Subgroups — #14517172

Order 1944.

173 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
2	(C₃×SL(2,𝔽₃))⋊C₉	C₃	1	4	yes	maximal
3	(Q₈⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
4	C₂×#6897	—	4	1	no	maximal
5	C₄×C₉²	—	3	1	no	—
6	#6897	—	4	1	no	Sylow
7	C₃²×SL(2,𝔽₃)	C₃²	1	1	yes	characteristic
8	C₃×Q₈×C₉	C₃²	1	4	yes	—
9	C₃×Q₈⋊C₉	C₃²	1	8	yes	—
10	C₂×C₉⋊C₉	—	4	8	no	—
11	C₂×C₃²⋊C₉	—	4	4	no	—
12	C₂×C₉²	A₄	1	1	yes	characteristic
13	C₃×C₄×C₉	—	3	4	no	—
14	C₉⋊C₉	—	4	8	no	—
15	C₃²⋊C₉	—	4	4	no	—
16	C₉²	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
17	C₃²×Q₈	C₃³	1	1	yes	characteristic
18	C₃×SL(2,𝔽₃)	—	3	4	no	—
19	Q₈×C₉	—	3	4	no	—
20	Q₈⋊C₉	—	3	8	no	—
21	C₂×C₃³	—	4	1	no	—
22	C₂×C₃×C₉	—	4	8	no	—
23	C₂×C₃×C₉	C₃×A₄	1	4	yes	—
24	C₃²×C₄	—	3	1	no	—
25	C₄×C₉	—	3	12	no	—
26	C₃³	—	4	1	no	—
27	C₃×C₉	—	4	8	no	—
28	C₃×C₉	C₃×SL(2,𝔽₃)	1	4	yes	—
29	C₃×Q₈	#737	1	4	yes	—
30	SL(2,𝔽₃)	—	9	1	no	—
31	C₂×C₃²	—	12	4	no	—
32	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
33	C₂×C₉	—	3	4	no	—
34	C₂×C₉	—	12	8	no	—
35	C₃×C₄	—	3	4	no	—
36	C₃²	—	12	4	no	—
37	C₃²	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
38	C₉	—	3	4	no	—
39	C₉	—	12	8	no	—
40	Q₈	#6897	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	36	1	no	—
42	C₂×C₃	#66436	1	4	yes	—
43	C₄	—	3	1	no	—
44	C₃	—	36	1	no	—
45	C₃	#10619912	1	4	yes	—
46	C₂	#11757765	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.