Subgroups — C₃×#500 #5374

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₃×#107	C₂	1	4	yes	maximal
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	#500	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₈	—	2	2	no	—
6	C₂×C₃×C₈	C₂²	1	2	yes	—
7	C₃×C₄⋊C₄	—	2	2	no	—
8	C₃×C₄⋊C₄	C₂²	1	4	yes	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₄⋊Q₈	C₂×C₃	1	2	yes	—
11	#107	C₂×C₃	1	4	yes	—
12	C₄×C₈	C₂×C₃	1	1	yes	characteristic
13	C₃×Q₈	—	4	4	no	—
14	C₂×C₃×C₄	—	2	4	no	—
15	C₂×C₃×C₄	D₄	1	1	yes	characteristic
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
18	C₃×C₈	Q₈	1	4	yes	complemented
19	C₂×Q₈	—	2	2	no	—
20	C₂×C₈	C₂²×C₃	1	2	yes	—
21	C₄⋊C₄	—	2	2	no	—
22	C₄⋊C₄	C₂²×C₃	1	4	yes	—
23	C₄²	C₂²×C₃	1	1	yes	characteristic
24	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
25	C₃×C₄	—	4	4	no	—
26	C₃×C₄	D₈	1	2	yes	—
27	C₃×C₄	Q₁₆	1	2	yes	—
28	C₃×C₄	C₂×Q₈	1	2	yes	—
29	Q₈	—	4	4	no	—
30	C₂×C₄	—	2	4	no	—
31	C₂×C₄	C₃×D₄	1	1	yes	characteristic
32	C₂×C₄	C₃×D₄	1	1	yes	characteristic
33	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
34	C₈	C₃×Q₈	1	4	yes	complemented
35	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
36	C₂×C₃	C₂×D₈	1	1	yes	characteristic
37	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
38	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
39	C₄	—	4	4	no	—
40	C₄	C₃×D₈	1	2	yes	—
41	C₄	C₃×Q₁₆	1	2	yes	—
42	C₄	C₂×C₃×Q₈	1	2	yes	—
43	C₃	#500	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	C₃×C₄⋊Q₈	1	1	yes	characteristic
45	C₂	C₂×C₃×D₈	1	1	yes	characteristic
46	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic

	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

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #500	C₃	direct (N × H)
18. C₃×C₈	Q₈	semidirect
34. C₈	C₃×Q₈	semidirect
43. C₃	#500	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄⋊Q₈	2
C₃×#107	2
C₃×C₄×C₈	2
#500	3

Subgroups — C3×#500 #5374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#500 #5374