Subgroups — C₃⋊C₈² #10589077

Order 576.

170 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₈×C₃⋊C₈	—	3	2	no	maximal
4	C₃²×C₄²	C₂²	1	1	yes	characteristic
5	C₂×C₃⋊(C₃⋊C₈)	C₄	1	2	yes	—
6	C₂×C₃×C₃⋊C₈	C₄	1	4	yes	—
7	C₃×C₄×C₈	—	3	2	no	—
8	C₄×C₃⋊C₈	—	3	2	no	—
9	C₄×C₃⋊C₈	—	6	1	no	—
10	C₄×C₃⋊C₈	D₃	1	2	yes	—
11	C₂×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃²×C₄	C₂×C₄	1	2	yes	—
13	C₃⋊(C₃⋊C₈)	C₈	1	4	yes	complemented
14	C₃×C₃⋊C₈	C₈	1	8	yes	complemented
15	C₈²	—	9	1	no	Sylow
16	C₂×C₃×C₈	—	3	4	no	—
17	C₃×C₄²	—	2	1	no	—
18	C₃×C₄²	C₂×D₃	1	2	yes	—
19	C₂×C₃⋊C₈	—	3	4	no	—
20	C₂×C₃⋊C₈	—	6	2	no	—
21	C₂×C₃⋊C₈	Dic₃	1	4	yes	—
22	C₂²×C₃²	C₄²	1	1	yes	characteristic
23	C₃²×C₄	C₂×C₈	1	2	yes	—
24	C₃²×C₄	C₂×C₈	1	4	yes	—
25	C₄×C₈	—	3	2	no	—
26	C₄×C₈	—	9	1	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	C₄×D₃	1	2	yes	—
30	C₂×C₃×C₄	C₄×D₃	1	2	yes	—
31	C₂×C₃×C₄	C₂×Dic₃	1	2	yes	—
32	C₃×C₈	—	3	8	no	—
33	C₃⋊C₈	—	3	8	no	—
34	C₃⋊C₈	—	6	4	no	—
35	C₃⋊C₈	C₃⋊C₈	1	8	yes	direct product factor
36	C₂×C₃²	C₄×C₈	1	2	yes	—
37	C₂×C₃²	C₄×C₈	1	1	yes	characteristic
38	C₂×C₈	—	3	4	no	—
39	C₂×C₈	—	9	2	no	—
40	C₄²	D₃²	1	1	yes	characteristic
41	C₂²×C₃	—	2	1	no	—
42	C₂²×C₃	C₄×Dic₃	1	2	yes	—
43	C₃×C₄	—	2	4	no	—
44	C₃×C₄	—	2	2	no	—
45	C₃×C₄	D₃×C₈	1	4	yes	—
46	C₃×C₄	D₃×C₈	1	4	yes	—
47	C₃×C₄	C₂×C₃⋊C₈	1	4	yes	—
48	C₃²	C₈²	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₄	D₃×Dic₃	1	2	yes	—
50	C₂×C₄	#624	1	1	yes	characteristic
51	C₈	—	3	8	no	—
52	C₈	—	9	4	no	—
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	C₄×C₃⋊C₈	1	2	yes	—
56	C₂×C₃	C₈×Dic₃	1	2	yes	—
57	C₂×C₃	C₈×Dic₃	1	2	yes	—
58	C₂²	Dic₃²	1	1	yes	characteristic
59	C₄	D₃×C₃⋊C₈	1	4	yes	—
60	C₄	#3710	1	2	yes	—
61	C₃	—	2	1	no	—
62	C₃	C₈×C₃⋊C₈	1	2	yes	complemented
63	C₂	Dic₃×C₃⋊C₈	1	2	yes	—
64	C₂	#63553	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄²	D₃²
commutator, hypocenter	C₃²	C₈²
Fitting, cosocle	C₃²×C₄²	C₂²
socle, prime radical	C₂²×C₃²	C₄²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
13. C₃⋊(C₃⋊C₈)	C₈	semidirect
14. C₃×C₃⋊C₈	C₈	semidirect
35. C₃⋊C₈	C₃⋊C₈	direct (N × H)
48. C₃²	C₈²	semidirect
62. C₃	C₈×C₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃⋊(C₃⋊C₈)	2
C₃×C₄×C₃⋊C₈	2
C₈×C₃⋊C₈	3

Subgroups — C3⋊C82 #10589077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊C₈² #10589077