Subgroups — C₃×#2030 #72745

Order 384.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#543	C₂	1	1	yes	maximal, characteristic
2	C₃×#381	C₂	1	3	yes	maximal
3	C₃×#342	C₂	1	3	yes	maximal
4	#2030	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×C₂²⋊Q₈	—	2	6	no	—
7	C₂×C₃×C₂²⋊C₄	C₂²	1	3	yes	—
8	C₂×C₃×C₂²⋊C₄	C₂²	1	3	yes	—
9	C₃×#95	—	2	6	no	—
10	#543	C₂×C₃	1	1	yes	characteristic
11	#381	C₂×C₃	1	3	yes	—
12	#342	C₂×C₃	1	3	yes	—
13	C₂⁴×C₃	C₂³	1	1	yes	characteristic
14	C₂×C₃×Q₈	—	2	2	no	—
15	C₂²×C₃×C₄	—	2	3	no	—
16	C₂²×C₃×C₄	—	2	3	no	—
17	C₂²×C₃×C₄	—	2	3	no	—
18	C₂²×C₃×C₄	D₄	1	6	yes	—
19	C₂²×C₃×C₄	Q₈	1	2	yes	complemented
20	C₃×C₄⋊C₄	—	2	6	no	—
21	C₃×C₂²⋊C₄	—	2	6	no	—
22	C₃×C₂²⋊C₄	—	2	6	no	—
23	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
24	C₂²⋊Q₈	—	2	6	no	—
25	C₂×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
26	C₂×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
27	#95	—	2	6	no	—
28	C₂³×C₃	—	4	2	no	—
29	C₂³×C₃	C₂×D₄	1	3	yes	—
30	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
31	C₂³×C₃	#41	1	3	yes	—
32	C₃×Q₈	—	8	2	no	—
33	C₂×C₃×C₄	—	2	6	no	—
34	C₂×C₃×C₄	—	2	6	no	—
35	C₂×C₃×C₄	—	4	1	no	—
36	C₂×C₃×C₄	—	4	3	no	—
37	C₂×C₃×C₄	—	4	6	no	—
38	C₂×C₃×C₄	—	4	6	no	—
39	C₂×C₃×C₄	—	4	3	no	—
40	C₂⁴	C₂³×C₃	1	1	yes	characteristic
41	C₂×Q₈	—	2	2	no	—
42	C₂²×C₄	—	2	3	no	—
43	C₂²×C₄	—	2	3	no	—
44	C₂²×C₄	—	2	3	no	—
45	C₂²×C₄	C₃×D₄	1	6	yes	—
46	C₂²×C₄	C₃×Q₈	1	2	yes	complemented
47	C₄⋊C₄	—	2	6	no	—
48	C₂²⋊C₄	—	2	6	no	—
49	C₂²⋊C₄	—	2	6	no	—
50	C₂²×C₃	—	2	6	no	—
51	C₂²×C₃	—	4	1	no	—
52	C₂²×C₃	—	4	3	no	—
53	C₂²×C₃	#120	1	1	yes	characteristic
54	C₂²×C₃	C₂²⋊Q₈	1	3	yes	—
55	C₂²×C₃	#124	1	3	yes	—
56	C₃×C₄	—	4	2	no	—
57	C₃×C₄	—	4	6	no	—
58	C₃×C₄	—	8	3	no	—
59	C₂³	—	4	2	no	—
60	C₂³	C₂×C₃×D₄	1	3	yes	—
61	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
62	C₂³	C₃×#41	1	3	yes	—
63	Q₈	—	8	2	no	—
64	C₂×C₄	—	2	6	no	—
65	C₂×C₄	—	2	6	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	4	3	no	—
68	C₂×C₄	—	4	6	no	—
69	C₂×C₄	—	4	6	no	—
70	C₂×C₄	—	4	3	no	—
71	C₂×C₃	—	2	3	no	—
72	C₂×C₃	—	2	3	no	—
73	C₂×C₃	#393	1	1	yes	characteristic
74	C₂×C₃	#458	1	2	yes	—
75	C₂²	—	2	6	no	—
76	C₂²	—	4	1	no	—
77	C₂²	—	4	3	no	—
78	C₂²	C₃×#120	1	1	yes	characteristic
79	C₂²	C₃×C₂²⋊Q₈	1	3	yes	—
80	C₂²	C₃×#124	1	3	yes	—
81	C₄	—	4	2	no	—
82	C₄	—	4	6	no	—
83	C₄	—	8	3	no	—
84	C₃	#2030	1	1	yes	characteristic, direct product factor, Sylow
85	C₂	—	2	3	no	—
86	C₂	—	2	3	no	—
87	C₂	C₃×#393	1	1	yes	characteristic
88	C₂	C₃×#458	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₃
prime radical	C₂⁴×C₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. #2030	C₃	direct (N × H)
19. C₂²×C₃×C₄	Q₈	semidirect
46. C₂²×C₄	C₃×Q₈	semidirect
84. C₃	#2030	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×#543	2
C₃×#381	2
C₃×#342	2
#2030	3

Subgroups — C3×#2030 #72745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2030 #72745