Subgroups — C₃×#1415 #67975

Order 384.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
4	#1415	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₈	—	2	1	no	—
6	C₃×D₁₆	—	2	1	no	—
7	C₃×D₁₆	C₄	1	2	yes	complemented
8	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₃×#107	—	2	1	no	—
10	C₃×C₃₂	—	2	1	no	—
11	C₂×D₁₆	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic, complemented
13	#366	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×D₄	—	4	1	no	—
15	C₃×D₈	—	2	2	no	—
16	C₃×D₈	—	4	1	no	—
17	C₂×C₃×C₈	D₄	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	4	1	no	—
19	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₃×C₁₆	D₄	1	1	yes	characteristic
21	C₂×D₈	—	2	1	no	—
22	D₁₆	—	2	1	no	—
23	D₁₆	C₃×C₄	1	2	yes	complemented
24	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
25	#107	—	2	1	no	—
26	C₃₂	—	2	1	no	—
27	C₂³×C₃	—	8	1	no	—
28	C₃×D₄	—	4	2	no	—
29	C₃×D₄	—	8	1	no	—
30	C₂×C₃×C₄	—	8	1	no	—
31	C₂×C₃×C₄	D₈	1	1	yes	characteristic
32	C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
33	C₃×C₈	SD₁₆	1	1	yes	characteristic
34	C₂×D₄	—	4	1	no	—
35	D₈	—	2	2	no	—
36	D₈	—	4	1	no	—
37	C₂×C₈	C₃×D₄	1	1	yes	characteristic
38	C₄⋊C₄	—	4	1	no	—
39	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
40	C₁₆	C₃×D₄	1	1	yes	characteristic
41	C₂²×C₃	—	8	2	no	—
42	C₂²×C₃	—	16	1	no	—
43	C₂²×C₃	—	16	1	no	—
44	C₂²×C₃	D₁₆	1	1	yes	characteristic
45	C₃×C₄	—	16	1	no	—
46	C₃×C₄	#102	1	1	yes	characteristic
47	C₃×C₄	SD₃₂	1	1	yes	characteristic
48	C₂³	—	8	1	no	—
49	D₄	—	4	2	no	—
50	D₄	—	8	1	no	—
51	C₂×C₄	—	8	1	no	—
52	C₂×C₄	C₃×D₈	1	1	yes	characteristic
53	C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
54	C₈	C₃×SD₁₆	1	1	yes	characteristic
55	C₂×C₃	—	16	2	no	—
56	C₂×C₃	#357	1	1	yes	characteristic
57	C₂×C₃	D₃₂	1	1	yes	characteristic
58	C₂×C₃	SD₆₄	1	1	yes	characteristic
59	C₂²	—	8	2	no	—
60	C₂²	—	16	1	no	—
61	C₂²	—	16	1	no	—
62	C₂²	C₃×D₁₆	1	1	yes	characteristic
63	C₄	—	16	1	no	—
64	C₄	C₃×#102	1	1	yes	characteristic
65	C₄	C₃×SD₃₂	1	1	yes	characteristic
66	C₃	#1415	1	1	yes	characteristic, direct product factor, Sylow
67	C₂	—	16	2	no	—
68	C₂	C₃×#357	1	1	yes	characteristic
69	C₂	C₃×D₃₂	1	1	yes	characteristic
70	C₂	C₃×SD₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₁₆
commutator	C₁₆	C₂×C₃×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
prime radical	C₂×C₃×D₁₆	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₃₂	C₂	semidirect
3. C₃×#366	C₂	semidirect
4. #1415	C₃	direct (N × H)
7. C₃×D₁₆	C₄	semidirect
12. C₂×C₃₂	C₂×C₃	semidirect
13. #366	C₂×C₃	semidirect
23. D₁₆	C₃×C₄	semidirect
66. C₃	#1415	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×D₁₆	2
C₂×C₃×C₃₂	2
C₃×#366	2
#1415	3

Subgroups — C3×#1415 #67975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1415 #67975