Subgroups — D₃×#383 #74294

Order 384.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
3	#4937	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×#95	C₂	1	6	yes	maximal
5	#4651	C₂	1	6	yes	maximal, complemented
6	C₂×#383	—	3	1	no	maximal, Sylow
7	C₂²×C₄×D₃	C₂²	1	4	yes	—
8	C₂²×C₄×D₃	C₂²	1	3	yes	—
9	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₃	C₂²	1	3	yes	—
11	C₄²×D₃	C₄	1	8	yes	complemented
12	C₃×#95	C₂²	1	6	yes	—
13	C₃⋊#95	C₂²	1	12	yes	—
14	C₃⋊#95	C₂²	1	6	yes	—
15	C₂²×C₄²	—	3	1	no	—
16	#383	—	3	1	no	—
17	#383	—	3	6	no	—
18	#383	D₃	1	1	yes	characteristic, direct product factor
19	C₂×#95	—	3	6	no	—
20	C₂³×D₃	C₂³	1	1	yes	characteristic
21	C₂²×C₃×C₄	C₂³	1	4	yes	—
22	C₂²×C₃×C₄	C₂³	1	3	yes	—
23	C₂²×Dic₃	C₂³	1	4	yes	—
24	C₂²×Dic₃	C₂³	1	3	yes	—
25	C₂×C₄×D₃	—	2	12	no	—
26	C₂×C₄×D₃	—	2	24	no	—
27	C₂×C₄×D₃	C₂×C₄	1	12	yes	—
28	C₃×C₄²	C₂×C₄	1	4	yes	complemented
29	C₄×Dic₃	C₂×C₄	1	12	yes	complemented
30	C₂³×C₄	—	3	3	no	—
31	C₂³×C₄	—	3	4	no	—
32	C₂×C₄²	—	3	3	no	—
33	C₂×C₄²	—	3	8	no	—
34	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
35	#95	—	3	12	no	—
36	#95	—	3	6	no	—
37	#95	C₂×D₃	1	6	yes	—
38	C₂³×C₃	C₂⁴	1	1	yes	characteristic
39	C₂²×D₃	C₂²×C₄	1	2	yes	—
40	C₂²×D₃	#41	1	12	yes	—
41	C₂×C₃×C₄	—	2	6	no	—
42	C₂×C₃×C₄	—	2	12	no	—
43	C₂×C₃×C₄	C₂²×C₄	1	6	yes	—
44	C₂×Dic₃	—	2	6	no	—
45	C₂×Dic₃	—	2	12	no	—
46	C₂×Dic₃	C₂²×C₄	1	6	yes	—
47	C₄×D₃	—	2	24	no	—
48	C₄×D₃	—	4	16	no	—
49	C₂⁴	—	3	1	no	—
50	C₂²×C₄	—	3	3	no	—
51	C₂²×C₄	—	3	12	no	—
52	C₂²×C₄	—	3	4	no	—
53	C₂²×C₄	—	6	12	no	—
54	C₂²×C₄	—	6	24	no	—
55	C₂²×C₄	C₂²×D₃	1	4	yes	—
56	C₂²×C₄	C₂²×D₃	1	3	yes	—
57	C₄²	—	3	12	no	—
58	C₄²	C₄×D₃	1	4	yes	complemented
59	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₃	C₂×#41	1	6	yes	—
61	C₂×D₃	#117	1	12	yes	—
62	C₂×D₃	#126	1	16	yes	—
63	C₃×C₄	—	2	6	no	—
64	C₃×C₄	—	4	4	no	—
65	Dic₃	—	2	6	no	—
66	Dic₃	—	4	4	no	—
67	C₂³	—	3	2	no	—
68	C₂³	—	3	12	no	—
69	C₂³	C₂³×D₃	1	1	yes	characteristic
70	C₂×C₄	—	2	6	no	—
71	C₂×C₄	—	2	12	no	—
72	C₂×C₄	—	3	6	no	—
73	C₂×C₄	—	6	24	no	—
74	C₂×C₄	—	6	6	no	—
75	C₂×C₄	—	6	12	no	—
76	C₂×C₄	—	12	16	no	—
77	C₂×C₄	C₂×C₄×D₃	1	6	yes	—
78	C₂×C₃	C₂×#117	1	3	yes	—
79	C₂×C₃	C₂×#126	1	4	yes	—
80	D₃	#383	1	8	yes	direct product factor
81	C₂²	—	3	16	no	—
82	C₂²	—	3	12	no	—
83	C₂²	C₂²×C₄×D₃	1	1	yes	characteristic
84	C₂²	D₃×#41	1	6	yes	—
85	C₄	—	2	6	no	—
86	C₄	—	4	4	no	—
87	C₄	—	6	6	no	—
88	C₄	—	12	4	no	—
89	C₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
90	C₂	—	3	8	no	—
91	C₂	D₃×#117	1	3	yes	—
92	C₂	D₃×#126	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄
Fitting	C₃×#383	C₂
socle, cosocle	C₂³×C₃	C₂⁴
prime radical	C₂³×D₃	C₂³
hypercenter	#383	D₃
hypocenter	C₃	C₂×#383
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. C₃×#383	C₂	semidirect
3. #4937	C₂	semidirect
5. #4651	C₂	semidirect
11. C₄²×D₃	C₄	semidirect
18. #383	D₃	direct (N × H)
28. C₃×C₄²	C₂×C₄	semidirect
29. C₄×Dic₃	C₂×C₄	semidirect
58. C₄²	C₄×D₃	semidirect
80. D₃	#383	direct (N × H)
89. C₃	C₂×#383	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₃	2
C₃×#383	2
#4937	2
D₃×#95	2
#4651	2
C₂×#383	3

Subgroups — D3×#383 #74294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#383 #74294