Subgroups — C₃×#89315 #13051180

Order 1344.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#89315	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×D₈	—	2	1	no	—
6	C₃×Dic₂₈	—	2	1	no	—
7	C₃×C₇×C₁₆	C₂²	1	1	yes	characteristic
8	C₇×D₁₆	C₂×C₃	1	1	yes	characteristic
9	Dic₅₆	C₂×C₃	1	1	yes	characteristic, complemented
10	C₇⋊C₃₂	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×SD₆₄	—	7	1	no	maximal, Hall
12	C₃×C₇×D₄	—	4	1	no	—
13	C₃×Dic₁₄	—	4	1	no	—
14	C₃×C₇×C₈	D₄	1	1	yes	characteristic
15	C₇×D₈	—	2	1	no	—
16	Dic₂₈	—	2	1	no	—
17	C₇×C₁₆	C₂²×C₃	1	1	yes	characteristic
18	C₃×Q₃₂	—	7	1	no	—
19	C₃×D₁₆	D₇	1	1	yes	characteristic
20	C₃×C₃₂	—	7	1	no	—
21	C₂²×C₃×C₇	—	8	1	no	—
22	C₃×C₄×C₇	D₈	1	1	yes	characteristic
23	C₃×Dic₇	—	8	1	no	—
24	SD₆₄	—	7	1	no	Sylow
25	C₇×D₄	—	4	1	no	—
26	Dic₁₄	—	4	1	no	—
27	C₇×C₈	C₃×D₄	1	1	yes	characteristic
28	C₃×Q₁₆	—	14	1	no	—
29	C₃×D₈	—	2	1	no	—
30	C₃×C₁₆	C₂×D₇	1	1	yes	characteristic
31	C₂×C₃×C₇	—	16	1	no	—
32	C₂×C₃×C₇	D₁₆	1	1	yes	characteristic
33	Q₃₂	—	7	1	no	—
34	D₁₆	C₃×D₇	1	1	yes	characteristic
35	C₃₂	—	7	1	no	—
36	C₂²×C₇	—	8	1	no	—
37	C₄×C₇	C₃×D₈	1	1	yes	characteristic
38	Dic₇	—	8	1	no	—
39	C₃×Q₈	—	28	1	no	—
40	C₃×D₄	—	4	1	no	—
41	C₃×C₈	C₂²⋊D₇	1	1	yes	characteristic
42	C₃×C₇	SD₆₄	1	1	yes	characteristic, complemented, Hall
43	Q₁₆	—	14	1	no	—
44	D₈	—	2	1	no	—
45	C₁₆	C₂×C₃×D₇	1	1	yes	characteristic
46	C₂×C₇	—	16	1	no	—
47	C₂×C₇	C₃×D₁₆	1	1	yes	characteristic
48	C₂²×C₃	—	8	1	no	—
49	C₃×C₄	—	56	1	no	—
50	C₃×C₄	#1141	1	1	yes	characteristic
51	Q₈	—	28	1	no	—
52	D₄	—	4	1	no	—
53	C₈	C₃×C₂²⋊D₇	1	1	yes	characteristic
54	C₇	C₃×SD₆₄	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃	—	16	1	no	—
56	C₂×C₃	#6400	1	1	yes	characteristic
57	C₂²	—	8	1	no	—
58	C₄	—	56	1	no	—
59	C₄	C₃×#1141	1	1	yes	characteristic
60	C₃	#89315	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	16	1	no	—
62	C₂	C₃×#6400	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#6400
commutator, cosocle	C₇×C₁₆	C₂²×C₃
Frattini	C₁₆	C₂×C₃×D₇
Fitting, prime radical	C₃×C₇×D₁₆	C₂
socle	C₂×C₃×C₇	D₁₆
hypercenter	C₃×D₁₆	D₇
hypocenter	C₇	C₃×SD₆₄
LCS	G ▷ C₇×C₁₆ ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆ ◁ C₃×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₅₆	C₂	semidirect
3. C₃×C₇⋊C₃₂	C₂	semidirect
4. #89315	C₃	direct (N × H)
9. Dic₅₆	C₂×C₃	semidirect
10. C₇⋊C₃₂	C₂×C₃	semidirect
42. C₃×C₇	SD₆₄	semidirect
54. C₇	C₃×SD₆₄	semidirect
60. C₃	#89315	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×C₇×D₁₆	2
C₃×Dic₅₆	2
C₃×C₇⋊C₃₂	2
#89315	3
C₃×SD₆₄	7

Subgroups — C3×#89315 #13051180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89315 #13051180