Subgroups — C₃×#73286 #11919642

Order 1152.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2276	C₃	1	1	yes	maximal, characteristic, complemented
2	#73286	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂²⋊SL(2,𝔽₃)	—	4	1	no	maximal
4	C₂×C₃×C₄²⋊C₃	—	4	3	no	maximal
5	C₃×#95⋊C₃	—	4	1	no	maximal
6	C₂×C₃×C₄×Q₈	—	3	1	no	—
7	C₃×C₄×C₄⋊C₄	—	3	3	no	—
8	C₃×#376	—	3	1	no	—
9	C₃×C₄²⋊C₃	—	4	3	no	—
10	#2276	C₃²	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₃×Q₈	A₄	1	1	yes	characteristic
12	C₂²⋊SL(2,𝔽₃)	—	4	3	no	—
13	C₃×C₄×Q₈	—	3	8	no	—
14	C₂×C₃×C₄⋊C₄	—	3	3	no	—
15	C₂×C₃×C₄²	—	3	3	no	—
16	C₂×C₃×C₄²	—	3	1	no	—
17	C₂×C₃×C₄²	A₄	1	3	yes	—
18	C₂×C₄²⋊C₃	—	4	9	no	—
19	C₃×#95	—	3	3	no	—
20	C₃×#95	A₄	1	1	yes	characteristic
21	#95⋊C₃	—	4	3	no	—
22	C₂×C₃×A₄	—	16	1	no	—
23	C₃×SL(2,𝔽₃)	—	16	4	no	—
24	C₂×C₄×Q₈	—	3	1	no	—
25	C₄×C₄⋊C₄	—	3	3	no	—
26	#376	—	3	1	no	—
27	C₂×C₃×Q₈	—	3	4	no	—
28	C₂²×C₃×C₄	—	3	1	no	—
29	C₂²×C₃×C₄	—	3	1	no	—
30	C₂²×C₃×C₄	—	3	3	no	—
31	C₃×C₄⋊C₄	—	3	12	no	—
32	C₃×C₄²	—	3	12	no	—
33	C₃×C₄²	—	4	3	no	—
34	C₃×C₄²	—	12	1	no	—
35	C₄²⋊C₃	—	4	9	no	—
36	C₃×A₄	—	16	1	no	—
37	C₂²×Q₈	C₃×A₄	1	1	yes	characteristic
38	C₄×Q₈	—	3	8	no	—
39	C₂×C₄⋊C₄	—	3	3	no	—
40	C₂×C₄²	—	3	3	no	—
41	C₂×C₄²	—	3	1	no	—
42	C₂×C₄²	C₃×A₄	1	3	yes	—
43	#95	—	3	3	no	—
44	#95	C₃×A₄	1	1	yes	characteristic
45	C₂³×C₃	C₂²⋊A₄	1	1	yes	characteristic
46	C₂×A₄	—	16	3	no	—
47	C₃×Q₈	—	3	4	no	—
48	C₃×Q₈	C₄²⋊C₃	1	4	yes	complemented
49	C₂×C₃×C₄	—	3	6	no	—
50	C₂×C₃×C₄	—	3	2	no	—
51	C₂×C₃×C₄	—	3	6	no	—
52	C₂×C₃×C₄	—	6	2	no	—
53	C₂×C₃×C₄	—	6	3	no	—
54	C₂×C₃×C₄	—	6	3	no	—
55	SL(2,𝔽₃)	—	16	12	no	—
56	C₂×C₃²	—	64	1	no	—
57	C₂×Q₈	—	3	4	no	—
58	C₂²×C₄	—	3	1	no	—
59	C₂²×C₄	—	3	1	no	—
60	C₂²×C₄	—	3	3	no	—
61	C₄⋊C₄	—	3	12	no	—
62	C₄²	—	3	12	no	—
63	C₄²	—	4	3	no	—
64	C₄²	—	12	1	no	—
65	C₂²×C₃	—	3	1	no	—
66	C₂²×C₃	—	3	1	no	—
67	C₂²×C₃	#997	1	1	yes	characteristic
68	A₄	—	16	3	no	—
69	C₃×C₄	—	3	4	no	—
70	C₃×C₄	—	6	6	no	—
71	C₃×C₄	—	6	2	no	—
72	C₃²	—	64	1	no	Sylow
73	C₂³	C₃×C₂²⋊A₄	1	1	yes	characteristic
74	Q₈	—	3	4	no	—
75	Q₈	C₃×C₄²⋊C₃	1	4	yes	complemented
76	C₂×C₄	—	3	6	no	—
77	C₂×C₄	—	3	2	no	—
78	C₂×C₄	—	3	6	no	—
79	C₂×C₄	—	6	2	no	—
80	C₂×C₄	—	6	3	no	—
81	C₂×C₄	—	6	3	no	—
82	C₂×C₃	—	3	1	no	—
83	C₂×C₃	—	3	1	no	—
84	C₂×C₃	—	64	3	no	—
85	C₂×C₃	C₂²⋊(C₄²⋊C₃)	1	1	yes	characteristic
86	C₂²	—	3	1	no	—
87	C₂²	—	3	1	no	—
88	C₂²	C₃×#997	1	1	yes	characteristic
89	C₄	—	3	4	no	—
90	C₄	—	6	6	no	—
91	C₄	—	6	2	no	—
92	C₃	—	64	3	no	—
93	C₃	#73286	1	1	yes	characteristic, direct product factor
94	C₂	—	3	1	no	—
95	C₂	—	3	1	no	—
96	C₂	C₃×C₂²⋊(C₄²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂²⋊(C₄²⋊C₃)
commutator, cosocle, hypocenter	#2276	C₃²
Frattini	C₂³	C₃×C₂²⋊A₄
Fitting	C₃×#2276	C₃
socle	C₂³×C₃	C₂²⋊A₄
LCS	G ▷ #2276
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#2276	C₃	semidirect
2. #73286	C₃	direct (N × H)
10. #2276	C₃²	semidirect
48. C₃×Q₈	C₄²⋊C₃	semidirect
75. Q₈	C₃×C₄²⋊C₃	semidirect
93. C₃	#73286	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2276	3
#73286	3
C₃×C₂²⋊SL(2,𝔽₃)	4
C₂×C₃×C₄²⋊C₃	4
C₃×#95⋊C₃	4

Subgroups — C3×#73286 #11919642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#73286 #11919642