Subgroups — C₃×#1712⋊C₃ #11919334

Order 1152.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#1712	C₃	1	1	yes	maximal, characteristic, complemented
3	#1712⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×#127⋊C₃	—	4	1	no	maximal
5	C₃×#493	—	3	1	no	—
6	C₃×#493	—	3	1	no	—
7	C₃×C₈²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₈²⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₃×C₄²⋊C₃	—	4	1	no	—
10	#1712	C₃²	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃×D₈	—	6	2	no	—
12	C₂×C₃×D₈	—	6	2	no	—
13	C₃×#127	—	3	1	no	—
14	C₃×#127	A₄	1	1	yes	characteristic
15	#127⋊C₃	—	4	3	no	—
16	C₃×C₄×C₈	—	3	1	no	—
17	C₂×C₃×A₄	—	16	1	no	—
18	#493	—	3	1	no	—
19	#493	—	3	1	no	—
20	C₈²	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₂×C₃×D₄	—	6	1	no	—
22	C₂×C₃×D₄	—	6	1	no	—
23	C₂×C₃×D₄	—	6	2	no	—
24	C₃×D₈	—	12	4	no	—
25	C₃×D₈	—	12	4	no	—
26	C₂×C₃×C₈	—	3	2	no	—
27	C₃×C₄²	C₂×A₄	1	1	yes	characteristic
28	C₄²⋊C₃	—	4	3	no	—
29	C₃×A₄	—	16	1	no	—
30	C₂×D₈	—	6	2	no	—
31	C₂×D₈	—	6	2	no	—
32	#127	—	3	1	no	—
33	#127	C₃×A₄	1	1	yes	characteristic
34	C₄×C₈	—	3	1	no	—
35	C₂³×C₃	—	4	1	no	—
36	C₂³×C₃	—	12	1	no	—
37	C₂×A₄	—	16	3	no	—
38	C₃×D₄	—	12	2	no	—
39	C₃×D₄	—	12	2	no	—
40	C₃×D₄	—	12	4	no	—
41	C₂×C₃×C₄	—	3	1	no	—
42	C₃×C₈	—	3	4	no	—
43	C₂×C₃²	—	64	1	no	—
44	C₂×D₄	—	6	1	no	—
45	C₂×D₄	—	6	1	no	—
46	C₂×D₄	—	6	2	no	—
47	D₈	—	12	4	no	—
48	D₈	—	12	4	no	—
49	C₂×C₈	—	3	2	no	—
50	C₄²	C₂×C₃×A₄	1	1	yes	characteristic
51	C₂²×C₃	—	24	1	no	—
52	C₂²×C₃	—	24	1	no	—
53	C₂²×C₃	—	24	2	no	—
54	C₂²×C₃	#127⋊C₃	1	1	yes	characteristic
55	A₄	—	16	3	no	—
56	C₃×C₄	—	3	2	no	—
57	C₃²	—	64	1	no	Sylow
58	C₂³	—	4	1	no	—
59	C₂³	—	12	1	no	—
60	D₄	—	12	2	no	—
61	D₄	—	12	2	no	—
62	D₄	—	12	4	no	—
63	C₂×C₄	—	3	1	no	—
64	C₈	—	3	4	no	—
65	C₂×C₃	—	3	1	no	—
66	C₂×C₃	—	16	1	no	—
67	C₂×C₃	—	48	1	no	—
68	C₂×C₃	—	64	3	no	—
69	C₂²	—	24	1	no	—
70	C₂²	—	24	1	no	—
71	C₂²	—	24	2	no	—
72	C₂²	C₃×#127⋊C₃	1	1	yes	characteristic
73	C₄	—	3	2	no	—
74	C₃	—	64	3	no	—
75	C₃	#1712⋊C₃	1	1	yes	characteristic, direct product factor
76	C₂	—	3	1	no	—
77	C₂	—	16	1	no	—
78	C₂	—	48	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#1712⋊C₃
commutator, cosocle, hypocenter	C₈²	C₂×C₃²
Frattini	C₄²	C₂×C₃×A₄
Fitting	C₃×#1712	C₃
socle	C₂²×C₃	#127⋊C₃
LCS	G ▷ C₈²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₈²⋊C₃	C₂	semidirect
2. C₃×#1712	C₃	semidirect
3. #1712⋊C₃	C₃	direct (N × H)
7. C₃×C₈²	C₂×C₃	semidirect
8. C₈²⋊C₃	C₂×C₃	semidirect
10. #1712	C₃²	semidirect
20. C₈²	C₂×C₃²	semidirect
75. C₃	#1712⋊C₃	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×C₈²⋊C₃	2
C₃×#1712	3
#1712⋊C₃	3
C₃×#127⋊C₃	4

Subgroups — C3×#1712⋊C3 #11919334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1712⋊C₃ #11919334