Subgroups — C₃⋊#10597713 #14273151

Order 1872.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	#10597794	C₃	1	1	yes	maximal, characteristic, complemented
3	#10597713	—	3	1	no	maximal
4	C₃⋊(Dic₁₃⋊C₃)	—	4	1	no	maximal
5	C₃×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
6	D₁₅₆	—	3	1	no	—
7	C₄×D₃₉	—	3	1	no	—
8	Q₈⋊(C₁₃⋊C₃)	—	2	1	no	—
9	Q₈⋊(C₁₃⋊C₃)	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₃⋊C₃	—	4	1	no	—
11	#6131	—	3	1	no	Hall
12	C₂×D₃₉	—	3	1	no	—
13	C₃×C₄×C₁₃	—	3	1	no	—
14	Dic₃₉	A₄	1	1	yes	characteristic
15	Dic₁₃⋊C₃	—	12	1	no	—
16	C₃⋊(#41⋊C₃)	—	13	1	no	maximal, Hall
17	C₃×C₁₃⋊C₃	—	4	1	no	Hall
18	Q₈×C₁₃	C₃×D₃	1	1	yes	characteristic
19	D₅₂	—	9	1	no	—
20	C₄×D₁₃	—	9	1	no	—
21	C₂×C₃×C₁₃	C₂×A₄	1	1	yes	characteristic
22	D₃₉	—	6	1	no	—
23	C₂×C₁₃⋊C₃	—	4	1	no	—
24	C₂×C₁₃⋊C₃	—	8	1	no	—
25	C₃×SL(2,𝔽₃)	—	13	1	no	—
26	C₂×D₁₃	—	9	1	no	—
27	C₄×C₁₃	—	3	1	no	—
28	Dic₁₃	—	3	1	no	—
29	#239	—	13	1	no	—
30	#41⋊C₃	—	39	1	no	—
31	C₃×C₁₃	#41⋊C₃	1	1	yes	characteristic, complemented
32	C₁₃⋊C₃	—	4	1	no	—
33	C₁₃⋊C₃	—	8	1	no	—
34	C₃×Dic₃	—	52	1	no	—
35	C₂×C₁₃	D₃×A₄	1	1	yes	characteristic
36	D₁₃	—	18	1	no	—
37	C₃×Q₈	D₁₃⋊C₃	1	1	yes	characteristic
38	D₁₂	—	39	1	no	—
39	C₄×D₃	—	39	1	no	—
40	SL(2,𝔽₃)	—	13	1	no	—
41	SL(2,𝔽₃)	—	26	1	no	—
42	C₂×C₃²	—	52	1	no	—
43	#41	—	39	1	no	Sylow
44	C₁₃	C₃⋊(#41⋊C₃)	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₃	—	39	1	no	—
46	C₃×C₄	—	3	1	no	—
47	C₃×C₄	—	156	1	no	—
48	Dic₃	—	13	1	no	—
49	C₃²	—	52	1	no	Sylow
50	Q₈	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic
51	D₄	—	117	1	no	—
52	C₂×C₄	—	117	1	no	—
53	C₂×C₃	—	52	1	no	—
54	C₂×C₃	—	104	1	no	—
55	C₂×C₃	D₁₃⋊A₄	1	1	yes	characteristic
56	D₃	—	78	1	no	—
57	C₂²	—	117	1	no	—
58	C₄	—	3	1	no	—
59	C₄	—	39	1	no	—
60	C₃	—	52	1	no	—
61	C₃	—	104	1	no	—
62	C₃	#10597713	1	1	yes	characteristic, complemented
63	C₂	—	234	1	no	—
64	C₂	C₃⋊(D₁₃⋊A₄)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(D₁₃⋊A₄)
commutator, Fitting, cosocle, hypocenter	C₃×Q₈×C₁₃	C₂×C₃
socle	C₂×C₃×C₁₃	C₂×A₄
LCS	G ▷ C₃×Q₈×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈⋊(C₁₃⋊C₃)	C₂	semidirect
2. #10597794	C₃	semidirect
9. Q₈⋊(C₁₃⋊C₃)	D₃	semidirect
31. C₃×C₁₃	#41⋊C₃	semidirect
44. C₁₃	C₃⋊(#41⋊C₃)	semidirect
62. C₃	#10597713	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈⋊(C₁₃⋊C₃)	2
#10597794	3
#10597713	3
C₃⋊(Dic₁₃⋊C₃)	4
C₃⋊(#41⋊C₃)	13

Subgroups — C3⋊#10597713 #14273151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#10597713 #14273151