Subgroups — C₃×#1273 #67833

Order 384.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₈	C₂	1	3	yes	maximal
2	#1273	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₂²×C₃×C₈	C₄	1	6	yes	—
4	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₈	—	2	6	no	—
6	C₂×C₄×C₈	C₂×C₃	1	3	yes	—
7	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
8	C₂×C₃×C₈	—	2	6	no	—
9	C₂×C₃×C₈	—	2	6	no	—
10	C₂×C₃×C₈	C₈	1	12	yes	complemented
11	C₃×C₄²	D₄	1	3	yes	—
12	C₃×C₄²	Q₈	1	1	yes	characteristic
13	C₂²×C₈	C₃×C₄	1	6	yes	—
14	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
15	C₄×C₈	—	2	6	no	—
16	C₂³×C₃	C₄²	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂²⋊C₄	1	3	yes	—
18	C₂×C₃×C₄	C₄⋊C₄	1	3	yes	—
19	C₂×C₃×C₄	C₂×C₈	1	6	yes	—
20	C₂×C₃×C₄	M₁₆	1	6	yes	—
21	C₃×C₈	—	2	12	no	—
22	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
23	C₂×C₈	—	2	6	no	—
24	C₂×C₈	—	2	6	no	—
25	C₂×C₈	C₃×C₈	1	12	yes	complemented
26	C₄²	C₃×D₄	1	3	yes	—
27	C₄²	C₃×Q₈	1	1	yes	characteristic
28	C₂²×C₃	#95	1	1	yes	characteristic
29	C₂²×C₃	C₄×C₈	1	3	yes	—
30	C₂²×C₃	#97	1	3	yes	—
31	C₃×C₄	C₂²⋊C₈	1	6	yes	—
32	C₃×C₄	C₄⋊C₈	1	6	yes	—
33	C₂³	C₃×C₄²	1	1	yes	characteristic
34	C₂×C₄	C₃×C₂²⋊C₄	1	3	yes	—
35	C₂×C₄	C₃×C₄⋊C₄	1	3	yes	—
36	C₂×C₄	C₂×C₃×C₈	1	6	yes	—
37	C₂×C₄	C₃×M₁₆	1	6	yes	—
38	C₈	—	2	12	no	—
39	C₂×C₃	C₈²	1	1	yes	characteristic
40	C₂×C₃	#322	1	3	yes	—
41	C₂×C₃	#336	1	3	yes	—
42	C₂²	C₃×#95	1	1	yes	characteristic
43	C₂²	C₃×C₄×C₈	1	3	yes	—
44	C₂²	C₃×#97	1	3	yes	—
45	C₄	C₃×C₂²⋊C₈	1	6	yes	—
46	C₄	C₃×C₄⋊C₈	1	6	yes	—
47	C₃	#1273	1	1	yes	characteristic, direct product factor, Sylow
48	C₂	C₃×C₈²	1	1	yes	characteristic
49	C₂	C₃×#322	1	3	yes	—
50	C₂	C₃×#336	1	3	yes	—

	subgroup	G/H
center	C₂×C₃×C₄²	C₂²
commutator	C₂	C₃×C₈²
Frattini, cosocle	C₂×C₄²	C₂²×C₃
socle, prime radical	C₂³×C₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. #1273	C₃	direct (N × H)
10. C₂×C₃×C₈	C₈	semidirect
25. C₂×C₈	C₃×C₈	semidirect
47. C₃	#1273	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×C₄×C₈	2
#1273	3

Subgroups — C3×#1273 #67833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1273 #67833