Subgroups — C₃×#1358 #67918

Order 384.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₃×#364	C₂	1	2	yes	maximal
3	#1358	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×Q₁₆	—	2	2	no	—
5	C₃×C₄⋊Q₈	C₄	1	2	yes	—
6	C₃×M₃₂	—	2	2	no	—
7	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
8	#494	C₂×C₃	1	1	yes	characteristic
9	#364	C₂×C₃	1	2	yes	—
10	C₂×C₃×Q₈	—	2	2	no	—
11	C₃×Q₁₆	—	4	2	no	—
12	C₃×Q₁₆	—	4	2	no	—
13	C₂×C₃×C₈	D₄	1	2	yes	—
14	C₃×C₄⋊C₄	—	4	2	no	—
15	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
16	C₃×C₁₆	—	4	2	no	—
17	C₂×Q₁₆	—	2	2	no	—
18	C₄⋊Q₈	C₃×C₄	1	2	yes	—
19	M₃₂	—	2	2	no	—
20	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
21	C₃×Q₈	—	4	4	no	—
22	C₂×C₃×C₄	—	2	1	no	—
23	C₂×C₃×C₄	—	4	2	no	—
24	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₃×C₈	D₈	1	2	yes	—
26	C₃×C₈	SD₁₆	1	2	yes	—
27	C₂×Q₈	—	2	2	no	—
28	Q₁₆	—	4	2	no	—
29	Q₁₆	—	4	2	no	—
30	C₂×C₈	C₃×D₄	1	2	yes	—
31	C₄⋊C₄	—	4	2	no	—
32	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
33	C₁₆	—	4	2	no	—
34	C₂²×C₃	#100	1	1	yes	characteristic
35	C₃×C₄	—	2	2	no	—
36	C₃×C₄	—	8	2	no	—
37	C₃×C₄	#102	1	2	yes	—
38	Q₈	—	4	4	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	4	2	no	—
41	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
42	C₈	C₃×D₈	1	2	yes	—
43	C₈	C₃×SD₁₆	1	2	yes	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	#331	1	1	yes	characteristic
46	C₂²	C₃×#100	1	1	yes	characteristic
47	C₄	—	2	2	no	—
48	C₄	—	8	2	no	—
49	C₄	C₃×#102	1	2	yes	—
50	C₃	#1358	1	1	yes	characteristic, direct product factor, Sylow
51	C₂	—	2	1	no	—
52	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	C₂²×C₃	#100
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
3. #1358	C₃	direct (N × H)
50. C₃	#1358	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×#494	2
C₃×#364	2
#1358	3

Subgroups — C3×#1358 #67918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1358 #67918