Subgroups — #1009

Order 96.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#239	C₂	1	2	yes	maximal, complemented
3	D₃×D₄	C₂	1	6	yes	maximal, complemented
4	#235	C₂	1	3	yes	maximal, complemented
5	C₂×D₁₂	C₂	1	3	yes	maximal, complemented
6	H(5,𝔽₂)	—	3	1	no	maximal, Sylow
7	C₂²×D₃	C₂²	1	6	yes	complemented
8	C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
9	C₃×D₄	C₂²	1	3	yes	complemented
10	C₂×C₃×C₄	C₂²	1	3	yes	complemented
11	#67	C₂²	1	6	yes	complemented
12	D₁₂	C₂²	1	3	yes	complemented
13	D₁₂	C₂²	1	6	yes	complemented
14	C₄×D₃	C₂²	1	6	yes	complemented
15	Dic₆	C₂²	1	1	yes	characteristic, complemented
16	#41	—	3	2	no	—
17	#41	—	3	3	no	—
18	#41	D₃	1	1	yes	characteristic, complemented
19	C₂×D₄	—	3	6	no	—
20	C₂×D₄	—	3	3	no	—
21	C₂²×C₃	C₂³	1	3	yes	—
22	C₂×D₃	—	4	6	no	—
23	C₂×D₃	C₂³	1	6	yes	—
24	C₃×C₄	C₂³	1	1	yes	characteristic
25	C₃×C₄	C₂³	1	3	yes	—
26	Dic₃	C₂³	1	2	yes	—
27	C₂³	—	3	6	no	—
28	Q₈	—	3	1	no	—
29	Q₈	C₂×D₃	1	1	yes	characteristic, complemented
30	D₄	—	3	6	no	—
31	D₄	—	3	6	no	—
32	D₄	—	3	3	no	—
33	D₄	C₂×D₃	1	3	yes	complemented
34	C₂×C₄	—	3	6	no	—
35	C₂×C₄	C₂×D₃	1	3	yes	complemented
36	C₂×C₃	—	2	3	no	—
37	C₂×C₃	C₂⁴	1	1	yes	characteristic
38	D₃	—	2	6	no	—
39	C₂²	—	3	6	no	—
40	C₂²	—	12	6	no	—
41	C₂²	C₂²×D₃	1	3	yes	—
42	C₄	—	3	2	no	—
43	C₄	C₂²×D₃	1	3	yes	—
44	C₄	C₂²×D₃	1	1	yes	characteristic
45	C₃	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	2	3	no	—
47	C₂	—	6	6	no	—
48	C₂	C₂³×D₃	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.