Subgroups — #11763731

Order 1088.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587538	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	—	2	1	no	—
9	C₈×C₁₇	C₈	1	2	yes	—
10	#3622	D₄	1	1	yes	characteristic
11	#3622	Q₈	1	1	yes	characteristic
12	C₂²×C₁₇	M₁₆	1	1	yes	characteristic
13	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
15	Dic₁₇	—	2	2	no	—
16	#364	—	17	1	no	maximal, Sylow
17	C₂×C₁₇	—	2	1	no	—
18	C₂×C₁₇	C₄⋊C₈	1	1	yes	characteristic
19	M₃₂	—	17	2	no	—
20	C₄×C₈	—	17	1	no	—
21	C₁₇	#364	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₈	—	17	1	no	—
23	C₂×C₈	#595	1	1	yes	characteristic
24	C₄²	—	17	1	no	—
25	C₁₆	—	34	2	no	—
26	C₂×C₄	—	34	1	no	—
27	C₂×C₄	C₂×#595	1	1	yes	characteristic
28	C₈	—	17	1	no	—
29	C₈	—	17	1	no	—
30	C₈	#3624	1	2	yes	—
31	C₂²	#63243	1	1	yes	characteristic
32	C₄	—	34	2	no	—
33	C₄	C₄⋊#595	1	1	yes	characteristic
34	C₄	C₂×#3624	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊#3624	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₁₇	#364	semidirect

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