. C₁₇	C₄⋊C₁₆	semidirect

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