Subgroups — C₂×C₃×#41 #1016

Order 96.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₄	C₂	1	3	yes	maximal, complemented
4	C₂²×C₃×C₄	C₂	1	3	yes	maximal, complemented
5	C₂×#41	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂³×C₃	C₂²	1	3	yes	—
7	C₃×Q₈	C₂²	1	4	yes	complemented
8	C₃×D₄	C₂²	1	12	yes	complemented
9	C₂×C₃×C₄	C₂²	1	3	yes	—
10	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄	C₂²	1	12	yes	complemented
12	#41	C₂×C₃	1	8	yes	direct product factor
13	C₂×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₄	C₂×C₃	1	3	yes	complemented
15	C₂²×C₄	C₂×C₃	1	3	yes	complemented
16	C₂²×C₃	—	2	6	no	—
17	C₂²×C₃	C₂³	1	6	yes	—
18	C₂²×C₃	C₂³	1	1	yes	characteristic
19	C₃×C₄	C₂³	1	6	yes	—
20	C₃×C₄	C₂³	1	2	yes	—
21	C₂³	C₂²×C₃	1	3	yes	—
22	Q₈	C₂²×C₃	1	4	yes	complemented
23	D₄	C₂²×C₃	1	12	yes	complemented
24	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
25	C₂×C₄	C₂²×C₃	1	3	yes	—
26	C₂×C₄	C₂²×C₃	1	12	yes	complemented
27	C₂×C₃	—	2	6	no	—
28	C₂×C₃	#41	1	2	yes	direct product factor
29	C₂×C₃	C₂⁴	1	1	yes	characteristic
30	C₂²	—	2	6	no	—
31	C₂²	C₂³×C₃	1	6	yes	—
32	C₂²	C₂³×C₃	1	1	yes	characteristic
33	C₄	C₂³×C₃	1	2	yes	—
34	C₄	C₂³×C₃	1	6	yes	—
35	C₃	C₂×#41	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	2	6	no	—
37	C₂	C₃×#41	1	2	yes	direct product factor
38	C₂	C₂⁴×C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₃
socle	C₂²×C₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

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.