Subgroups — C₃×#1411 #67971

Order 384.

94 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×#356	C₂	1	2	yes	maximal
3	#1411	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×Q₁₆	—	2	2	no	—
5	C₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₃×#101	—	2	2	no	—
8	C₃×C₄×C₈	C₄	1	1	yes	characteristic
9	#494	C₂×C₃	1	1	yes	characteristic
10	#356	C₂×C₃	1	2	yes	—
11	C₂×C₃×Q₈	—	2	1	no	—
12	C₂×C₃×Q₈	D₄	1	2	yes	—
13	C₃×Q₁₆	—	4	4	no	—
14	C₃×M₁₆	—	4	2	no	—
15	C₂×C₃×C₈	—	2	1	no	—
16	C₃×C₄⋊C₄	—	4	1	no	—
17	C₃×C₄⋊C₄	—	4	1	no	—
18	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
19	C₂×Q₁₆	—	2	2	no	—
20	C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
21	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
22	#101	—	2	2	no	—
23	C₄×C₈	C₃×C₄	1	1	yes	characteristic
24	C₃×Q₈	—	4	2	no	—
25	C₃×Q₈	—	4	2	no	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	—	4	1	no	—
29	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₈	—	2	2	no	—
31	C₃×C₈	—	8	2	no	—
32	C₂×Q₈	—	2	1	no	—
33	C₂×Q₈	C₃×D₄	1	2	yes	—
34	Q₁₆	—	4	4	no	—
35	M₁₆	—	4	2	no	—
36	C₂×C₈	—	2	1	no	—
37	C₄⋊C₄	—	4	1	no	—
38	C₄⋊C₄	—	4	1	no	—
39	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂²×C₃	#99	1	1	yes	characteristic
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	4	2	no	—
44	C₃×C₄	—	8	1	no	—
45	Q₈	—	4	2	no	—
46	Q₈	—	4	2	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	8	2	no	—
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	#353	1	1	yes	characteristic
55	C₂²	C₃×#99	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	2	1	no	—
58	C₄	—	4	2	no	—
59	C₄	—	8	1	no	—
60	C₃	#1411	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2	1	no	—
62	C₂	C₃×#353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#353
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	C₄⋊Q₈	C₂²×C₃
prime radical	C₂²×C₃	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1411	C₃	direct (N × H)
60. C₃	#1411	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×#356	2
#1411	3

Subgroups — C3×#1411 #67971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1411 #67971