Subgroups — #14543945

Order 2176.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763735	C₂	1	2	yes	maximal
2	C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587534	—	2	2	no	—
4	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
5	C₁₇×C₃₂	C₄	1	1	yes	characteristic, complemented
6	#10587465	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#595	—	4	2	no	—
8	C₈×D₁₇	D₄	1	1	yes	characteristic
9	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
10	#63214	Q₈	1	1	yes	characteristic
11	C₂×#595	—	8	2	no	—
12	C₄×D₁₇	D₈	1	1	yes	characteristic
13	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
14	#3622	Q₁₆	1	1	yes	characteristic
15	#1423	—	17	1	no	maximal, Sylow
16	C₂×D₁₇	D₁₆	1	1	yes	characteristic
17	#595	—	16	2	no	—
18	C₄×C₁₇	#107	1	1	yes	characteristic
19	Dic₁₇	Q₃₂	1	1	yes	characteristic
20	C₂×C₃₂	—	17	1	no	—
21	#366	—	17	2	no	—
22	C₂×C₁₇	#366	1	1	yes	characteristic
23	D₁₇	D₃₂	1	1	yes	characteristic
24	D₁₇	Q₆₄	1	1	yes	characteristic
25	C₂×C₁₆	—	17	1	no	—
26	#107	—	34	2	no	—
27	C₃₂	—	17	1	no	—
28	C₃₂	#595	1	1	yes	characteristic, complemented
29	C₁₇	#1423	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	—	17	1	no	—
31	C₄⋊C₄	—	68	2	no	—
32	C₁₆	—	17	1	no	—
33	C₁₆	C₂×#595	1	1	yes	characteristic
34	C₂×C₄	—	17	1	no	—
35	C₂×C₄	—	136	2	no	—
36	C₈	—	17	1	no	—
37	C₈	C₄⋊#595	1	1	yes	characteristic
38	C₂²	—	17	1	no	—
39	C₄	—	272	2	no	—
40	C₄	—	17	1	no	—
41	C₄	#10587534	1	1	yes	characteristic
42	C₂	—	17	1	no	—
43	C₂	—	17	1	no	—
44	C₂	#11763735	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.