Subgroups — #11763719

Order 1088.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587630	C₂	1	1	yes	maximal, characteristic
2	#10587545	C₂	1	2	yes	maximal
3	C₂×Q₈×C₁₇	C₄	1	1	yes	characteristic
4	C₂×Dic₃₄	C₂²	1	1	yes	characteristic
5	#63247	—	2	2	no	—
6	#63225	—	2	2	no	—
7	C₄×Dic₁₇	C₄	1	1	yes	characteristic
8	Q₈×C₁₇	—	4	1	no	—
9	C₂×C₄×C₁₇	—	2	1	no	—
10	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₁₇	—	2	1	no	—
12	C₂×Dic₁₇	D₄	1	2	yes	—
13	Dic₃₄	—	4	1	no	—
14	#3624	—	4	2	no	—
15	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₁₇	—	2	1	no	—
17	C₄×C₁₇	—	4	1	no	—
18	Dic₁₇	—	2	2	no	—
19	Dic₁₇	—	2	2	no	—
20	#356	—	17	1	no	maximal, Sylow
21	C₂×C₁₇	—	2	1	no	—
22	C₂×C₁₇	#99	1	1	yes	characteristic
23	C₄⋊Q₈	—	17	1	no	—
24	#101	—	17	2	no	—
25	C₁₇	#356	1	1	yes	characteristic, complemented, Sylow
26	C₂×Q₈	—	17	1	no	—
27	C₂×Q₈	#595	1	1	yes	characteristic
28	M₁₆	—	34	2	no	—
29	C₄⋊C₄	—	34	2	no	—
30	C₄²	—	17	1	no	—
31	Q₈	—	4	1	no	—
32	Q₈	—	68	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	17	2	no	—
35	C₂×C₄	—	34	1	no	—
36	C₂×C₄	C₂×#595	1	1	yes	characteristic
37	C₈	—	68	2	no	—
38	C₂²	C₂²⋊#595	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	—	34	2	no	—
42	C₄	—	34	2	no	—
43	C₂	—	2	1	no	—
44	C₂	#10587551	1	1	yes	characteristic

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

N	H ≅ G/N	type
25. C₁₇	#356	semidirect

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