Subgroups — #11763724

Order 1088.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587605	C₂	1	1	yes	maximal, characteristic
2	#10587536	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587529	C₂	1	1	yes	maximal, characteristic, complemented
4	#63256	—	2	1	no	—
5	#63243	—	2	1	no	—
6	Q₁₆×C₁₇	C₄	1	1	yes	characteristic
7	#63230	—	2	1	no	—
8	D₁₃₆	C₄	1	1	yes	characteristic
9	C₈×D₁₇	C₂²	1	1	yes	characteristic
10	#63216	—	2	1	no	—
11	Q₈×C₁₇	—	2	1	no	—
12	D₆₈	—	2	1	no	—
13	D₆₈	—	4	1	no	—
14	C₄×D₁₇	—	4	1	no	—
15	C₄×D₁₇	D₄	1	1	yes	characteristic
16	#3624	—	4	1	no	—
17	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#3622	D₄	1	1	yes	characteristic
19	C₂×D₁₇	—	4	1	no	—
20	C₂×D₁₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₇	—	4	1	no	—
22	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₇	D₈	1	1	yes	characteristic
24	#359	—	17	1	no	maximal, Sylow
25	C₂×C₁₇	#102	1	1	yes	characteristic
26	D₁₇	—	2	1	no	—
27	D₁₇	—	8	1	no	—
28	#135	—	17	1	no	—
29	C₂×C₁₆	—	17	1	no	—
30	#108	—	17	1	no	—
31	C₁₇	#359	1	1	yes	characteristic, complemented, Sylow
32	#41	—	34	1	no	—
33	Q₁₆	#595	1	1	yes	characteristic
34	SD₁₆	—	34	1	no	—
35	D₈	—	17	1	no	—
36	M₁₆	—	34	1	no	—
37	C₂×C₈	—	17	1	no	—
38	C₁₆	—	34	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	34	1	no	—
41	D₄	—	68	1	no	—
42	C₂×C₄	—	17	1	no	—
43	C₂×C₄	—	68	1	no	—
44	C₈	—	17	1	no	—
45	C₈	—	68	1	no	—
46	C₈	C₂×#595	1	1	yes	characteristic
47	C₂²	—	17	1	no	—
48	C₂²	—	68	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	17	1	no	—
51	C₄	C₂²⋊#595	1	1	yes	characteristic
52	C₂	—	34	1	no	—
53	C₂	—	136	1	no	—
54	C₂	#10587547	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.