Subgroups — C₃×#73318 #11857071

Order 1152.

2673 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#874	C₂	1	14	yes	maximal, complemented
2	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2867	—	3	1	no	maximal
4	#73318	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃×D₁₂	C₂²	1	28	yes	—
6	C₂×C₃²×C₄²	C₂²	1	7	yes	—
7	C₃×#874	—	2	56	no	—
8	C₂×C₃×#127	—	3	14	no	—
9	C₂×#874	C₂×C₃	1	14	yes	complemented
10	C₃×C₄³	—	2	1	no	—
11	C₃×C₄³	D₃	1	1	yes	characteristic, complemented
12	C₃×C₄³	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂³×C₃×D₃	C₂³	1	8	yes	—
14	C₂²×C₃²×C₄	C₂³	1	7	yes	—
15	C₂×C₃×D₁₂	—	2	168	no	—
16	C₃²×C₄²	D₄	1	28	yes	complemented
17	#2867	—	3	1	no	Sylow
18	C₂²×C₃×D₄	—	3	28	no	—
19	C₂²×D₁₂	C₂²×C₃	1	28	yes	—
20	C₃×#127	—	6	56	no	—
21	C₂×C₃×C₄²	—	2	7	no	—
22	C₂×C₃×C₄²	C₂×D₃	1	7	yes	—
23	C₂×C₃×C₄²	C₂²×C₃	1	7	yes	—
24	#874	—	2	56	no	—
25	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
26	C₂²×C₃×D₃	—	2	56	no	—
27	C₂×C₃²×C₄	C₂×D₄	1	42	yes	—
28	C₃×D₁₂	—	4	112	no	—
29	C₂×#127	—	3	14	no	—
30	C₄³	C₃×D₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃	—	3	8	no	—
32	C₂³×D₃	C₂³×C₃	1	8	yes	—
33	C₂×C₃×D₄	—	6	168	no	—
34	C₂²×C₃×C₄	—	2	7	no	—
35	C₂²×C₃×C₄	C₂²×D₃	1	7	yes	—
36	C₂²×C₃×C₄	C₂³×C₃	1	7	yes	—
37	C₂×D₁₂	—	2	168	no	—
38	C₃×C₄²	—	2	28	no	—
39	C₃×C₄²	D₁₂	1	28	yes	complemented
40	C₃×C₄²	C₃×D₄	1	28	yes	complemented
41	C₂²×C₃²	C₂²×D₄	1	7	yes	—
42	C₂×C₃×D₃	—	4	56	no	—
43	C₃²×C₄	#127	1	28	yes	complemented
44	C₂²×D₄	—	3	28	no	—
45	#127	—	6	56	no	—
46	C₂×C₄²	C₂×C₃×D₃	1	7	yes	—
47	C₂³×C₃	—	2	1	no	—
48	C₂³×C₃	—	6	56	no	—
49	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
50	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
51	C₂²×D₃	—	2	56	no	—
52	C₃×D₄	—	12	112	no	—
53	C₂×C₃×C₄	—	2	42	no	—
54	C₂×C₃×C₄	C₂×D₁₂	1	42	yes	—
55	C₂×C₃×C₄	C₂×C₃×D₄	1	42	yes	—
56	D₁₂	—	4	112	no	—
57	C₂×C₃²	C₂×#127	1	7	yes	—
58	C₃×D₃	—	8	8	no	—
59	C₂⁴	—	3	8	no	—
60	C₂×D₄	—	6	168	no	—
61	C₂²×C₄	C₂²×C₃×D₃	1	7	yes	—
62	C₄²	C₃×D₁₂	1	28	yes	complemented
63	C₂²×C₃	—	2	7	no	—
64	C₂²×C₃	—	12	56	no	—
65	C₂²×C₃	C₂²×D₁₂	1	7	yes	—
66	C₂²×C₃	C₂²×C₃×D₄	1	7	yes	—
67	C₂×D₃	—	4	56	no	—
68	C₃×C₄	—	2	28	no	—
69	C₃×C₄	#874	1	28	yes	complemented
70	C₃×C₄	C₃×#127	1	28	yes	complemented
71	C₃²	#2867	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	6	56	no	—
73	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
74	D₄	—	12	112	no	—
75	C₂×C₄	C₂×C₃×D₁₂	1	42	yes	—
76	C₂×C₃	—	2	7	no	—
77	C₂×C₃	—	24	8	no	—
78	C₂×C₃	C₂×#874	1	7	yes	—
79	C₂×C₃	C₂×C₃×#127	1	7	yes	—
80	D₃	—	8	8	no	—
81	C₂²	—	12	56	no	—
82	C₂²	C₂²×C₃×D₁₂	1	7	yes	—
83	C₄	C₃×#874	1	28	yes	complemented
84	C₃	—	2	1	no	—
85	C₃	#73318	1	1	yes	characteristic, direct product factor
86	C₃	C₃×#2867	1	1	yes	characteristic, complemented
87	C₂	—	24	8	no	—
88	C₂	C₂×C₃×#874	1	7	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂³×C₃	C₂⁴×C₃
Frattini	C₂³	C₂³×C₃×D₃
Fitting	C₃²×C₄³	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₃×C₄³	D₃
hypocenter	C₃	C₃×#2867
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄³

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#874	C₂	semidirect
2. C₃²×C₄³	C₂	semidirect
4. #73318	C₃	direct (N × H)
9. C₂×#874	C₂×C₃	semidirect
11. C₃×C₄³	D₃	semidirect
12. C₃×C₄³	C₂×C₃	semidirect
16. C₃²×C₄²	D₄	semidirect
30. C₄³	C₃×D₃	semidirect
39. C₃×C₄²	D₁₂	semidirect
40. C₃×C₄²	C₃×D₄	semidirect
43. C₃²×C₄	#127	semidirect
62. C₄²	C₃×D₁₂	semidirect
69. C₃×C₄	#874	semidirect
70. C₃×C₄	C₃×#127	semidirect
71. C₃²	#2867	semidirect
83. C₄	C₃×#874	semidirect
85. C₃	#73318	direct (N × H)
86. C₃	C₃×#2867	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#874	2
C₃²×C₄³	2
C₃×#2867	3
#73318	3

Subgroups — C3×#73318 #11857071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#73318 #11857071