Subgroups — C₃×#1359 #67919

Order 384.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#492	C₂	1	1	yes	maximal, characteristic
2	C₃×#364	C₂	1	2	yes	maximal, complemented
3	#1359	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×SD₁₆	—	2	2	no	—
5	C₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₃×#127	C₄	1	1	yes	characteristic
7	C₃×M₃₂	—	2	2	no	—
8	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
9	#492	C₂×C₃	1	1	yes	characteristic
10	#364	C₂×C₃	1	2	yes	complemented
11	C₂×C₃×Q₈	—	2	1	no	—
12	C₂×C₃×D₄	—	2	1	no	—
13	C₂×C₃×D₄	—	4	1	no	—
14	C₃×SD₁₆	—	4	2	no	—
15	C₃×SD₁₆	—	4	2	no	—
16	C₂×C₃×C₈	D₄	1	2	yes	—
17	C₃×C₄⋊C₄	—	4	1	no	—
18	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
19	C₃×C₁₆	—	4	2	no	—
20	C₂×SD₁₆	—	2	2	no	—
21	C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
22	#127	C₃×C₄	1	1	yes	characteristic
23	M₃₂	—	2	2	no	—
24	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
25	C₂³×C₃	—	4	1	no	—
26	C₃×Q₈	—	4	2	no	—
27	C₃×D₄	—	4	2	no	—
28	C₃×D₄	—	8	2	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	4	1	no	—
31	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₃×C₈	D₈	1	2	yes	—
33	C₃×C₈	SD₁₆	1	2	yes	—
34	C₂×Q₈	—	2	1	no	—
35	C₂×D₄	—	2	1	no	—
36	C₂×D₄	—	4	1	no	—
37	SD₁₆	—	4	2	no	—
38	SD₁₆	—	4	2	no	—
39	C₂×C₈	C₃×D₄	1	2	yes	—
40	C₄⋊C₄	—	4	1	no	—
41	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
42	C₁₆	—	4	2	no	—
43	C₂²×C₃	—	8	2	no	—
44	C₂²×C₃	—	8	1	no	—
45	C₂²×C₃	#100	1	1	yes	characteristic
46	C₃×C₄	—	2	2	no	—
47	C₃×C₄	—	8	1	no	—
48	C₃×C₄	#102	1	2	yes	—
49	C₂³	—	4	1	no	—
50	Q₈	—	4	2	no	—
51	D₄	—	4	2	no	—
52	D₄	—	8	2	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	4	1	no	—
55	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
56	C₈	C₃×D₈	1	2	yes	—
57	C₈	C₃×SD₁₆	1	2	yes	—
58	C₂×C₃	—	2	1	no	—
59	C₂×C₃	—	16	1	no	—
60	C₂×C₃	#331	1	1	yes	characteristic
61	C₂²	—	8	2	no	—
62	C₂²	—	8	1	no	—
63	C₂²	C₃×#100	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	8	1	no	—
66	C₄	C₃×#102	1	2	yes	—
67	C₃	#1359	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	C₃×#331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#331
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	C₄×C₈	C₂²×C₃
prime radical	C₃×#127	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#364	C₂	semidirect
3. #1359	C₃	direct (N × H)
10. #364	C₂×C₃	semidirect
67. C₃	#1359	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×#492	2
C₃×#364	2
#1359	3

Subgroups — C3×#1359 #67919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1359 #67919