Subgroups — C₃×#480 #5354

Order 192.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#107	C₂	1	2	yes	maximal, complemented
4	C₃×#102	C₂	1	2	yes	maximal, complemented
5	C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#480	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₄	—	2	1	no	—
8	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄	—	2	1	no	—
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	2	yes	—
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	#121	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
18	#107	C₂×C₃	1	2	yes	complemented
19	#102	C₂×C₃	1	2	yes	complemented
20	C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂³×C₃	—	2	1	no	—
22	C₂³×C₃	D₄	1	1	yes	characteristic
23	C₃×D₄	—	2	2	no	—
24	C₃×D₄	—	4	2	no	—
25	C₂×C₃×C₄	—	2	2	no	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	—	4	2	no	—
29	C₂×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	—	2	2	no	—
32	C₂×D₄	—	2	1	no	—
33	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
34	C₂²×C₄	—	2	1	no	—
35	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
36	C₂×C₈	C₂²×C₃	1	2	yes	—
37	C₄⋊C₄	—	2	1	no	—
38	C₄⋊C₄	C₂²×C₃	1	2	yes	—
39	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
40	C₂²⋊C₄	—	2	1	no	—
41	C₂²×C₃	—	2	1	no	—
42	C₂²×C₃	—	2	1	no	—
43	C₂²×C₃	—	4	1	no	—
44	C₂²×C₃	—	4	1	no	—
45	C₂²×C₃	—	4	1	no	—
46	C₂²×C₃	D₈	1	2	yes	—
47	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	—	4	2	no	—
50	C₃×C₄	—	4	1	no	—
51	C₃×C₄	#41	1	2	yes	—
52	C₂³	—	2	1	no	—
53	C₂³	C₃×D₄	1	1	yes	characteristic
54	D₄	—	2	2	no	—
55	D₄	—	4	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	C₃×D₄	1	1	yes	characteristic
61	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₂×C₃	—	2	2	no	—
64	C₂×C₃	—	8	1	no	—
65	C₂×C₃	#123	1	1	yes	characteristic
66	C₂×C₃	C₂×D₈	1	1	yes	characteristic
67	C₂×C₃	#137	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	4	1	no	—
71	C₂²	—	4	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	C₃×D₈	1	2	yes	—
74	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	2	no	—
77	C₄	—	4	1	no	—
78	C₄	C₃×#41	1	2	yes	—
79	C₃	#480	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	2	2	no	—
81	C₂	—	8	1	no	—
82	C₂	C₃×#123	1	1	yes	characteristic
83	C₂	C₂×C₃×D₈	1	1	yes	characteristic
84	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	C₃×#121	C₂
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
2. C₂×C₃×C₄⋊C₄	C₂	semidirect
3. C₃×#107	C₂	semidirect
4. C₃×#102	C₂	semidirect
5. C₃×C₂²⋊C₈	C₂	semidirect
6. #480	C₃	direct (N × H)
17. C₂×C₄⋊C₄	C₂×C₃	semidirect
18. #107	C₂×C₃	semidirect
19. #102	C₂×C₃	semidirect
20. C₂²⋊C₈	C₂×C₃	semidirect
79. C₃	#480	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×#121	2
C₂×C₃×C₄⋊C₄	2
C₃×#107	2
C₃×#102	2
C₃×C₂²⋊C₈	2
#480	3

Subgroups — C3×#480 #5354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#480 #5354