Subgroups — C₃×#73290 #11919650

Order 1152.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2811	C₃	1	1	yes	maximal, characteristic, complemented
2	#73290	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂²⋊SL(2,𝔽₃)	—	4	2	no	maximal
4	C₂×C₃×C₄²⋊C₃	—	4	3	no	maximal
5	C₃×#395	—	3	2	no	—
6	C₃×#391	—	3	3	no	—
7	C₃×C₄²⋊C₃	—	4	3	no	—
8	#2811	C₃²	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₃×Q₈	—	3	1	no	—
10	C₂²×C₃×Q₈	A₄	1	2	yes	—
11	C₂²⋊SL(2,𝔽₃)	—	4	6	no	—
12	C₂×C₃×C₄⋊C₄	—	3	3	no	—
13	C₂×C₃×C₄²	A₄	1	3	yes	—
14	C₂×C₄²⋊C₃	—	4	9	no	—
15	C₃×#95	—	3	6	no	—
16	C₂×C₃×A₄	—	16	1	no	—
17	C₃×SL(2,𝔽₃)	—	16	8	no	—
18	#395	—	3	2	no	—
19	#391	—	3	3	no	—
20	C₂×C₃×Q₈	—	3	4	no	—
21	C₂×C₃×Q₈	—	12	2	no	—
22	C₂×C₃×Q₈	—	12	1	no	—
23	C₂×C₃×Q₈	—	12	1	no	—
24	C₂²×C₃×C₄	—	3	3	no	—
25	C₂²×C₃×C₄	—	3	2	no	—
26	C₃×C₄⋊C₄	—	12	3	no	—
27	C₃×C₄²	—	4	3	no	—
28	C₄²⋊C₃	—	4	9	no	—
29	C₃×A₄	—	16	1	no	—
30	C₂²×Q₈	—	3	1	no	—
31	C₂²×Q₈	C₃×A₄	1	2	yes	—
32	C₂×C₄⋊C₄	—	3	3	no	—
33	C₂×C₄²	C₃×A₄	1	3	yes	—
34	#95	—	3	6	no	—
35	C₂³×C₃	C₂²⋊A₄	1	1	yes	characteristic
36	C₂×A₄	—	16	3	no	—
37	C₃×Q₈	—	4	8	no	—
38	C₃×Q₈	—	12	4	no	—
39	C₂×C₃×C₄	—	3	6	no	—
40	C₂×C₃×C₄	—	6	3	no	—
41	C₂×C₃×C₄	—	6	3	no	—
42	C₂×C₃×C₄	—	6	6	no	—
43	SL(2,𝔽₃)	—	16	24	no	—
44	C₂×C₃²	—	64	1	no	—
45	C₂×Q₈	—	3	4	no	—
46	C₂×Q₈	—	12	2	no	—
47	C₂×Q₈	—	12	1	no	—
48	C₂×Q₈	—	12	1	no	—
49	C₂²×C₄	—	3	3	no	—
50	C₂²×C₄	—	3	2	no	—
51	C₄⋊C₄	—	12	3	no	—
52	C₄²	—	4	3	no	—
53	C₂²×C₃	—	3	1	no	—
54	C₂²×C₃	—	3	1	no	—
55	C₂²×C₃	#997	1	1	yes	characteristic
56	A₄	—	16	3	no	—
57	C₃×C₄	—	6	6	no	—
58	C₃×C₄	—	12	2	no	—
59	C₃²	—	64	1	no	Sylow
60	C₂³	C₃×C₂²⋊A₄	1	1	yes	characteristic
61	Q₈	—	4	8	no	—
62	Q₈	—	12	4	no	—
63	C₂×C₄	—	3	6	no	—
64	C₂×C₄	—	6	3	no	—
65	C₂×C₄	—	6	3	no	—
66	C₂×C₄	—	6	6	no	—
67	C₂×C₃	—	3	1	no	—
68	C₂×C₃	—	3	1	no	—
69	C₂×C₃	—	64	3	no	—
70	C₂×C₃	#5464	1	1	yes	characteristic
71	C₂²	—	3	1	no	—
72	C₂²	—	3	1	no	—
73	C₂²	C₃×#997	1	1	yes	characteristic
74	C₄	—	6	6	no	—
75	C₄	—	12	2	no	—
76	C₃	—	64	3	no	—
77	C₃	#73290	1	1	yes	characteristic, direct product factor
78	C₂	—	3	1	no	—
79	C₂	—	3	1	no	—
80	C₂	C₃×#5464	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#5464
commutator, cosocle, hypocenter	#2811	C₃²
Frattini	C₂³	C₃×C₂²⋊A₄
Fitting	C₃×#2811	C₃
socle	C₂³×C₃	C₂²⋊A₄
LCS	G ▷ #2811
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#2811	C₃	semidirect
2. #73290	C₃	direct (N × H)
8. #2811	C₃²	semidirect
77. C₃	#73290	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×#2811	3
#73290	3
C₃×C₂²⋊SL(2,𝔽₃)	4
C₂×C₃×C₄²⋊C₃	4

Subgroups — C3×#73290 #11919650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#73290 #11919650