Subgroups — C₃×#89317 #13051182

Order 1344.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	#89317	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×Q₁₆	—	2	1	no	—
6	C₃×Dic₂₈	—	2	1	no	—
7	C₃×C₇×C₁₆	C₂²	1	1	yes	characteristic
8	C₇×Q₃₂	C₂×C₃	1	1	yes	characteristic
9	Dic₅₆	C₂×C₃	1	1	yes	characteristic
10	C₇⋊C₃₂	C₂×C₃	1	1	yes	characteristic
11	C₃×Q₆₄	—	7	1	no	maximal, Hall
12	C₃×C₇×Q₈	—	4	1	no	—
13	C₃×Dic₁₄	—	4	1	no	—
14	C₃×C₇×C₈	D₄	1	1	yes	characteristic
15	C₇×Q₁₆	—	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×Q₃₂	D₇	1	1	yes	characteristic
20	C₃×C₃₂	—	7	1	no	—
21	C₃×C₄×C₇	—	8	1	no	—
22	C₃×C₄×C₇	D₈	1	1	yes	characteristic
23	C₃×Dic₇	—	8	1	no	—
24	Q₆₄	—	7	1	no	Sylow
25	C₇×Q₈	—	4	1	no	—
26	Dic₁₄	—	4	1	no	—
27	C₇×C₈	C₃×D₄	1	1	yes	characteristic
28	C₃×Q₁₆	—	2	1	no	—
29	C₃×Q₁₆	—	14	1	no	—
30	C₃×C₁₆	C₂×D₇	1	1	yes	characteristic
31	C₂×C₃×C₇	D₁₆	1	1	yes	characteristic
32	Q₃₂	—	7	1	no	—
33	Q₃₂	C₃×D₇	1	1	yes	characteristic
34	C₃₂	—	7	1	no	—
35	C₄×C₇	—	8	1	no	—
36	C₄×C₇	C₃×D₈	1	1	yes	characteristic
37	Dic₇	—	8	1	no	—
38	C₃×Q₈	—	4	1	no	—
39	C₃×Q₈	—	28	1	no	—
40	C₃×C₈	C₂²⋊D₇	1	1	yes	characteristic
41	C₃×C₇	Q₆₄	1	1	yes	characteristic, complemented, Hall
42	Q₁₆	—	2	1	no	—
43	Q₁₆	—	14	1	no	—
44	C₁₆	C₂×C₃×D₇	1	1	yes	characteristic
45	C₂×C₇	C₃×D₁₆	1	1	yes	characteristic
46	C₃×C₄	—	8	1	no	—
47	C₃×C₄	—	56	1	no	—
48	C₃×C₄	#1141	1	1	yes	characteristic
49	Q₈	—	4	1	no	—
50	Q₈	—	28	1	no	—
51	C₈	C₃×C₂²⋊D₇	1	1	yes	characteristic
52	C₇	C₃×Q₆₄	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃	#6400	1	1	yes	characteristic
54	C₄	—	8	1	no	—
55	C₄	—	56	1	no	—
56	C₄	C₃×#1141	1	1	yes	characteristic
57	C₃	#89317	1	1	yes	characteristic, direct product factor, Sylow
58	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	C₃×C₇×Q₃₂	C₂
socle, prime radical	C₂×C₃×C₇	D₁₆
hypercenter	C₃×Q₃₂	D₇
hypocenter	C₇	C₃×Q₆₄
LCS	G ▷ C₇×C₁₆ ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆ ◁ C₃×Q₃₂

Complements

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

N	H ≅ G/N	type
4. #89317	C₃	direct (N × H)
41. C₃×C₇	Q₆₄	semidirect
52. C₇	C₃×Q₆₄	semidirect
57. C₃	#89317	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×Q₃₂	2
C₃×Dic₅₆	2
C₃×C₇⋊C₃₂	2
#89317	3
C₃×Q₆₄	7

Subgroups — C3×#89317 #13051182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89317 #13051182