Subgroups — C₂×C₃×#564⋊C₃ #11919842

Order 1152.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#564⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×#564	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#564⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×C₄²⋊C₃	—	4	5	no	maximal
5	C₃×#564	—	3	5	no	—
6	C₃×#564	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×#125	—	3	5	no	—
8	#564⋊C₃	C₂×C₃	1	3	yes	direct product factor
9	C₃×C₄²⋊C₃	—	4	5	no	—
10	C₂×#564	C₃²	1	1	yes	characteristic, complemented, Sylow
11	C₃×#125	—	3	30	no	—
12	C₃×#125	—	3	5	no	—
13	C₃×#125	—	3	5	no	—
14	C₂×C₃×C₄⋊C₄	—	3	10	no	—
15	C₂×C₃×C₄²	A₄	1	5	yes	—
16	C₂×C₄²⋊C₃	—	4	15	no	—
17	C₂×C₃×A₄	—	16	1	no	—
18	#564	—	3	5	no	—
19	#564	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₂×#125	—	3	5	no	—
21	C₂²×C₃×C₄	—	3	5	no	—
22	C₃×C₄⋊C₄	—	3	10	no	—
23	C₃×C₄⋊C₄	—	3	30	no	—
24	C₃×C₄²	—	3	5	no	—
25	C₃×C₄²	C₂×A₄	1	5	yes	—
26	C₄²⋊C₃	—	4	15	no	—
27	C₃×A₄	—	16	1	no	—
28	#125	—	3	30	no	—
29	#125	—	3	5	no	—
30	#125	—	3	5	no	—
31	C₂×C₄⋊C₄	—	3	10	no	—
32	C₂×C₄²	C₃×A₄	1	5	yes	—
33	C₂³×C₃	C₂²⋊A₄	1	1	yes	characteristic
34	C₂×A₄	—	16	3	no	—
35	C₂×C₃×C₄	—	3	5	no	—
36	C₂×C₃×C₄	—	3	5	no	—
37	C₂×C₃×C₄	—	6	5	no	—
38	C₂×C₃×C₄	—	6	5	no	—
39	C₂×C₃²	—	64	1	no	—
40	C₂²×C₄	—	3	5	no	—
41	C₄⋊C₄	—	3	10	no	—
42	C₄⋊C₄	—	3	30	no	—
43	C₄²	—	3	5	no	—
44	C₄²	C₂×C₃×A₄	1	5	yes	—
45	C₂²×C₃	—	3	1	no	—
46	C₂²×C₃	—	3	1	no	—
47	C₂²×C₃	C₂×C₂²⋊A₄	1	1	yes	characteristic
48	A₄	—	16	3	no	—
49	C₃×C₄	—	6	5	no	—
50	C₃×C₄	—	6	5	no	—
51	C₃²	—	64	1	no	Sylow
52	C₂³	C₃×C₂²⋊A₄	1	1	yes	characteristic
53	C₂×C₄	—	3	5	no	—
54	C₂×C₄	—	3	5	no	—
55	C₂×C₄	—	6	5	no	—
56	C₂×C₄	—	6	5	no	—
57	C₂×C₃	—	3	1	no	—
58	C₂×C₃	—	3	1	no	—
59	C₂×C₃	—	64	3	no	—
60	C₂×C₃	#564⋊C₃	1	1	yes	characteristic, direct product factor
61	C₂²	—	3	1	no	—
62	C₂²	—	3	1	no	—
63	C₂²	C₂×C₃×C₂²⋊A₄	1	1	yes	characteristic
64	C₄	—	6	5	no	—
65	C₄	—	6	5	no	—
66	C₃	—	64	3	no	—
67	C₃	C₂×#564⋊C₃	1	1	yes	characteristic, direct product factor
68	C₂	—	3	1	no	—
69	C₂	—	3	1	no	—
70	C₂	C₃×#564⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#564⋊C₃
commutator, cosocle, hypocenter	#564	C₂×C₃²
Frattini	C₂²	C₂×C₃×C₂²⋊A₄
Fitting	C₂×C₃×#564	C₃
socle	C₂³×C₃	C₂²⋊A₄
LCS	G ▷ #564
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#564⋊C₃	C₂	direct (N × H)
2. C₂×C₃×#564	C₃	semidirect
3. C₂×#564⋊C₃	C₃	direct (N × H)
6. C₃×#564	C₂×C₃	semidirect
8. #564⋊C₃	C₂×C₃	direct (N × H)
10. C₂×#564	C₃²	semidirect
19. #564	C₂×C₃²	semidirect
60. C₂×C₃	#564⋊C₃	direct (N × H)
67. C₃	C₂×#564⋊C₃	direct (N × H)
70. C₂	C₃×#564⋊C₃	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×#564⋊C₃	2
C₂×C₃×#564	3
C₂×#564⋊C₃	3
C₂×C₃×C₄²⋊C₃	4

Subgroups — C2×C3×#564⋊C3 #11919842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#564⋊C₃ #11919842