Subgroups — C₃²×#1843 #11768892

Order 1152.

768 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄⋊C₈	C₂	1	6	yes	maximal
2	C₃²×#376	C₂	1	1	yes	maximal, characteristic
3	C₃×#1843	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×C₄⋊C₈	—	2	12	no	—
7	C₃²×#95	C₄	1	4	yes	—
8	C₂×C₃×C₄⋊C₈	C₂×C₃	1	24	yes	—
9	C₃×#376	C₂×C₃	1	4	yes	—
10	C₂²×C₃²×C₄	C₂×C₄	1	6	yes	—
11	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
12	C₂×C₃²×C₈	—	2	12	no	—
13	C₃²×C₄²	D₄	1	6	yes	—
14	C₃²×C₄²	Q₈	1	6	yes	—
15	#1843	C₃²	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₃×C₈	C₂²×C₃	1	16	yes	—
17	C₂×C₃×C₄²	C₂²×C₃	1	12	yes	—
18	C₃×C₄⋊C₈	—	2	48	no	—
19	C₃×#95	C₃×C₄	1	16	yes	—
20	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₃²×C₄	—	2	12	no	—
22	C₂×C₃²×C₄	C₄⋊C₄	1	12	yes	—
23	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
24	C₂×C₃²×C₄	C₂×Q₈	1	3	yes	—
25	C₃²×C₈	—	4	4	no	—
26	C₂×C₄⋊C₈	C₂×C₃²	1	6	yes	—
27	#376	C₂×C₃²	1	1	yes	characteristic
28	C₂²×C₃×C₄	C₂×C₃×C₄	1	24	yes	—
29	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
30	C₂×C₃×C₈	—	2	48	no	—
31	C₃×C₄²	C₃×D₄	1	24	yes	—
32	C₃×C₄²	C₃×Q₈	1	24	yes	—
33	C₂²×C₃²	C₂×C₄⋊C₄	1	3	yes	—
34	C₂²×C₃²	#131	1	4	yes	—
35	C₃²×C₄	—	2	12	no	—
36	C₃²×C₄	#127	1	1	yes	characteristic
37	C₃²×C₄	C₄⋊Q₈	1	3	yes	—
38	C₂²×C₈	C₂²×C₃²	1	4	yes	—
39	C₂×C₄²	C₂²×C₃²	1	3	yes	—
40	C₄⋊C₈	—	2	12	no	—
41	#95	C₃²×C₄	1	4	yes	—
42	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
43	C₂×C₃×C₄	—	2	48	no	—
44	C₂×C₃×C₄	C₃×C₄⋊C₄	1	48	yes	—
45	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
46	C₂×C₃×C₄	C₂×C₃×Q₈	1	12	yes	—
47	C₃×C₈	—	4	16	no	—
48	C₂×C₃²	#384	1	1	yes	characteristic
49	C₂×C₃²	#424	1	6	yes	—
50	C₂²×C₄	C₂×C₃²×C₄	1	6	yes	—
51	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
52	C₂×C₈	—	2	12	no	—
53	C₄²	C₃²×D₄	1	6	yes	—
54	C₄²	C₃²×Q₈	1	6	yes	—
55	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	12	yes	—
56	C₂²×C₃	C₃×#131	1	16	yes	—
57	C₃×C₄	—	2	48	no	—
58	C₃×C₄	C₃×#127	1	4	yes	—
59	C₃×C₄	C₃×C₄⋊Q₈	1	12	yes	—
60	C₃²	#1843	1	1	yes	characteristic, direct product factor, Sylow
61	C₂³	C₂²×C₃²×C₄	1	1	yes	characteristic
62	C₂×C₄	—	2	12	no	—
63	C₂×C₄	C₃²×C₄⋊C₄	1	12	yes	—
64	C₂×C₄	C₂×C₃²×D₄	1	3	yes	—
65	C₂×C₄	C₂×C₃²×Q₈	1	3	yes	—
66	C₈	—	4	4	no	—
67	C₂×C₃	C₃×#384	1	4	yes	—
68	C₂×C₃	C₃×#424	1	24	yes	—
69	C₂²	C₂×C₃²×C₄⋊C₄	1	3	yes	—
70	C₂²	C₃²×#131	1	4	yes	—
71	C₄	—	2	12	no	—
72	C₄	C₃²×#127	1	1	yes	characteristic
73	C₄	C₃²×C₄⋊Q₈	1	3	yes	—
74	C₃	C₃×#1843	1	4	yes	direct product factor
75	C₂	C₃²×#384	1	1	yes	characteristic
76	C₂	C₃²×#424	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×#1843	C₃	direct (N × H)
15. #1843	C₃²	direct (N × H)
60. C₃²	#1843	direct (N × H)
74. C₃	C₃×#1843	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄⋊C₈	2
C₃²×#376	2
C₃×#1843	3

Subgroups — C32×#1843 #11768892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1843 #11768892