Subgroups — C₃×#1307 #67867

Order 384.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#432	C₂	1	2	yes	maximal
2	C₃×#423	C₂	1	1	yes	maximal, characteristic
3	#1307	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×M₁₆	C₄	1	2	yes	—
5	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
6	C₃×C₄⋊C₈	—	2	2	no	—
7	C₃×C₄⋊C₈	—	2	2	no	—
8	C₃×C₂²⋊C₈	C₄	1	4	yes	—
9	C₃×#97	—	2	2	no	—
10	#432	C₂×C₃	1	2	yes	—
11	#423	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
14	C₃×M₁₆	—	4	2	no	—
15	C₂×C₃×C₈	—	2	4	no	—
16	C₂×C₃×C₈	—	2	2	no	—
17	C₃×C₄²	D₄	1	1	yes	characteristic
18	C₃×C₄²	D₄	1	2	yes	—
19	C₃×C₄²	Q₈	1	1	yes	characteristic
20	C₂×M₁₆	C₃×C₄	1	2	yes	—
21	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
22	C₄⋊C₈	—	2	2	no	—
23	C₄⋊C₈	—	2	2	no	—
24	C₂²⋊C₈	C₃×C₄	1	4	yes	—
25	#97	—	2	2	no	—
26	C₂³×C₃	C₄²	1	1	yes	characteristic
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	4	2	no	—
30	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
31	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
34	C₃×C₈	—	4	4	no	—
35	C₃×C₈	—	4	2	no	—
36	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
37	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
38	M₁₆	—	4	2	no	—
39	C₂×C₈	—	2	4	no	—
40	C₂×C₈	—	2	2	no	—
41	C₄²	C₃×D₄	1	1	yes	characteristic
42	C₄²	C₃×D₄	1	2	yes	—
43	C₄²	C₃×Q₈	1	1	yes	characteristic
44	C₂²×C₃	—	2	1	no	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	#95	1	1	yes	characteristic
47	C₃×C₄	—	2	1	no	—
48	C₃×C₄	—	2	2	no	—
49	C₃×C₄	—	2	2	no	—
50	C₃×C₄	#100	1	1	yes	characteristic
51	C₃×C₄	#101	1	1	yes	characteristic
52	C₂³	C₃×C₄²	1	1	yes	characteristic
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	4	2	no	—
56	C₂×C₄	C₃×C₂²⋊C₄	1	2	yes	—
57	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄	C₃×C₄⋊C₄	1	2	yes	—
60	C₈	—	4	4	no	—
61	C₈	—	4	2	no	—
62	C₂×C₃	—	4	1	no	—
63	C₂×C₃	#343	1	1	yes	characteristic
64	C₂×C₃	#344	1	2	yes	—
65	C₂²	—	2	1	no	—
66	C₂²	—	2	2	no	—
67	C₂²	C₃×#95	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	2	no	—
70	C₄	—	2	2	no	—
71	C₄	C₃×#100	1	1	yes	characteristic
72	C₄	C₃×#101	1	1	yes	characteristic
73	C₃	#1307	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	—	4	1	no	—
75	C₂	C₃×#343	1	1	yes	characteristic
76	C₂	C₃×#344	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	#95
commutator	C₂³	C₃×C₄²
Frattini, cosocle	C₂×C₄²	C₂²×C₃
prime radical	C₂³×C₃	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
3. #1307	C₃	direct (N × H)
73. C₃	#1307	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#432	2
C₃×#423	2
#1307	3

Subgroups — C3×#1307 #67867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1307 #67867