Subgroups — C₃×#2864 #84728

Order 384.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#389	C₂	1	4	yes	maximal
2	C₃×#387	C₂	1	8	yes	maximal
3	C₃×#382	C₂	1	2	yes	maximal
4	C₃×C₄³	C₂	1	1	yes	maximal, characteristic
5	#2864	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	—
7	C₂×C₃×C₄⋊C₄	C₂²	1	8	yes	—
8	C₂×C₃×C₄²	C₂²	1	4	yes	—
9	C₂×C₃×C₄²	C₂²	1	2	yes	—
10	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
11	C₃×#95	C₂²	1	8	yes	—
12	C₃×#95	C₂²	1	8	yes	—
13	#389	C₂×C₃	1	4	yes	—
14	#387	C₂×C₃	1	8	yes	—
15	#382	C₂×C₃	1	2	yes	—
16	C₄³	C₂×C₃	1	1	yes	characteristic
17	C₂²×C₃×C₄	C₂³	1	8	yes	—
18	C₂²×C₃×C₄	C₂³	1	2	yes	—
19	C₂²×C₃×C₄	C₂³	1	4	yes	—
20	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₃×C₄⋊C₄	—	2	16	no	—
22	C₃×C₄⋊C₄	—	2	8	no	—
23	C₃×C₄²	—	2	8	no	—
24	C₃×C₄²	—	2	4	no	—
25	C₃×C₄²	Q₈	1	4	yes	—
26	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	—
27	C₂×C₄⋊C₄	C₂²×C₃	1	8	yes	—
28	C₂×C₄²	C₂²×C₃	1	4	yes	—
29	C₂×C₄²	C₂²×C₃	1	2	yes	—
30	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
31	#95	C₂²×C₃	1	8	yes	—
32	#95	C₂²×C₃	1	8	yes	—
33	C₂³×C₃	C₂⁴	1	1	yes	characteristic
34	C₂×C₃×C₄	—	2	4	no	—
35	C₂×C₃×C₄	—	2	4	no	—
36	C₂×C₃×C₄	—	2	4	no	—
37	C₂×C₃×C₄	—	2	8	no	—
38	C₂×C₃×C₄	—	2	16	no	—
39	C₂×C₃×C₄	C₂×Q₈	1	4	yes	—
40	C₂×C₃×C₄	C₂×Q₈	1	2	yes	—
41	C₂×C₃×C₄	#41	1	8	yes	—
42	C₂×C₃×C₄	#41	1	4	yes	—
43	C₂²×C₄	C₂³×C₃	1	8	yes	—
44	C₂²×C₄	C₂³×C₃	1	2	yes	—
45	C₂²×C₄	C₂³×C₃	1	4	yes	—
46	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
47	C₄⋊C₄	—	2	16	no	—
48	C₄⋊C₄	—	2	8	no	—
49	C₄²	—	2	8	no	—
50	C₄²	—	2	4	no	—
51	C₄²	C₃×Q₈	1	4	yes	—
52	C₂²×C₃	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₃	C₂×#41	1	2	yes	—
54	C₂²×C₃	C₂×#41	1	4	yes	—
55	C₃×C₄	—	2	8	no	—
56	C₃×C₄	—	2	4	no	—
57	C₃×C₄	—	4	8	no	—
58	C₃×C₄	#125	1	4	yes	—
59	C₂³	C₂⁴×C₃	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	2	4	no	—
63	C₂×C₄	—	2	8	no	—
64	C₂×C₄	—	2	16	no	—
65	C₂×C₄	C₂×C₃×Q₈	1	4	yes	—
66	C₂×C₄	C₂×C₃×Q₈	1	2	yes	—
67	C₂×C₄	C₃×#41	1	8	yes	—
68	C₂×C₄	C₃×#41	1	4	yes	—
69	C₂×C₃	C₂×#125	1	1	yes	characteristic
70	C₂×C₃	#529	1	4	yes	—
71	C₂×C₃	#533	1	2	yes	—
72	C₂²	C₂²×C₃×Q₈	1	1	yes	characteristic
73	C₂²	C₂×C₃×#41	1	2	yes	—
74	C₂²	C₂×C₃×#41	1	4	yes	—
75	C₄	—	2	8	no	—
76	C₄	—	2	4	no	—
77	C₄	—	4	8	no	—
78	C₄	C₃×#125	1	4	yes	—
79	C₃	#2864	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	C₂×C₃×#125	1	1	yes	characteristic
81	C₂	C₃×#529	1	4	yes	—
82	C₂	C₃×#533	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. #2864	C₃	direct (N × H)
79. C₃	#2864	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×#389	2
C₃×#387	2
C₃×#382	2
C₃×C₄³	2
#2864	3

Subgroups — C3×#2864 #84728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2864 #84728