Subgroups — C₃×#557 #5887

Order 192.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	3	yes	maximal
2	C₃×#125	C₂	1	6	yes	maximal
3	C₃×C₄×Q₈	C₂	1	2	yes	maximal
4	C₃×C₄×Q₈	C₂	1	3	yes	maximal
5	C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
6	#557	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	3	yes	—
8	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₃×C₄⋊C₄	C₂²	1	6	yes	—
11	C₃×C₄⋊C₄	C₂²	1	3	yes	—
12	C₃×C₄⋊C₄	C₂²	1	6	yes	—
13	C₃×C₄⋊C₄	C₂²	1	6	yes	—
14	C₃×C₄²	C₂²	1	6	yes	—
15	C₃×C₄²	C₂²	1	3	yes	—
16	C₄⋊Q₈	C₂×C₃	1	3	yes	—
17	#125	C₂×C₃	1	6	yes	—
18	C₄×Q₈	C₂×C₃	1	2	yes	—
19	C₄×Q₈	C₂×C₃	1	3	yes	—
20	C₄×Q₈	C₂×C₃	1	1	yes	characteristic
21	C₃×Q₈	—	2	6	no	—
22	C₃×Q₈	Q₈	1	4	yes	complemented
23	C₂×C₃×C₄	C₂³	1	2	yes	—
24	C₂×C₃×C₄	C₂³	1	3	yes	—
25	C₂×C₃×C₄	C₂³	1	6	yes	—
26	C₂×C₃×C₄	C₂³	1	3	yes	—
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₂×Q₈	C₂²×C₃	1	3	yes	—
29	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
30	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
31	C₄⋊C₄	C₂²×C₃	1	6	yes	—
32	C₄⋊C₄	C₂²×C₃	1	3	yes	—
33	C₄⋊C₄	C₂²×C₃	1	6	yes	—
34	C₄⋊C₄	C₂²×C₃	1	6	yes	—
35	C₄²	C₂²×C₃	1	6	yes	—
36	C₄²	C₂²×C₃	1	3	yes	—
37	C₂²×C₃	C₂⁴	1	1	yes	characteristic
38	C₃×C₄	—	2	6	no	—
39	C₃×C₄	—	2	2	no	—
40	C₃×C₄	—	2	3	no	—
41	C₃×C₄	C₂×Q₈	1	6	yes	—
42	C₃×C₄	#41	1	2	yes	—
43	Q₈	—	2	6	no	—
44	Q₈	C₃×Q₈	1	4	yes	complemented
45	C₂×C₄	C₂³×C₃	1	2	yes	—
46	C₂×C₄	C₂³×C₃	1	3	yes	—
47	C₂×C₄	C₂³×C₃	1	6	yes	—
48	C₂×C₄	C₂³×C₃	1	3	yes	—
49	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
50	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
51	C₂×C₃	C₂×#41	1	1	yes	characteristic
52	C₂×C₃	2₋¹⁺⁴	1	1	yes	characteristic
53	C₂²	C₂⁴×C₃	1	1	yes	characteristic
54	C₄	—	2	6	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	3	no	—
57	C₄	C₂×C₃×Q₈	1	6	yes	—
58	C₄	C₃×#41	1	2	yes	—
59	C₃	#557	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	C₂²×C₃×Q₈	1	1	yes	characteristic
61	C₂	C₂×C₃×#41	1	1	yes	characteristic
62	C₂	C₃×2₋¹⁺⁴	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. #557	C₃	direct (N × H)
22. C₃×Q₈	Q₈	semidirect
44. Q₈	C₃×Q₈	semidirect
59. C₃	#557	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×#125	2
C₃×C₄×Q₈	2
#557	3

Subgroups — C3×#557 #5887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#557 #5887