Subgroups — C₃×#2844 #84708

Order 384.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#400	C₂	1	6	yes	maximal
2	C₃×#395	C₂	1	6	yes	maximal
3	C₃×#382	C₂	1	3	yes	maximal
4	#2844	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×Q₈	C₂²	1	2	yes	—
6	C₂×C₃×C₄⋊C₄	C₂²	1	3	yes	—
7	C₂×C₃×C₄⋊C₄	C₂²	1	3	yes	—
8	C₂×C₃×C₄⋊C₄	C₂²	1	6	yes	—
9	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₃×#95	C₂²	1	12	yes	—
11	C₃×#95	C₂²	1	6	yes	—
12	C₃×#95	C₂²	1	2	yes	—
13	#400	C₂×C₃	1	6	yes	—
14	#395	C₂×C₃	1	6	yes	—
15	#382	C₂×C₃	1	3	yes	—
16	C₂×C₃×Q₈	—	4	6	no	—
17	C₂²×C₃×C₄	C₂³	1	6	yes	—
18	C₂²×C₃×C₄	C₂³	1	6	yes	—
19	C₂²×C₃×C₄	C₂³	1	3	yes	—
20	C₃×C₄⋊C₄	—	4	3	no	—
21	C₃×C₄⋊C₄	—	4	3	no	—
22	C₃×C₄⋊C₄	—	4	6	no	—
23	C₃×C₄²	Q₈	1	4	yes	complemented
24	C₂²×Q₈	C₂²×C₃	1	2	yes	—
25	C₂×C₄⋊C₄	C₂²×C₃	1	3	yes	—
26	C₂×C₄⋊C₄	C₂²×C₃	1	3	yes	—
27	C₂×C₄⋊C₄	C₂²×C₃	1	6	yes	—
28	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
29	#95	C₂²×C₃	1	12	yes	—
30	#95	C₂²×C₃	1	6	yes	—
31	#95	C₂²×C₃	1	2	yes	—
32	C₂³×C₃	C₂⁴	1	1	yes	characteristic
33	C₃×Q₈	—	4	8	no	—
34	C₂×C₃×C₄	—	2	3	no	—
35	C₂×C₃×C₄	—	2	3	no	—
36	C₂×C₃×C₄	—	2	6	no	—
37	C₂×C₃×C₄	—	2	6	no	—
38	C₂×C₃×C₄	—	2	12	no	—
39	C₂×C₃×C₄	—	2	12	no	—
40	C₂×C₃×C₄	C₂×Q₈	1	6	yes	—
41	C₂×Q₈	—	4	6	no	—
42	C₂²×C₄	C₂³×C₃	1	6	yes	—
43	C₂²×C₄	C₂³×C₃	1	6	yes	—
44	C₂²×C₄	C₂³×C₃	1	3	yes	—
45	C₄⋊C₄	—	4	3	no	—
46	C₄⋊C₄	—	4	3	no	—
47	C₄⋊C₄	—	4	6	no	—
48	C₄²	C₃×Q₈	1	4	yes	complemented
49	C₂²×C₃	C₂²×Q₈	1	1	yes	characteristic
50	C₂²×C₃	H(5,𝔽₂)	1	3	yes	—
51	C₂²×C₃	2₋¹⁺⁴	1	3	yes	—
52	C₃×C₄	—	2	6	no	—
53	C₃×C₄	—	4	6	no	—
54	C₃×C₄	—	4	6	no	—
55	C₂³	C₂⁴×C₃	1	1	yes	characteristic
56	Q₈	—	4	8	no	—
57	C₂×C₄	—	2	3	no	—
58	C₂×C₄	—	2	3	no	—
59	C₂×C₄	—	2	6	no	—
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	—	2	12	no	—
62	C₂×C₄	—	2	12	no	—
63	C₂×C₄	C₂×C₃×Q₈	1	6	yes	—
64	C₂×C₃	#544	1	3	yes	—
65	C₂×C₃	H(3,𝔽₄)	1	1	yes	characteristic
66	C₂×C₃	#563	1	3	yes	—
67	C₂²	C₂²×C₃×Q₈	1	1	yes	characteristic
68	C₂²	C₃×H(5,𝔽₂)	1	3	yes	—
69	C₂²	C₃×2₋¹⁺⁴	1	3	yes	—
70	C₄	—	2	6	no	—
71	C₄	—	4	6	no	—
72	C₄	—	4	6	no	—
73	C₃	#2844	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	C₃×#544	1	3	yes	—
75	C₂	C₃×H(3,𝔽₄)	1	1	yes	characteristic
76	C₂	C₃×#563	1	3	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
4. #2844	C₃	direct (N × H)
23. C₃×C₄²	Q₈	semidirect
48. C₄²	C₃×Q₈	semidirect
73. C₃	#2844	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×#400	2
C₃×#395	2
C₃×#382	2
#2844	3

Subgroups — C3×#2844 #84708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2844 #84708