Subgroups — C₃×#67593 #11773060

Order 1152.

117 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#4506	C₂	1	2	yes	maximal
3	C₃×#1425	—	3	1	no	maximal
4	#67593	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
6	C₃×#819	—	2	2	no	—
7	C₃²×C₃₂	C₄	1	2	yes	—
8	C₂×C₃×C₃₂	—	2	1	no	—
9	C₂×C₃×C₃₂	D₃	1	1	yes	characteristic
10	C₂×C₃×C₃₂	C₂×C₃	1	1	yes	characteristic
11	C₃×#368	—	3	2	no	—
12	#4506	C₂×C₃	1	2	yes	—
13	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
14	C₃×#208	—	4	2	no	—
15	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃²×C₁₆	Q₈	1	1	yes	characteristic
17	#1425	—	3	1	no	Sylow
18	C₂×C₃×C₁₆	—	2	1	no	—
19	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
20	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic
21	C₃×#108	—	6	2	no	—
22	#819	—	2	2	no	—
23	C₃×C₃₂	—	2	2	no	—
24	C₃×C₃₂	Dic₃	1	2	yes	—
25	C₃×C₃₂	C₃×C₄	1	2	yes	—
26	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
27	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
28	C₃²×C₈	Q₁₆	1	1	yes	characteristic
29	C₃×C₃⋊C₈	—	8	2	no	—
30	C₂×C₃₂	C₃×D₃	1	1	yes	characteristic
31	#368	—	3	2	no	—
32	C₃×M₁₆	—	12	2	no	—
33	C₂×C₃×C₈	—	2	1	no	—
34	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
35	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
36	#208	—	4	2	no	—
37	C₃×C₁₆	—	2	1	no	—
38	C₃×C₁₆	—	2	1	no	—
39	C₃×C₁₆	Dic₆	1	1	yes	characteristic
40	C₃×C₁₆	C₂×Dic₃	1	1	yes	characteristic
41	C₃×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
42	C₃×C₁₆	C₃×Q₈	1	1	yes	characteristic
43	C₂²×C₃²	Q₃₂	1	1	yes	characteristic
44	C₃²×C₄	#107	1	1	yes	characteristic
45	C₃²×C₄	D₁₆	1	1	yes	characteristic
46	C₂×C₁₆	C₂×C₃×D₃	1	1	yes	characteristic
47	#108	—	6	2	no	—
48	C₃₂	C₃×Dic₃	1	2	yes	—
49	C₂×C₃×C₄	—	2	1	no	—
50	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
51	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
52	C₃×C₈	—	2	1	no	—
53	C₃×C₈	—	2	1	no	—
54	C₃×C₈	—	24	2	no	—
55	C₃×C₈	Dic₁₂	1	1	yes	characteristic
56	C₃×C₈	C₄⋊Dic₃	1	1	yes	characteristic
57	C₃×C₈	C₃×C₄⋊C₄	1	1	yes	characteristic
58	C₃×C₈	C₃×Q₁₆	1	1	yes	characteristic
59	C₃⋊C₈	—	8	2	no	—
60	C₂×C₃²	—	2	1	no	—
61	C₂×C₃²	#366	1	1	yes	characteristic
62	M₁₆	—	12	2	no	—
63	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
64	C₁₆	C₃×Dic₆	1	1	yes	characteristic
65	C₁₆	C₂×C₃×Dic₃	1	1	yes	characteristic
66	C₂²×C₃	—	2	1	no	—
67	C₂²×C₃	Dic₂₄	1	1	yes	characteristic
68	C₂²×C₃	C₃×Q₃₂	1	1	yes	characteristic
69	C₃×C₄	—	2	1	no	—
70	C₃×C₄	—	2	1	no	—
71	C₃×C₄	D₄₈	1	1	yes	characteristic
72	C₃×C₄	#818	1	1	yes	characteristic
73	C₃×C₄	C₃×#107	1	1	yes	characteristic
74	C₃×C₄	C₃×D₁₆	1	1	yes	characteristic
75	C₃²	#1425	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₄	C₃×D₂₄	1	1	yes	characteristic
77	C₈	—	24	2	no	—
78	C₈	C₃×Dic₁₂	1	1	yes	characteristic
79	C₈	C₃×C₄⋊Dic₃	1	1	yes	characteristic
80	C₂×C₃	—	2	2	no	—
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	—	2	1	no	—
83	C₂×C₃	—	2	1	no	—
84	C₂×C₃	#4504	1	1	yes	characteristic
85	C₂×C₃	C₃×#366	1	1	yes	characteristic
86	C₂²	C₃×Dic₂₄	1	1	yes	characteristic
87	C₄	C₃×D₄₈	1	1	yes	characteristic
88	C₄	C₃×#818	1	1	yes	characteristic
89	C₃	—	2	1	no	—
90	C₃	#67593	1	1	yes	characteristic, direct product factor
91	C₃	C₃×#1425	1	1	yes	characteristic, complemented
92	C₂	—	2	1	no	—
93	C₂	C₃×#4504	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₄₈
commutator	C₃×C₁₆	C₂×C₃×C₄
Frattini	C₂×C₁₆	C₂×C₃×D₃
Fitting	C₂×C₃²×C₃₂	C₂
socle	C₂×C₃²	#366
prime radical	C₂²×C₃²	Q₃₂
cosocle	C₂×C₃×C₁₆	C₂²×C₃
hypercenter	C₂×C₃×C₃₂	D₃
hypocenter	C₃	C₃×#1425
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ C₂×C₃×C₃₂

Complements

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

N	H ≅ G/N	type
4. #67593	C₃	direct (N × H)
75. C₃²	#1425	semidirect
90. C₃	#67593	direct (N × H)
91. C₃	C₃×#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₃₂	2
C₃×#4506	2
C₃×#1425	3
#67593	3

Subgroups — C3×#67593 #11773060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67593 #11773060