Subgroups — C₃×#1412 #67972

Order 384.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#490	C₂	1	1	yes	maximal, characteristic
2	C₃×#353	C₂	1	2	yes	maximal
3	#1412	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃×#127	C₂²	1	1	yes	characteristic
5	C₃×#125	C₄	1	1	yes	characteristic, complemented
6	C₃×#102	—	2	2	no	—
7	C₃×#99	—	2	2	no	—
8	C₃×#97	C₄	1	1	yes	characteristic, complemented
9	#490	C₂×C₃	1	1	yes	characteristic
10	#353	C₂×C₃	1	2	yes	—
11	C₂×C₃×D₄	—	4	1	no	—
12	C₂×C₃×D₄	D₄	1	2	yes	—
13	C₂×C₃×C₈	—	2	1	no	—
14	C₃×C₄⋊C₄	—	2	1	no	—
15	C₃×C₄⋊C₄	—	4	1	no	—
16	C₃×C₂²⋊C₄	—	4	2	no	—
17	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
18	#127	C₂²×C₃	1	1	yes	characteristic
19	#125	C₃×C₄	1	1	yes	characteristic, complemented
20	#102	—	2	2	no	—
21	#99	—	2	2	no	—
22	#97	C₃×C₄	1	1	yes	characteristic, complemented
23	C₂³×C₃	—	2	2	no	—
24	C₃×D₄	—	4	2	no	—
25	C₃×D₄	—	8	2	no	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	—	4	1	no	—
28	C₂×C₃×C₄	—	8	2	no	—
29	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₈	—	4	1	no	—
31	C₂×D₄	—	4	1	no	—
32	C₂×D₄	C₃×D₄	1	2	yes	—
33	C₂×C₈	—	2	1	no	—
34	C₄⋊C₄	—	2	1	no	—
35	C₄⋊C₄	—	4	1	no	—
36	C₂²⋊C₄	—	4	2	no	—
37	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
38	C₂²×C₃	—	4	2	no	—
39	C₂²×C₃	—	8	2	no	—
40	C₂²×C₃	#99	1	1	yes	characteristic
41	C₃×C₄	—	2	1	no	—
42	C₃×C₄	—	4	1	no	—
43	C₃×C₄	—	8	1	no	—
44	C₃×C₄	—	16	2	no	—
45	C₂³	—	2	2	no	—
46	D₄	—	4	2	no	—
47	D₄	—	8	2	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	—	8	2	no	—
51	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
52	C₈	—	4	1	no	—
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	—	8	2	no	—
55	C₂×C₃	#354	1	1	yes	characteristic
56	C₂²	—	4	2	no	—
57	C₂²	—	8	2	no	—
58	C₂²	C₃×#99	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	8	1	no	—
62	C₄	—	16	2	no	—
63	C₃	#1412	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	—	2	1	no	—
65	C₂	—	8	2	no	—
66	C₂	C₃×#354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#354
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	#127	C₂²×C₃
prime radical	C₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#127 ◁ G

Complements

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

N	H ≅ G/N	type
3. #1412	C₃	direct (N × H)
5. C₃×#125	C₄	semidirect
8. C₃×#97	C₄	semidirect
19. #125	C₃×C₄	semidirect
22. #97	C₃×C₄	semidirect
63. C₃	#1412	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×#490	2
C₃×#353	2
#1412	3

Subgroups — C3×#1412 #67972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1412 #67972