Subgroups — C₃×#491 #5365

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#125	C₂	1	1	yes	maximal, characteristic
3	C₃×#103	C₂	1	4	yes	maximal
4	C₃×#97	C₂	1	1	yes	maximal, characteristic
5	#491	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	C₂²	1	2	yes	—
7	C₂×C₃×C₈	C₂²	1	2	yes	—
8	C₃×C₄⋊C₄	—	2	2	no	—
9	C₃×C₄⋊C₄	—	2	2	no	—
10	C₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₃×C₄²	C₂²	1	1	yes	characteristic
12	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
13	#125	C₂×C₃	1	1	yes	characteristic
14	#103	C₂×C₃	1	4	yes	—
15	#97	C₂×C₃	1	1	yes	characteristic
16	C₃×Q₈	—	2	4	no	—
17	C₂×C₃×C₄	—	2	2	no	—
18	C₂×C₃×C₄	—	2	2	no	—
19	C₂×C₃×C₄	D₄	1	2	yes	—
20	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₃×C₈	—	2	2	no	—
22	C₂×Q₈	C₂²×C₃	1	2	yes	—
23	C₂×C₈	C₂²×C₃	1	2	yes	—
24	C₄⋊C₄	—	2	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄⋊C₄	C₂²×C₃	1	2	yes	—
27	C₄²	C₂²×C₃	1	1	yes	characteristic
28	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
29	C₃×C₄	—	2	2	no	—
30	C₃×C₄	—	4	2	no	—
31	C₃×C₄	—	4	2	no	—
32	C₃×C₄	#41	1	2	yes	—
33	Q₈	—	2	4	no	—
34	C₂×C₄	—	2	2	no	—
35	C₂×C₄	—	2	2	no	—
36	C₂×C₄	C₃×D₄	1	2	yes	—
37	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
38	C₈	—	2	2	no	—
39	C₂×C₃	#124	1	1	yes	characteristic
40	C₂×C₃	#137	1	2	yes	—
41	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	4	2	no	—
44	C₄	—	4	2	no	—
45	C₄	C₃×#41	1	2	yes	—
46	C₃	#491	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	C₃×#124	1	1	yes	characteristic
48	C₂	C₃×#137	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

Complements

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

N	H ≅ G/N	type
5. #491	C₃	direct (N × H)
46. C₃	#491	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×#103	2
C₃×#97	2
#491	3

Subgroups — C3×#491 #5365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#491 #5365