Subgroups — C₃×#1452 #72167

Order 384.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#431	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#322	C₂	1	4	yes	maximal, complemented
4	#1452	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₈	C₄	1	2	yes	—
6	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₃×C₄⋊C₈	C₄	1	4	yes	—
8	C₃×C₂²⋊C₈	C₄	1	4	yes	—
9	C₃×C₄×C₈	C₄	1	2	yes	—
10	C₃×C₄×C₈	C₂²	1	2	yes	—
11	C₃×C₄×C₈	C₂²	1	4	yes	—
12	#431	C₂×C₃	1	2	yes	—
13	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic
14	#322	C₂×C₃	1	4	yes	complemented
15	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
16	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	—	2	4	no	—
18	C₂×C₃×C₈	C₂×C₄	1	4	yes	—
19	C₂×C₃×C₈	C₂×C₄	1	8	yes	—
20	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄²	C₂×C₄	1	2	yes	—
22	C₃×C₄²	C₂³	1	1	yes	characteristic
23	C₂²×C₈	C₃×C₄	1	2	yes	—
24	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
25	C₄⋊C₈	C₃×C₄	1	4	yes	—
26	C₂²⋊C₈	C₃×C₄	1	4	yes	—
27	C₄×C₈	C₃×C₄	1	2	yes	—
28	C₄×C₈	C₂²×C₃	1	2	yes	—
29	C₄×C₈	C₂²×C₃	1	4	yes	—
30	C₂³×C₃	C₄²	1	1	yes	characteristic
31	C₂×C₃×C₄	—	2	4	no	—
32	C₂×C₃×C₄	C₄²	1	2	yes	—
33	C₂×C₃×C₄	C₄²	1	1	yes	characteristic
34	C₂×C₃×C₄	M₁₆	1	4	yes	—
35	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
37	C₃×C₈	—	2	4	no	—
38	C₃×C₈	—	2	8	no	—
39	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
40	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₈	—	2	4	no	—
42	C₂×C₈	C₂×C₃×C₄	1	4	yes	—
43	C₂×C₈	C₂×C₃×C₄	1	8	yes	—
44	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
45	C₄²	C₂×C₃×C₄	1	2	yes	—
46	C₄²	C₂³×C₃	1	1	yes	characteristic
47	C₂²×C₃	—	2	2	no	—
48	C₂²×C₃	#97	1	2	yes	—
49	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
50	C₃×C₄	—	2	2	no	—
51	C₃×C₄	#97	1	2	yes	—
52	C₃×C₄	C₂×M₁₆	1	2	yes	—
53	C₃×C₄	#131	1	4	yes	—
54	C₂³	C₃×C₄²	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	C₃×C₄²	1	2	yes	—
57	C₂×C₄	C₃×C₄²	1	1	yes	characteristic
58	C₂×C₄	C₃×M₁₆	1	4	yes	—
59	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
60	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
61	C₈	—	2	4	no	—
62	C₈	—	2	8	no	—
63	C₂×C₃	—	2	2	no	—
64	C₂×C₃	C₂×#97	1	1	yes	characteristic
65	C₂×C₃	#405	1	2	yes	—
66	C₂²	—	2	2	no	—
67	C₂²	C₃×#97	1	2	yes	—
68	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	C₃×#97	1	2	yes	—
71	C₄	C₂×C₃×M₁₆	1	2	yes	—
72	C₄	C₃×#131	1	4	yes	—
73	C₃	#1452	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	—	2	2	no	—
75	C₂	C₂×C₃×#97	1	1	yes	characteristic
76	C₂	C₃×#405	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×#322	C₂	semidirect
4. #1452	C₃	direct (N × H)
14. #322	C₂×C₃	semidirect
73. C₃	#1452	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×#431	2
C₂×C₃×C₄×C₈	2
C₃×#322	2
#1452	3

Subgroups — C3×#1452 #72167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1452 #72167