Subgroups — C₃×#479 #5353

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₃×#106	C₂	1	1	yes	maximal, characteristic
5	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₃×#103	C₂	1	1	yes	maximal, characteristic
7	C₃×#103	C₂	1	1	yes	maximal, characteristic
8	#479	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	—	2	1	no	—
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	—	2	1	no	—
15	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₄²	—	2	1	no	—
19	C₃×C₄²	C₂²	1	1	yes	characteristic
20	#125	C₂×C₃	1	1	yes	characteristic
21	C₄×Q₈	C₂×C₃	1	1	yes	characteristic
22	#107	C₂×C₃	1	1	yes	characteristic
23	#106	C₂×C₃	1	1	yes	characteristic
24	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
25	#103	C₂×C₃	1	1	yes	characteristic
26	#103	C₂×C₃	1	1	yes	characteristic
27	C₃×Q₈	—	2	1	no	—
28	C₃×Q₈	Q₈	1	2	yes	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	1	no	—
33	C₂×C₃×C₄	D₄	1	1	yes	characteristic
34	C₂×C₃×C₄	D₄	1	1	yes	characteristic
35	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
36	C₃×C₈	—	2	1	no	—
37	C₃×C₈	—	2	1	no	—
38	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
45	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
46	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
47	C₄²	—	2	1	no	—
48	C₄²	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
50	C₃×C₄	—	2	2	no	—
51	C₃×C₄	—	2	1	no	—
52	C₃×C₄	—	2	1	no	—
53	C₃×C₄	—	4	1	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
57	C₃×C₄	#41	1	1	yes	characteristic
58	Q₈	—	2	1	no	—
59	Q₈	C₃×Q₈	1	2	yes	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	C₃×D₄	1	1	yes	characteristic
65	C₂×C₄	C₃×D₄	1	1	yes	characteristic
66	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
70	C₂×C₃	#135	1	1	yes	characteristic
71	C₂×C₃	#137	1	1	yes	characteristic
72	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	4	1	no	—
79	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
80	C₄	C₃×#41	1	1	yes	characteristic
81	C₃	#479	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	C₃×C₂²⋊Q₈	1	1	yes	characteristic
83	C₂	C₃×#135	1	1	yes	characteristic
84	C₂	C₃×#137	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
8. #479	C₃	direct (N × H)
81. C₃	#479	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×#125	2
C₃×C₄×Q₈	2
C₃×#107	2
C₃×#106	2
C₃×C₄⋊C₈	2
C₃×#103	2
#479	3

Subgroups — C3×#479 #5353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#479 #5353