Subgroups — C₃×#484 #5358

Order 192.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	2	yes	maximal, complemented
4	C₃×#103	C₂	1	2	yes	maximal, complemented
5	C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#484	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄	—	2	1	no	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	—	2	1	no	—
13	C₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₂²⋊C₄	—	2	1	no	—
16	C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
18	#107	C₂×C₃	1	2	yes	complemented
19	#103	C₂×C₃	1	2	yes	complemented
20	C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
21	C₂³×C₃	D₄	1	1	yes	characteristic
22	C₃×Q₈	—	2	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
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	—	4	2	no	—
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	C₂²×C₃	1	1	yes	characteristic
32	C₂²×C₄	—	2	1	no	—
33	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₈	C₂²×C₃	1	2	yes	—
35	C₄⋊C₄	—	2	1	no	—
36	C₄⋊C₄	—	2	1	no	—
37	C₄⋊C₄	C₂²×C₃	1	2	yes	—
38	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
39	C₂²⋊C₄	—	2	1	no	—
40	C₂²×C₃	—	2	1	no	—
41	C₂²×C₃	—	2	1	no	—
42	C₂²×C₃	Q₁₆	1	2	yes	—
43	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
44	C₃×C₄	—	2	1	no	—
45	C₃×C₄	—	4	1	no	—
46	C₃×C₄	—	4	1	no	—
47	C₃×C₄	—	4	2	no	—
48	C₃×C₄	#41	1	2	yes	—
49	C₂³	C₃×D₄	1	1	yes	characteristic
50	Q₈	—	2	2	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	4	2	no	—
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	—	2	2	no	—
60	C₂×C₃	#123	1	1	yes	characteristic
61	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
62	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	—	2	1	no	—
65	C₂²	C₃×Q₁₆	1	2	yes	—
66	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	4	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	4	1	no	—
71	C₄	C₃×#41	1	2	yes	—
72	C₃	#484	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	2	2	no	—
74	C₂	C₃×#123	1	1	yes	characteristic
75	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic
76	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂³×C₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#107	C₂	semidirect
4. C₃×#103	C₂	semidirect
6. #484	C₃	direct (N × H)
18. #107	C₂×C₃	semidirect
19. #103	C₂×C₃	semidirect
72. C₃	#484	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×C₂²⋊Q₈	2
C₂×C₃×C₄⋊C₄	2
C₃×#107	2
C₃×#103	2
C₃×C₂²⋊C₈	2
#484	3

Subgroups — C3×#484 #5358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#484 #5358