Subgroups — C₃×#475 #5349

Order 192.

96 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×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#106	C₂	1	2	yes	maximal
4	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×#103	C₂	1	2	yes	maximal
6	#475	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×C₈	C₂²	1	2	yes	—
10	C₃×C₄⋊C₄	—	2	1	no	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₃×C₄²	—	2	1	no	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
17	C₄×Q₈	C₂×C₃	1	1	yes	characteristic
18	#106	C₂×C₃	1	2	yes	—
19	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
20	#103	C₂×C₃	1	2	yes	—
21	C₃×Q₈	—	2	1	no	—
22	C₃×Q₈	—	4	2	no	—
23	C₃×Q₈	Q₈	1	2	yes	complemented
24	C₂×C₃×C₄	—	2	1	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×C₈	C₂²×C₃	1	2	yes	—
34	C₄⋊C₄	—	2	1	no	—
35	C₄⋊C₄	—	2	1	no	—
36	C₄⋊C₄	C₂²×C₃	1	2	yes	—
37	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
38	C₄²	—	2	1	no	—
39	C₄²	C₂²×C₃	1	1	yes	characteristic
40	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	4	2	no	—
44	C₃×C₄	—	4	1	no	—
45	C₃×C₄	SD₁₆	1	2	yes	—
46	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
47	C₃×C₄	#41	1	1	yes	characteristic
48	Q₈	—	2	1	no	—
49	Q₈	—	4	2	no	—
50	Q₈	C₃×Q₈	1	2	yes	complemented
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	C₃×D₄	1	1	yes	characteristic
55	C₂×C₄	C₃×D₄	1	1	yes	characteristic
56	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
57	C₈	—	2	2	no	—
58	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
60	C₂×C₃	#137	1	1	yes	characteristic
61	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
62	C₄	—	2	2	no	—
63	C₄	—	2	1	no	—
64	C₄	—	4	2	no	—
65	C₄	—	4	1	no	—
66	C₄	C₃×SD₁₆	1	2	yes	—
67	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
68	C₄	C₃×#41	1	1	yes	characteristic
69	C₃	#475	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	C₃×C₂²⋊Q₈	1	1	yes	characteristic
71	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic
72	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
6. #475	C₃	direct (N × H)
23. C₃×Q₈	Q₈	semidirect
50. Q₈	C₃×Q₈	semidirect
69. C₃	#475	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×C₄×Q₈	2
C₃×#106	2
C₃×C₄⋊C₈	2
C₃×#103	2
#475	3

Subgroups — C3×#475 #5349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#475 #5349