Subgroups — C₃²×#1840 #11768889

Order 1152.

588 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#376	C₂	1	1	yes	maximal, characteristic
2	C₃²×#336	C₂	1	6	yes	maximal
3	C₃×#1840	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²×C₈	C₂²	1	4	yes	—
5	C₂×C₃²×C₄²	C₂²	1	3	yes	—
6	C₃²×#95	C₄	1	4	yes	—
7	C₃×#376	C₂×C₃	1	4	yes	—
8	C₃×#336	C₂×C₃	1	24	yes	—
9	C₂²×C₃²×C₄	C₂×C₄	1	6	yes	—
10	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
11	C₂×C₃²×C₈	—	2	12	no	—
12	C₃²×C₄²	—	2	6	no	—
13	#1840	C₃²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₃×C₈	C₂²×C₃	1	16	yes	—
15	C₂×C₃×C₄²	C₂²×C₃	1	12	yes	—
16	C₃×#95	C₃×C₄	1	16	yes	—
17	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₃²×C₄	—	2	6	no	—
19	C₂×C₃²×C₄	—	2	12	no	—
20	C₂×C₃²×C₄	#41	1	6	yes	—
21	C₃²×C₈	—	4	4	no	—
22	#376	C₂×C₃²	1	1	yes	characteristic
23	#336	C₂×C₃²	1	6	yes	—
24	C₂²×C₃×C₄	C₂×C₃×C₄	1	24	yes	—
25	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
26	C₂×C₃×C₈	—	2	48	no	—
27	C₃×C₄²	—	2	24	no	—
28	C₂²×C₃²	#117	1	3	yes	—
29	C₂²×C₃²	#131	1	4	yes	—
30	C₃²×C₄	—	4	6	no	—
31	C₃²×C₄	#126	1	4	yes	—
32	C₂²×C₈	C₂²×C₃²	1	4	yes	—
33	C₂×C₄²	C₂²×C₃²	1	3	yes	—
34	#95	C₃²×C₄	1	4	yes	—
35	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
36	C₂×C₃×C₄	—	2	24	no	—
37	C₂×C₃×C₄	—	2	48	no	—
38	C₂×C₃×C₄	C₃×#41	1	24	yes	—
39	C₃×C₈	—	4	16	no	—
40	C₂×C₃²	#383	1	1	yes	characteristic
41	C₂×C₃²	#433	1	6	yes	—
42	C₂²×C₄	C₂×C₃²×C₄	1	6	yes	—
43	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
44	C₂×C₈	—	2	12	no	—
45	C₄²	—	2	6	no	—
46	C₂²×C₃	C₃×#117	1	12	yes	—
47	C₂²×C₃	C₃×#131	1	16	yes	—
48	C₃×C₄	—	4	24	no	—
49	C₃×C₄	C₃×#126	1	16	yes	—
50	C₃²	#1840	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³	C₂²×C₃²×C₄	1	1	yes	characteristic
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	2	12	no	—
54	C₂×C₄	C₃²×#41	1	6	yes	—
55	C₈	—	4	4	no	—
56	C₂×C₃	C₃×#383	1	4	yes	—
57	C₂×C₃	C₃×#433	1	24	yes	—
58	C₂²	C₃²×#117	1	3	yes	—
59	C₂²	C₃²×#131	1	4	yes	—
60	C₄	—	4	6	no	—
61	C₄	C₃²×#126	1	4	yes	—
62	C₃	C₃×#1840	1	4	yes	direct product factor
63	C₂	C₃²×#383	1	1	yes	characteristic
64	C₂	C₃²×#433	1	6	yes	—

	subgroup	G/H
center	C₂²×C₃²×C₄	C₂³
commutator	C₂³	C₂²×C₃²×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#1840	C₃	direct (N × H)
13. #1840	C₃²	direct (N × H)
50. C₃²	#1840	direct (N × H)
62. C₃	C₃×#1840	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#376	2
C₃²×#336	2
C₃×#1840	3

Subgroups — C32×#1840 #11768889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1840 #11768889