Subgroups — C₃×H(3,𝔽₄) #5891

Order 192.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#124	C₂	1	9	yes	maximal, complemented
2	C₃×#120	C₂	1	6	yes	maximal, complemented
3	H(3,𝔽₄)	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁴×C₃	C₂²	1	2	yes	complemented
5	C₂×C₃×Q₈	C₂²	1	3	yes	complemented
6	C₂×C₃×D₄	C₂²	1	9	yes	—
7	C₃×C₂²⋊C₄	C₂²	1	18	yes	complemented
8	C₃×C₄²	C₂²	1	3	yes	complemented
9	#124	C₂×C₃	1	9	yes	complemented
10	#120	C₂×C₃	1	6	yes	complemented
11	C₂³×C₃	—	4	6	no	—
12	C₂³×C₃	C₂³	1	6	yes	—
13	C₃×Q₈	—	4	3	no	—
14	C₃×D₄	—	4	9	no	—
15	C₂×C₃×C₄	C₂³	1	9	yes	—
16	C₂⁴	C₂²×C₃	1	2	yes	complemented
17	C₂×Q₈	C₂²×C₃	1	3	yes	complemented
18	C₂×D₄	C₂²×C₃	1	9	yes	—
19	C₂²⋊C₄	C₂²×C₃	1	18	yes	complemented
20	C₄²	C₂²×C₃	1	3	yes	complemented
21	C₂²×C₃	—	2	18	no	—
22	C₂²×C₃	—	4	8	no	—
23	C₂²×C₃	C₂⁴	1	1	yes	characteristic
24	C₃×C₄	—	2	9	no	—
25	C₂³	—	4	6	no	—
26	C₂³	C₂³×C₃	1	6	yes	—
27	Q₈	—	4	3	no	—
28	D₄	—	4	9	no	—
29	C₂×C₄	C₂³×C₃	1	9	yes	—
30	C₂×C₃	—	4	6	no	—
31	C₂×C₃	H(5,𝔽₂)	1	3	yes	—
32	C₂²	—	2	18	no	—
33	C₂²	—	4	8	no	—
34	C₂²	C₂⁴×C₃	1	1	yes	characteristic
35	C₄	—	2	9	no	—
36	C₃	H(3,𝔽₄)	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	4	6	no	—
38	C₂	C₃×H(5,𝔽₂)	1	3	yes	—

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