Subgroups — C₉×#101 #63403

Order 288.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×M₁₆	C₂	1	2	yes	maximal
3	C₃×#101	C₃	1	1	yes	maximal, characteristic
4	Q₈×C₉	—	2	2	no	—
5	C₂×C₄×C₉	C₄	1	2	yes	—
6	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₈×C₉	—	2	2	no	—
8	C₂×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
9	C₃×M₁₆	C₂×C₃	1	2	yes	—
10	C₂²×C₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₉	—	2	2	no	—
12	C₄×C₉	D₄	1	2	yes	—
13	#101	C₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₃×Q₈	—	2	2	no	—
15	C₂×C₃×C₄	C₃×C₄	1	2	yes	—
16	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
17	C₃×C₈	—	2	2	no	—
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×Q₈	C₂×C₉	1	1	yes	characteristic
21	M₁₆	C₂×C₉	1	2	yes	—
22	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
23	C₃×C₄	—	2	2	no	—
24	C₃×C₄	C₃×D₄	1	2	yes	—
25	C₉	#101	1	1	yes	characteristic, direct product factor, Sylow
26	Q₈	—	2	2	no	—
27	C₂×C₄	C₄×C₉	1	2	yes	—
28	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
29	C₈	—	2	2	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
32	C₂²	C₂×C₄×C₉	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	D₄×C₉	1	2	yes	—
35	C₃	C₃×#101	1	1	yes	characteristic
36	C₂	—	2	1	no	—
37	C₂	C₉×C₂²⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. #101	C₉	direct (N × H)
25. C₉	#101	direct (N × H)

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