Subgroups — D₃×#322 #68066

Order 384.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₃×C₈	C₂	1	2	yes	maximal
3	C₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#4455	C₂	1	1	yes	maximal, characteristic, complemented
5	#4454	C₂	1	2	yes	maximal, complemented
6	C₂×#322	—	3	1	no	maximal, Sylow
7	C₂×D₃×C₈	C₄	1	4	yes	—
8	C₂×D₃×C₈	C₄	1	2	yes	—
9	C₄²×D₃	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₈	C₂²	1	2	yes	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	C₈×Dic₃	C₄	1	4	yes	—
13	C₈×Dic₃	C₄	1	2	yes	—
14	C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₃⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₈	—	3	1	no	—
17	C₂×C₄×C₈	—	3	2	no	—
18	#322	—	3	2	no	—
19	#322	—	3	1	no	—
20	#322	D₃	1	1	yes	characteristic, direct product factor
21	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₃	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₈	C₂×C₄	1	4	yes	—
24	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
25	C₃×C₄²	C₂³	1	1	yes	characteristic
26	C₄×Dic₃	C₂×C₄	1	2	yes	—
27	C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₃⋊C₈	C₂×C₄	1	2	yes	—
30	D₃×C₈	—	2	8	no	—
31	D₃×C₈	C₈	1	8	yes	complemented
32	C₂²×C₈	—	3	2	no	—
33	C₂²×C₈	—	3	4	no	—
34	C₂×C₄²	—	3	1	no	—
35	C₄×C₈	—	3	2	no	—
36	C₄×C₈	—	3	4	no	—
37	C₄×C₈	—	3	1	no	—
38	C₄×C₈	—	3	2	no	—
39	C₄×C₈	C₂×D₃	1	2	yes	—
40	C₄×C₈	C₂×D₃	1	1	yes	characteristic
41	C₂²×D₃	C₄²	1	1	yes	characteristic
42	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
44	C₂×Dic₃	C₄²	1	1	yes	characteristic
45	C₂×Dic₃	C₄²	1	2	yes	—
46	C₄×D₃	C₂×C₈	1	4	yes	—
47	C₄×D₃	M₁₆	1	8	yes	—
48	C₃×C₈	—	2	4	no	—
49	C₃×C₈	C₂×C₈	1	4	yes	complemented
50	C₃⋊C₈	—	2	4	no	—
51	C₃⋊C₈	C₂×C₈	1	4	yes	complemented
52	C₂²×C₄	—	3	1	no	—
53	C₂²×C₄	—	3	2	no	—
54	C₂×C₈	—	3	2	no	—
55	C₂×C₈	—	3	8	no	—
56	C₂×C₈	—	3	4	no	—
57	C₂×C₈	—	6	8	no	—
58	C₂×C₈	C₄×D₃	1	4	yes	—
59	C₂×C₈	C₄×D₃	1	2	yes	—
60	C₄²	—	3	1	no	—
61	C₄²	—	3	2	no	—
62	C₄²	C₂²×D₃	1	1	yes	characteristic
63	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×D₃	C₄×C₈	1	2	yes	—
65	C₂×D₃	#97	1	4	yes	—
66	C₃×C₄	C₂²×C₈	1	2	yes	—
67	C₃×C₄	C₂×M₁₆	1	4	yes	—
68	Dic₃	C₄×C₈	1	2	yes	—
69	Dic₃	#97	1	4	yes	—
70	C₂³	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	3	4	no	—
74	C₂×C₄	—	3	8	no	—
75	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
76	C₂×C₄	C₂×C₄×D₃	1	2	yes	—
77	C₈	—	2	4	no	—
78	C₈	—	3	4	no	—
79	C₈	—	6	4	no	—
80	C₈	D₃×C₈	1	4	yes	complemented
81	C₂×C₃	C₂×C₄×C₈	1	1	yes	characteristic
82	C₂×C₃	C₂×#97	1	2	yes	—
83	D₃	#322	1	4	yes	direct product factor
84	C₂²	—	3	2	no	—
85	C₂²	—	3	4	no	—
86	C₂²	C₄²×D₃	1	1	yes	characteristic
87	C₄	—	3	2	no	—
88	C₄	—	3	4	no	—
89	C₄	C₂×D₃×C₈	1	2	yes	—
90	C₄	D₃×M₁₆	1	4	yes	—
91	C₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	3	4	no	—
93	C₂	C₄×D₃×C₈	1	1	yes	characteristic
94	C₂	D₃×#97	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₃
commutator	C₂×C₃	C₂×C₄×C₈
Fitting	C₃×#322	C₂
socle	C₂²×C₃	C₂×C₄²
prime radical	C₂²×D₃	C₄²
cosocle	C₃×C₄²	C₂³
hypercenter	#322	D₃
hypocenter	C₃	C₂×#322
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. C₃×#322	C₂	semidirect
4. #4455	C₂	semidirect
5. #4454	C₂	semidirect
20. #322	D₃	direct (N × H)
31. D₃×C₈	C₈	semidirect
49. C₃×C₈	C₂×C₈	semidirect
51. C₃⋊C₈	C₂×C₈	semidirect
80. C₈	D₃×C₈	semidirect
83. D₃	#322	direct (N × H)
91. C₃	C₂×#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×C₈	2
C₃×#322	2
#4455	2
#4454	2
C₂×#322	3

Subgroups — D3×#322 #68066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#322 #68066