Subgroups — C₃×#67592 #11773049

Order 1152.

129 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×#4504	C₂	1	2	yes	maximal
3	C₃×#1424	—	3	1	no	maximal
4	#67592	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
6	C₃×#818	—	2	2	no	—
7	C₃²×C₃₂	C₄	1	2	yes	complemented
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×#366	—	3	2	no	—
12	#4504	C₂×C₃	1	2	yes	—
13	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
14	C₃×C₄⋊Dic₃	—	4	2	no	—
15	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃²×C₁₆	Q₈	1	1	yes	characteristic
17	#1424	—	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×#107	—	6	2	no	—
22	#818	—	2	2	no	—
23	C₃×C₃₂	—	2	2	no	—
24	C₃×C₃₂	Dic₃	1	2	yes	complemented
25	C₃×C₃₂	C₃×C₄	1	2	yes	complemented
26	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
27	C₂×C₃×Dic₃	—	8	2	no	—
28	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
29	C₃²×C₈	Q₁₆	1	1	yes	characteristic
30	C₂×C₃₂	C₃×D₃	1	1	yes	characteristic
31	#366	—	3	2	no	—
32	C₂×C₃×C₈	—	2	1	no	—
33	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
34	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
35	C₃×C₄⋊C₄	—	12	2	no	—
36	C₄⋊Dic₃	—	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	D₁₆	1	1	yes	characteristic
44	C₃²×C₄	#107	1	1	yes	characteristic
45	C₃²×C₄	Q₃₂	1	1	yes	characteristic
46	C₃×Dic₃	—	16	2	no	—
47	C₂×C₁₆	C₂×C₃×D₃	1	1	yes	characteristic
48	#107	—	6	2	no	—
49	C₃₂	C₃×Dic₃	1	2	yes	complemented
50	C₂×C₃×C₄	—	2	1	no	—
51	C₂×C₃×C₄	—	24	2	no	—
52	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
53	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
54	C₂×Dic₃	—	8	2	no	—
55	C₃×C₈	—	2	1	no	—
56	C₃×C₈	—	2	1	no	—
57	C₃×C₈	Dic₁₂	1	1	yes	characteristic
58	C₃×C₈	C₄⋊Dic₃	1	1	yes	characteristic
59	C₃×C₈	C₃×C₄⋊C₄	1	1	yes	characteristic
60	C₃×C₈	C₃×Q₁₆	1	1	yes	characteristic
61	C₂×C₃²	#366	1	1	yes	characteristic
62	C₂×C₃²	SD₆₄	1	2	yes	—
63	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
64	C₄⋊C₄	—	12	2	no	—
65	C₁₆	C₃×Dic₆	1	1	yes	characteristic
66	C₁₆	C₂×C₃×Dic₃	1	1	yes	characteristic
67	C₂²×C₃	—	2	1	no	—
68	C₂²×C₃	D₄₈	1	1	yes	characteristic
69	C₂²×C₃	C₃×D₁₆	1	1	yes	characteristic
70	C₃×C₄	—	2	1	no	—
71	C₃×C₄	—	2	1	no	—
72	C₃×C₄	—	48	2	no	—
73	C₃×C₄	Dic₂₄	1	1	yes	characteristic
74	C₃×C₄	#818	1	1	yes	characteristic
75	C₃×C₄	C₃×#107	1	1	yes	characteristic
76	C₃×C₄	C₃×Q₃₂	1	1	yes	characteristic
77	Dic₃	—	16	2	no	—
78	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₄	—	24	2	no	—
80	C₂×C₄	C₃×D₂₄	1	1	yes	characteristic
81	C₈	C₃×Dic₁₂	1	1	yes	characteristic
82	C₈	C₃×C₄⋊Dic₃	1	1	yes	characteristic
83	C₂×C₃	—	2	2	no	—
84	C₂×C₃	—	2	1	no	—
85	C₂×C₃	#4449	1	2	yes	—
86	C₂×C₃	#4504	1	1	yes	characteristic
87	C₂×C₃	C₃×#366	1	1	yes	characteristic
88	C₂×C₃	C₃×SD₆₄	1	2	yes	—
89	C₂²	C₃×D₄₈	1	1	yes	characteristic
90	C₄	—	48	2	no	—
91	C₄	C₃×Dic₂₄	1	1	yes	characteristic
92	C₄	C₃×#818	1	1	yes	characteristic
93	C₃	—	2	1	no	—
94	C₃	#67592	1	1	yes	characteristic, direct product factor
95	C₃	C₃×#1424	1	1	yes	characteristic, complemented
96	C₂	C₃×#4449	1	2	yes	—
97	C₂	C₃×#4504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄₈
commutator	C₃×C₁₆	C₂×C₃×C₄
Frattini	C₂×C₁₆	C₂×C₃×D₃
Fitting	C₂×C₃²×C₃₂	C₂
socle, prime radical	C₂²×C₃²	D₁₆
cosocle	C₂×C₃×C₁₆	C₂²×C₃
hypercenter	C₂×C₃×C₃₂	D₃
hypocenter	C₃	C₃×#1424
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ 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. #67592	C₃	direct (N × H)
7. C₃²×C₃₂	C₄	semidirect
24. C₃×C₃₂	Dic₃	semidirect
25. C₃×C₃₂	C₃×C₄	semidirect
49. C₃₂	C₃×Dic₃	semidirect
78. C₃²	#1424	semidirect
94. C₃	#67592	direct (N × H)
95. C₃	C₃×#1424	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×#4504	2
C₃×#1424	3
#67592	3

Subgroups — C3×#67592 #11773049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#67592 #11773049