Subgroups — C₃×#1384 #67944

Order 384.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×#427	C₂	1	2	yes	maximal
3	#1384	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
5	C₃×#117	—	2	2	no	—
6	C₃×M₃₂	—	2	2	no	—
7	C₂×C₃×C₁₆	C₄	1	2	yes	complemented
8	C₃×#107	—	2	2	no	—
9	C₃×#106	C₄	1	4	yes	complemented
10	C₂×M₃₂	C₂×C₃	1	1	yes	characteristic
11	#427	C₂×C₃	1	2	yes	—
12	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
13	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₃×C₈	D₄	1	2	yes	—
16	C₂×C₃×C₈	Q₈	1	1	yes	characteristic
17	C₃×C₄⋊C₄	—	2	4	no	—
18	C₃×C₂²⋊C₄	—	4	2	no	—
19	C₃×C₄²	—	4	2	no	—
20	C₃×C₁₆	—	2	2	no	—
21	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
22	#117	—	2	2	no	—
23	M₃₂	—	2	2	no	—
24	C₂×C₁₆	C₃×C₄	1	2	yes	complemented
25	#107	—	2	2	no	—
26	#106	C₃×C₄	1	4	yes	complemented
27	C₂³×C₃	D₈	1	1	yes	characteristic
28	C₂×C₃×C₄	—	4	4	no	—
29	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
30	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₃×C₄	SD₁₆	1	2	yes	—
32	C₂×C₃×C₄	Q₁₆	1	1	yes	characteristic
33	C₃×C₈	C₄²	1	1	yes	characteristic
34	C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
35	C₃×C₈	C₄⋊C₄	1	2	yes	—
36	C₂²×C₄	C₃×D₄	1	1	yes	characteristic
37	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
38	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
39	C₂×C₈	C₃×D₄	1	2	yes	—
40	C₂×C₈	C₃×Q₈	1	1	yes	characteristic
41	C₄⋊C₄	—	2	4	no	—
42	C₂²⋊C₄	—	4	2	no	—
43	C₄²	—	4	2	no	—
44	C₁₆	—	2	2	no	—
45	C₂²×C₃	—	4	1	no	—
46	C₂²×C₃	#102	1	2	yes	—
47	C₂²×C₃	#107	1	1	yes	characteristic
48	C₃×C₄	—	8	4	no	—
49	C₃×C₄	#95	1	1	yes	characteristic
50	C₃×C₄	#103	1	2	yes	—
51	C₃×C₄	#106	1	1	yes	characteristic
52	C₂³	C₃×D₈	1	1	yes	characteristic
53	C₂×C₄	—	4	4	no	—
54	C₂×C₄	C₃×C₂²⋊C₄	1	2	yes	—
55	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄	C₃×SD₁₆	1	2	yes	—
57	C₂×C₄	C₃×Q₁₆	1	1	yes	characteristic
58	C₈	C₃×C₄²	1	1	yes	characteristic
59	C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
60	C₈	C₃×C₄⋊C₄	1	2	yes	—
61	C₂×C₃	—	2	2	no	—
62	C₂×C₃	—	2	1	no	—
63	C₂×C₃	#340	1	1	yes	characteristic
64	C₂²	—	4	1	no	—
65	C₂²	C₃×#102	1	2	yes	—
66	C₂²	C₃×#107	1	1	yes	characteristic
67	C₄	—	8	4	no	—
68	C₄	C₃×#95	1	1	yes	characteristic
69	C₄	C₃×#103	1	2	yes	—
70	C₄	C₃×#106	1	1	yes	characteristic
71	C₃	#1384	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	C₃×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#106
commutator	C₈	C₃×C₄²
Frattini, cosocle	C₂²×C₈	C₂²×C₃
socle	C₂×C₃	#340
prime radical	C₂³×C₃	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1384	C₃	direct (N × H)
7. C₂×C₃×C₁₆	C₄	semidirect
9. C₃×#106	C₄	semidirect
24. C₂×C₁₆	C₃×C₄	semidirect
26. #106	C₃×C₄	semidirect
71. C₃	#1384	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×M₃₂	2
C₃×#427	2
#1384	3

Subgroups — C3×#1384 #67944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1384 #67944