Subgroups — C₃×#1381 #67941

Order 384.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#108	C₂	1	2	yes	maximal
3	#1381	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×M₁₆	—	2	2	no	—
5	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₁₆	—	2	2	no	—
7	C₂×C₃×C₁₆	C₄	1	2	yes	—
8	C₃×#108	—	2	2	no	—
9	C₃×#108	C₄	1	4	yes	—
10	C₂²×C₁₆	C₂×C₃	1	1	yes	characteristic
11	C₂×#108	C₂×C₃	1	2	yes	—
12	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
13	C₃×M₁₆	—	2	4	no	—
14	C₃×M₁₆	—	4	2	no	—
15	C₂×C₃×C₈	—	4	2	no	—
16	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₃×C₈	D₄	1	2	yes	—
19	C₂×C₃×C₈	Q₈	1	1	yes	characteristic
20	C₃×C₁₆	—	2	2	no	—
21	C₂×M₁₆	—	2	2	no	—
22	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₁₆	—	2	2	no	—
24	C₂×C₁₆	C₃×C₄	1	2	yes	—
25	#108	—	2	2	no	—
26	#108	C₃×C₄	1	4	yes	—
27	C₂³×C₃	Q₁₆	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
29	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₃×C₄	D₈	1	1	yes	characteristic
31	C₂×C₃×C₄	SD₁₆	1	2	yes	—
32	C₃×C₈	—	4	4	no	—
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	M₁₆	—	2	4	no	—
38	M₁₆	—	4	2	no	—
39	C₂×C₈	—	4	2	no	—
40	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
42	C₂×C₈	C₃×D₄	1	2	yes	—
43	C₂×C₈	C₃×Q₈	1	1	yes	characteristic
44	C₁₆	—	2	2	no	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	#103	1	2	yes	—
47	C₂²×C₃	#107	1	1	yes	characteristic
48	C₃×C₄	#95	1	1	yes	characteristic
49	C₃×C₄	#102	1	2	yes	—
50	C₃×C₄	#106	1	1	yes	characteristic
51	C₂³	C₃×Q₁₆	1	1	yes	characteristic
52	C₂×C₄	C₃×C₂²⋊C₄	1	2	yes	—
53	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄	C₃×D₈	1	1	yes	characteristic
55	C₂×C₄	C₃×SD₁₆	1	2	yes	—
56	C₈	—	4	4	no	—
57	C₈	C₃×C₄²	1	1	yes	characteristic
58	C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
59	C₈	C₃×C₄⋊C₄	1	2	yes	—
60	C₂×C₃	—	2	2	no	—
61	C₂×C₃	#340	1	1	yes	characteristic
62	C₂×C₃	#368	1	2	yes	—
63	C₂²	—	2	2	no	—
64	C₂²	C₃×#103	1	2	yes	—
65	C₂²	C₃×#107	1	1	yes	characteristic
66	C₄	C₃×#95	1	1	yes	characteristic
67	C₄	C₃×#102	1	2	yes	—
68	C₄	C₃×#106	1	1	yes	characteristic
69	C₃	#1381	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	2	2	no	—
71	C₂	C₃×#340	1	1	yes	characteristic
72	C₂	C₃×#368	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₈
commutator	C₈	C₃×C₄²
Frattini, cosocle	C₂²×C₈	C₂²×C₃
socle	C₂²×C₃	#107
prime radical	C₂³×C₃	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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. #1381	C₃	direct (N × H)
69. C₃	#1381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₁₆	2
C₂×C₃×#108	2
#1381	3

Subgroups — C3×#1381 #67941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1381 #67941