Subgroups — C₃×#494 #5368

Order 192.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	4	yes	maximal
2	C₃×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	#494	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₈	C₂²	1	4	yes	—
6	C₃×Q₁₆	—	2	8	no	—
7	C₂×C₃×C₈	C₂²	1	2	yes	—
8	C₃×C₄⋊C₄	—	2	4	no	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆	C₂×C₃	1	4	yes	—
11	C₄⋊Q₈	C₂×C₃	1	2	yes	—
12	C₄×C₈	C₂×C₃	1	1	yes	characteristic
13	C₃×Q₈	—	2	8	no	—
14	C₂×C₃×C₄	—	2	4	no	—
15	C₂×C₃×C₄	D₄	1	2	yes	—
16	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
17	C₃×C₈	D₄	1	4	yes	—
18	C₂×Q₈	C₂²×C₃	1	4	yes	—
19	Q₁₆	—	2	8	no	—
20	C₂×C₈	C₂²×C₃	1	2	yes	—
21	C₄⋊C₄	—	2	4	no	—
22	C₄²	C₂²×C₃	1	1	yes	characteristic
23	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
24	C₃×C₄	—	4	4	no	—
25	C₃×C₄	Q₁₆	1	4	yes	complemented
26	C₃×C₄	C₂×D₄	1	2	yes	—
27	Q₈	—	2	8	no	—
28	C₂×C₄	—	2	4	no	—
29	C₂×C₄	C₃×D₄	1	2	yes	—
30	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
31	C₈	C₃×D₄	1	4	yes	—
32	C₂×C₃	#127	1	1	yes	characteristic
33	C₂×C₃	C₂×Q₁₆	1	2	yes	—
34	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
35	C₄	—	4	4	no	—
36	C₄	C₃×Q₁₆	1	4	yes	complemented
37	C₄	C₂×C₃×D₄	1	2	yes	—
38	C₃	#494	1	1	yes	characteristic, direct product factor, Sylow
39	C₂	C₃×#127	1	1	yes	characteristic
40	C₂	C₂×C₃×Q₁₆	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ 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.