Subgroups — C₃×#2241 #72956

Order 384.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₃×#494	C₂	1	1	yes	maximal, characteristic
3	C₃×#358	C₂	1	4	yes	maximal
4	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
5	#2241	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₁₆	—	2	1	no	—
7	C₂×C₃×Q₁₆	C₂²	1	2	yes	—
8	C₃×C₄⋊Q₈	—	2	1	no	—
9	C₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₃×C₁₆	C₂²	1	2	yes	—
11	C₃×#107	—	2	1	no	—
12	C₃×#107	C₂²	1	2	yes	—
13	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
14	#500	C₂×C₃	1	1	yes	characteristic
15	#494	C₂×C₃	1	1	yes	characteristic
16	#358	C₂×C₃	1	4	yes	—
17	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×Q₈	—	2	2	no	—
19	C₂×C₃×Q₈	—	4	1	no	—
20	C₃×Q₁₆	—	2	4	no	—
21	C₃×Q₁₆	—	4	2	no	—
22	C₂×C₃×C₈	D₄	1	1	yes	characteristic
23	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
24	C₃×C₄⋊C₄	—	2	2	no	—
25	C₃×C₄⋊C₄	—	4	1	no	—
26	C₃×C₄⋊C₄	—	4	1	no	—
27	C₃×C₄⋊C₄	—	4	1	no	—
28	C₃×C₄²	D₄	1	1	yes	characteristic
29	C₃×C₁₆	—	2	2	no	—
30	C₂×Q₁₆	—	2	1	no	—
31	C₂×Q₁₆	C₂²×C₃	1	2	yes	—
32	C₄⋊Q₈	—	2	1	no	—
33	C₄⋊Q₈	—	2	1	no	—
34	C₂×C₁₆	C₂²×C₃	1	2	yes	—
35	#107	—	2	1	no	—
36	#107	C₂²×C₃	1	2	yes	—
37	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
38	C₃×Q₈	—	4	2	no	—
39	C₃×Q₈	—	4	2	no	—
40	C₃×Q₈	—	8	2	no	—
41	C₂×C₃×C₄	—	4	2	no	—
42	C₂×C₃×C₄	—	4	2	no	—
43	C₂×C₃×C₄	D₈	1	1	yes	characteristic
44	C₂×C₃×C₄	D₈	1	1	yes	characteristic
45	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
46	C₃×C₈	SD₁₆	1	2	yes	—
47	C₃×C₈	#41	1	2	yes	—
48	C₂×Q₈	—	2	2	no	—
49	C₂×Q₈	—	4	1	no	—
50	Q₁₆	—	2	4	no	—
51	Q₁₆	—	4	2	no	—
52	C₂×C₈	C₃×D₄	1	1	yes	characteristic
53	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
54	C₄⋊C₄	—	2	2	no	—
55	C₄⋊C₄	—	4	1	no	—
56	C₄⋊C₄	—	4	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₄²	C₃×D₄	1	1	yes	characteristic
59	C₁₆	—	2	2	no	—
60	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
61	C₃×C₄	—	8	2	no	—
62	C₃×C₄	—	8	2	no	—
63	C₃×C₄	SD₃₂	1	2	yes	—
64	C₃×C₄	Q₃₂	1	2	yes	—
65	C₃×C₄	#124	1	1	yes	characteristic
66	C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
67	Q₈	—	4	2	no	—
68	Q₈	—	4	2	no	—
69	Q₈	—	8	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	4	2	no	—
72	C₂×C₄	C₃×D₈	1	1	yes	characteristic
73	C₂×C₄	C₃×D₈	1	1	yes	characteristic
74	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
75	C₈	C₃×SD₁₆	1	2	yes	—
76	C₈	C₃×#41	1	2	yes	—
77	C₂×C₃	#486	1	1	yes	characteristic
78	C₂×C₃	C₂×SD₃₂	1	1	yes	characteristic
79	C₂×C₃	C₂×Q₃₂	1	1	yes	characteristic
80	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
81	C₄	—	8	2	no	—
82	C₄	—	8	2	no	—
83	C₄	C₃×SD₃₂	1	2	yes	—
84	C₄	C₃×Q₃₂	1	2	yes	—
85	C₄	C₃×#124	1	1	yes	characteristic
86	C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
87	C₃	#2241	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	C₃×#486	1	1	yes	characteristic
89	C₂	C₂×C₃×SD₃₂	1	1	yes	characteristic
90	C₂	C₂×C₃×Q₃₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. #2241	C₃	direct (N × H)
87. C₃	#2241	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×#500	2
C₃×#494	2
C₃×#358	2
C₃×C₄×C₁₆	2
#2241	3

Subgroups — C3×#2241 #72956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2241 #72956