Subgroups — #11763716

Order 1088.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587561	C₂	1	1	yes	maximal, characteristic
2	#10587539	C₂	1	2	yes	maximal
3	C₂×D₆₈	C₂²	1	1	yes	characteristic
4	C₂×Dic₃₄	C₄	1	1	yes	characteristic, complemented
5	C₂²⋊#595	—	2	2	no	—
6	C₄²×C₁₇	C₄	1	1	yes	characteristic, complemented
7	#63227	—	2	2	no	—
8	C₂²×D₁₇	D₄	1	2	yes	—
9	C₂×#595	—	4	2	no	—
10	C₂×C₄×C₁₇	—	2	1	no	—
11	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₇	—	2	1	no	—
13	D₆₈	—	4	1	no	—
14	Dic₃₄	—	4	1	no	—
15	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₁₇	—	2	2	no	—
17	C₂×D₁₇	—	4	2	no	—
18	#595	—	8	2	no	—
19	C₄×C₁₇	—	2	1	no	—
20	C₄×C₁₇	—	4	1	no	—
21	Dic₁₇	—	4	1	no	—
22	#354	—	17	1	no	maximal, Sylow
23	C₂×C₁₇	—	2	1	no	—
24	C₂×C₁₇	#99	1	1	yes	characteristic
25	D₁₇	—	4	2	no	—
26	#124	—	17	1	no	—
27	#99	—	17	2	no	—
28	C₁₇	#354	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₈	—	17	1	no	—
30	C₂×D₄	—	17	1	no	—
31	C₂²⋊C₄	—	34	2	no	—
32	C₂²⋊C₄	—	34	2	no	—
33	C₄²	#595	1	1	yes	characteristic, complemented
34	C₂³	—	17	2	no	—
35	Q₈	—	68	1	no	—
36	D₄	—	68	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	34	1	no	—
39	C₂×C₄	—	68	2	no	—
40	C₂×C₄	C₂×#595	1	1	yes	characteristic
41	C₂²	—	34	2	no	—
42	C₂²	—	68	2	no	—
43	C₂²	C₂²⋊#595	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	68	1	no	—
47	C₄	—	136	2	no	—
48	C₂	—	2	1	no	—
49	C₂	—	68	2	no	—
50	C₂	#10587539	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.