Subgroups — C₃×D₈₈ #10587164

Order 528.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄₄	C₂	1	2	yes	maximal, complemented
2	C₃×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×D₁₁	—	2	2	no	—
5	C₃×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	D₄₄	C₂×C₃	1	2	yes	complemented
7	C₈×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₁	D₄	1	1	yes	characteristic
9	C₃×D₁₁	—	4	2	no	—
10	C₃×D₈	—	11	1	no	maximal, Hall
11	C₂×D₁₁	—	2	2	no	—
12	C₄×C₁₁	C₂²×C₃	1	1	yes	characteristic
13	C₃×C₁₁	D₈	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄	—	11	2	no	—
15	C₃×C₈	D₁₁	1	1	yes	characteristic, complemented
16	C₂×C₁₁	C₃×D₄	1	1	yes	characteristic
17	D₁₁	—	4	2	no	—
18	D₈	—	11	1	no	Sylow
19	C₂²×C₃	—	22	2	no	—
20	C₃×C₄	C₂×D₁₁	1	1	yes	characteristic
21	C₁₁	C₃×D₈	1	1	yes	characteristic, complemented, Sylow
22	D₄	—	11	2	no	—
23	C₈	C₃×D₁₁	1	1	yes	characteristic, complemented
24	C₂×C₃	—	44	2	no	—
25	C₂×C₃	D₄₄	1	1	yes	characteristic
26	C₂²	—	22	2	no	—
27	C₄	C₂×C₃×D₁₁	1	1	yes	characteristic
28	C₃	D₈₈	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	44	2	no	—
30	C₂	C₃×D₄₄	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.