Subgroups — C₃×#489 #5363

Order 192.

100 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, complemented
2	C₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×#103	C₂	1	2	yes	maximal, complemented
4	C₃×#102	C₂	1	2	yes	maximal
5	C₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	#489	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	—	2	1	no	—
8	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₂²⋊C₄	—	2	1	no	—
14	C₃×C₂²⋊C₄	—	2	1	no	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
17	#124	C₂×C₃	1	1	yes	characteristic
18	#103	C₂×C₃	1	2	yes	complemented
19	#102	C₂×C₃	1	2	yes	—
20	#97	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂³×C₃	—	2	1	no	—
22	C₃×Q₈	—	2	2	no	—
23	C₃×Q₈	—	4	2	no	—
24	C₃×D₄	—	2	2	no	—
25	C₂×C₃×C₄	—	2	1	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	D₄	1	1	yes	characteristic
28	C₂×C₃×C₄	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
30	C₃×C₈	—	2	2	no	—
31	C₂×Q₈	—	2	1	no	—
32	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
33	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₈	C₂²×C₃	1	2	yes	—
35	C₄⋊C₄	—	2	1	no	—
36	C₄⋊C₄	C₂²×C₃	1	2	yes	—
37	C₂²⋊C₄	—	2	1	no	—
38	C₂²⋊C₄	—	2	1	no	—
39	C₄²	C₂²×C₃	1	1	yes	characteristic
40	C₂²×C₃	—	4	1	no	—
41	C₂²×C₃	—	4	1	no	—
42	C₂²×C₃	—	4	1	no	—
43	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
44	C₃×C₄	—	2	1	no	—
45	C₃×C₄	—	2	1	no	—
46	C₃×C₄	—	4	1	no	—
47	C₃×C₄	—	4	2	no	—
48	C₃×C₄	#41	1	2	yes	—
49	C₂³	—	2	1	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	4	2	no	—
52	D₄	—	2	2	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	C₃×D₄	1	1	yes	characteristic
56	C₂×C₄	C₃×D₄	1	1	yes	characteristic
57	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₂×C₃	—	8	1	no	—
60	C₂×C₃	#124	1	1	yes	characteristic
61	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
62	C₂×C₃	#137	1	1	yes	characteristic
63	C₂²	—	4	1	no	—
64	C₂²	—	4	1	no	—
65	C₂²	—	4	1	no	—
66	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	—	4	1	no	—
70	C₄	—	4	2	no	—
71	C₄	C₃×#41	1	2	yes	—
72	C₃	#489	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	8	1	no	—
74	C₂	C₃×#124	1	1	yes	characteristic
75	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
76	C₂	C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂²
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
1. C₃×C₄⋊Q₈	C₂	semidirect
3. C₃×#103	C₂	semidirect
5. C₃×#97	C₂	semidirect
6. #489	C₃	direct (N × H)
16. C₄⋊Q₈	C₂×C₃	semidirect
18. #103	C₂×C₃	semidirect
20. #97	C₂×C₃	semidirect
72. C₃	#489	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×#124	2
C₃×#103	2
C₃×#102	2
C₃×#97	2
#489	3

Subgroups — C3×#489 #5363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#489 #5363