Subgroups — C₂³×#3622 #11763566

Order 1088.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3622	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₁₇	C₄	1	7	yes	—
5	C₂²×C₄×C₁₇	C₂²	1	7	yes	—
6	C₂×#3622	C₂²	1	28	yes	direct product factor
7	C₂³×C₁₇	C₈	1	8	yes	complemented
8	C₂³×C₁₇	C₂×C₄	1	7	yes	—
9	C₂×C₄×C₁₇	C₂×C₄	1	21	yes	—
10	C₂×C₄×C₁₇	C₂³	1	7	yes	—
11	#3622	C₂³	1	8	yes	direct product factor
12	C₂²×C₁₇	C₂×C₈	1	28	yes	complemented
13	C₂²×C₁₇	C₂²×C₄	1	7	yes	—
14	C₄×C₁₇	C₂²×C₄	1	7	yes	—
15	C₄×C₁₇	C₂⁴	1	1	yes	characteristic
16	C₂³×C₈	—	17	1	no	maximal, Sylow
17	C₂×C₁₇	C₂²×C₈	1	14	yes	complemented
18	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
19	C₂³×C₄	D₁₇	1	1	yes	characteristic
20	C₂²×C₈	—	17	14	no	—
21	C₁₇	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂⁴	Dic₁₇	1	1	yes	characteristic
23	C₂²×C₄	Dic₁₇	1	7	yes	—
24	C₂²×C₄	C₂×D₁₇	1	7	yes	—
25	C₂×C₈	—	17	28	no	—
26	C₂³	#3622	1	8	yes	direct product factor
27	C₂³	C₂×Dic₁₇	1	7	yes	—
28	C₂×C₄	C₂×Dic₁₇	1	21	yes	—
29	C₂×C₄	C₂²×D₁₇	1	7	yes	—
30	C₈	—	17	8	no	—
31	C₂²	C₂×#3622	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₁₇	1	7	yes	—
33	C₄	C₂²×Dic₁₇	1	7	yes	—
34	C₄	C₂³×D₁₇	1	1	yes	characteristic
35	C₂	C₂²×#3622	1	14	yes	direct product factor
36	C₂	C₂³×Dic₁₇	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.