Subgroups — C₃×#1658⋊C₃ #11919328

Order 1152.

114 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, complemented
2	C₃×#1658	C₃	1	1	yes	maximal, characteristic, complemented
3	#1658⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×#127⋊C₃	—	4	1	no	maximal
5	C₃×#564	C₂×C₃	1	1	yes	characteristic, complemented
6	#564⋊C₃	C₂×C₃	1	3	yes	complemented
7	C₃×#490	—	3	1	no	—
8	C₃×#330	—	3	1	no	—
9	C₃×C₄²⋊C₃	—	4	1	no	—
10	C₃×C₄²⋊C₃	—	8	2	no	—
11	#1658	C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₃×#127	A₄	1	1	yes	characteristic
13	C₃×#125	—	3	1	no	—
14	C₃×#125	—	6	2	no	—
15	#127⋊C₃	—	4	3	no	—
16	C₃×#102	—	6	2	no	—
17	C₃×#97	—	3	1	no	—
18	C₂×C₃×A₄	—	16	1	no	—
19	#564	C₂×C₃²	1	1	yes	characteristic, complemented
20	#490	—	3	1	no	—
21	#330	—	3	1	no	—
22	C₂×C₃×D₄	—	6	1	no	—
23	C₂×C₃×C₈	—	6	1	no	—
24	C₃×C₄⋊C₄	—	3	2	no	—
25	C₃×C₄⋊C₄	—	6	2	no	—
26	C₃×C₄⋊C₄	—	6	2	no	—
27	C₃×C₄²	—	2	2	no	—
28	C₃×C₄²	C₂×A₄	1	1	yes	characteristic
29	C₄²⋊C₃	—	4	3	no	—
30	C₄²⋊C₃	—	8	6	no	—
31	C₃×A₄	—	16	1	no	—
32	#127	C₃×A₄	1	1	yes	characteristic
33	#125	—	3	1	no	—
34	#125	—	6	2	no	—
35	#102	—	6	2	no	—
36	#97	—	3	1	no	—
37	C₂³×C₃	—	4	1	no	—
38	C₂×A₄	—	16	3	no	—
39	C₃×D₄	—	12	2	no	—
40	C₂×C₃×C₄	—	3	1	no	—
41	C₂×C₃×C₄	—	6	2	no	—
42	C₃×C₈	—	12	1	no	—
43	C₂×C₃²	—	64	1	no	—
44	C₂×D₄	—	6	1	no	—
45	C₂×C₈	—	6	1	no	—
46	C₄⋊C₄	—	3	2	no	—
47	C₄⋊C₄	—	6	2	no	—
48	C₄⋊C₄	—	6	2	no	—
49	C₄²	—	2	2	no	—
50	C₄²	C₂×C₃×A₄	1	1	yes	characteristic
51	C₂²×C₃	—	24	1	no	—
52	C₂²×C₃	#120⋊C₃	1	1	yes	characteristic
53	A₄	—	16	3	no	—
54	C₃×C₄	—	6	1	no	—
55	C₃×C₄	—	12	2	no	—
56	C₃²	—	64	1	no	Sylow
57	C₂³	—	4	1	no	—
58	D₄	—	12	2	no	—
59	C₂×C₄	—	3	1	no	—
60	C₂×C₄	—	6	2	no	—
61	C₈	—	12	1	no	—
62	C₂×C₃	—	3	1	no	—
63	C₂×C₃	—	16	1	no	—
64	C₂×C₃	—	64	3	no	—
65	C₂²	—	24	1	no	—
66	C₂²	C₃×#120⋊C₃	1	1	yes	characteristic
67	C₄	—	6	1	no	—
68	C₄	—	12	2	no	—
69	C₃	—	64	3	no	—
70	C₃	#1658⋊C₃	1	1	yes	characteristic, direct product factor
71	C₂	—	3	1	no	—
72	C₂	—	16	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#1658⋊C₃
commutator, cosocle, hypocenter	#564	C₂×C₃²
Frattini	C₄²	C₂×C₃×A₄
Fitting	C₃×#1658	C₃
socle	C₂²×C₃	#120⋊C₃
LCS	G ▷ #564
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#564⋊C₃	C₂	semidirect
2. C₃×#1658	C₃	semidirect
3. #1658⋊C₃	C₃	direct (N × H)
5. C₃×#564	C₂×C₃	semidirect
6. #564⋊C₃	C₂×C₃	semidirect
11. #1658	C₃²	semidirect
19. #564	C₂×C₃²	semidirect
70. C₃	#1658⋊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
C₃×#1658	3
#1658⋊C₃	3
C₃×#127⋊C₃	4

Subgroups — C3×#1658⋊C3 #11919328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1658⋊C₃ #11919328