Subgroups — C₃×#1336 #67896

Order 384.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#443	C₂	1	1	yes	maximal, characteristic
2	C₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#1336	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#135	C₄	1	1	yes	characteristic
6	C₃×#131	—	2	1	no	—
7	C₃×M₃₂	—	2	1	no	—
8	C₃×#108	C₄	1	1	yes	characteristic
9	C₃×#104	—	2	1	no	—
10	C₃×C₄×C₈	—	2	1	no	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	#443	C₂×C₃	1	1	yes	characteristic
13	#364	C₂×C₃	1	1	yes	characteristic, complemented
14	#322	C₂×C₃	1	1	yes	characteristic, complemented
15	C₃×#41	—	2	1	no	—
16	C₃×Q₁₆	C₈	1	1	yes	characteristic, complemented
17	C₃×SD₁₆	—	2	1	no	—
18	C₃×D₈	C₈	1	1	yes	characteristic, complemented
19	C₃×M₁₆	—	2	1	no	—
20	C₃×M₁₆	—	4	1	no	—
21	C₂×C₃×C₈	—	2	2	no	—
22	C₂×C₃×C₈	—	4	1	no	—
23	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₈	D₄	1	1	yes	characteristic
25	C₃×C₄²	D₄	1	1	yes	characteristic
26	C₃×C₁₆	—	4	1	no	—
27	#135	C₃×C₄	1	1	yes	characteristic
28	#131	—	2	1	no	—
29	M₃₂	—	2	1	no	—
30	#108	C₃×C₄	1	1	yes	characteristic
31	#104	—	2	1	no	—
32	C₄×C₈	—	2	1	no	—
33	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₃×Q₈	—	2	1	no	—
35	C₃×D₄	—	2	1	no	—
36	C₃×D₄	—	4	1	no	—
37	C₂×C₃×C₄	—	2	1	no	—
38	C₂×C₃×C₄	—	4	1	no	—
39	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
40	C₃×C₈	—	4	2	no	—
41	C₃×C₈	—	4	1	no	—
42	C₃×C₈	C₂×C₈	1	1	yes	characteristic
43	C₃×C₈	M₁₆	1	1	yes	characteristic
44	C₃×C₈	D₈	1	1	yes	characteristic
45	C₃×C₈	SD₁₆	1	1	yes	characteristic
46	#41	—	2	1	no	—
47	Q₁₆	C₃×C₈	1	1	yes	characteristic, complemented
48	SD₁₆	—	2	1	no	—
49	D₈	C₃×C₈	1	1	yes	characteristic, complemented
50	M₁₆	—	2	1	no	—
51	M₁₆	—	4	1	no	—
52	C₂×C₈	—	2	2	no	—
53	C₂×C₈	—	4	1	no	—
54	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂×C₈	C₃×D₄	1	1	yes	characteristic
56	C₄²	C₃×D₄	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₂²×C₃	—	4	1	no	—
59	C₂²×C₃	#104	1	1	yes	characteristic
60	C₃×C₄	—	2	2	no	—
61	C₃×C₄	—	4	1	no	—
62	C₃×C₄	C₂²⋊C₈	1	1	yes	characteristic
63	C₃×C₄	#102	1	1	yes	characteristic
64	Q₈	—	2	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	4	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
70	C₈	—	4	2	no	—
71	C₈	—	4	1	no	—
72	C₈	C₂×C₃×C₈	1	1	yes	characteristic
73	C₈	C₃×M₁₆	1	1	yes	characteristic
74	C₈	C₃×D₈	1	1	yes	characteristic
75	C₈	C₃×SD₁₆	1	1	yes	characteristic
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	8	1	no	—
78	C₂×C₃	D₄⋊C₈	1	1	yes	characteristic
79	C₂²	—	4	1	no	—
80	C₂²	C₃×#104	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	4	1	no	—
83	C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
84	C₄	C₃×#102	1	1	yes	characteristic
85	C₃	#1336	1	1	yes	characteristic, direct product factor, Sylow
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	C₃×D₄⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#102
commutator	C₈	C₂×C₃×C₈
Frattini, cosocle	C₄×C₈	C₂²×C₃
socle	C₂×C₃	D₄⋊C₈
prime radical	C₃×#135	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#364	C₂	semidirect
3. C₃×#322	C₂	semidirect
4. #1336	C₃	direct (N × H)
13. #364	C₂×C₃	semidirect
14. #322	C₂×C₃	semidirect
16. C₃×Q₁₆	C₈	semidirect
18. C₃×D₈	C₈	semidirect
47. Q₁₆	C₃×C₈	semidirect
49. D₈	C₃×C₈	semidirect
85. C₃	#1336	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×#443	2
C₃×#364	2
C₃×#322	2
#1336	3

Subgroups — C3×#1336 #67896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1336 #67896