Subgroups — C₃×#2842 #84706

Order 384.

548 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#399	C₂	1	4	yes	maximal, complemented
2	C₃×#396	C₂	1	8	yes	maximal, complemented
3	C₃×#379	C₂	1	3	yes	maximal
4	#2842	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁵×C₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄⋊C₄	C₂²	1	12	yes	complemented
7	C₂×C₃×C₂²⋊C₄	C₂²	1	12	yes	—
8	C₂×C₃×C₂²⋊C₄	C₂²	1	6	yes	—
9	C₃×#95	C₂²	1	4	yes	complemented
10	#399	C₂×C₃	1	4	yes	complemented
11	#396	C₂×C₃	1	8	yes	complemented
12	#379	C₂×C₃	1	3	yes	—
13	C₂⁴×C₃	—	4	6	no	—
14	C₂⁴×C₃	Q₈	1	4	yes	—
15	C₂⁴×C₃	C₂³	1	2	yes	—
16	C₂⁴×C₃	C₂³	1	1	yes	characteristic
17	C₂²×C₃×C₄	C₂³	1	12	yes	—
18	C₃×C₄⋊C₄	—	4	12	no	—
19	C₃×C₂²⋊C₄	—	4	12	no	—
20	C₃×C₂²⋊C₄	—	4	6	no	—
21	C₂⁵	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₄⋊C₄	C₂²×C₃	1	12	yes	complemented
23	C₂×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
24	C₂×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
25	#95	C₂²×C₃	1	4	yes	complemented
26	C₂³×C₃	—	2	12	no	—
27	C₂³×C₃	—	2	6	no	—
28	C₂³×C₃	—	4	12	no	—
29	C₂³×C₃	—	4	16	no	—
30	C₂³×C₃	C₂×Q₈	1	4	yes	—
31	C₂³×C₃	C₂×Q₈	1	2	yes	—
32	C₂³×C₃	C₂⁴	1	1	yes	characteristic
33	C₂×C₃×C₄	—	2	24	no	—
34	C₂×C₃×C₄	—	2	12	no	—
35	C₂⁴	—	4	6	no	—
36	C₂⁴	C₃×Q₈	1	4	yes	—
37	C₂⁴	C₂³×C₃	1	2	yes	—
38	C₂⁴	C₂³×C₃	1	1	yes	characteristic
39	C₂²×C₄	C₂³×C₃	1	12	yes	—
40	C₄⋊C₄	—	4	12	no	—
41	C₂²⋊C₄	—	4	12	no	—
42	C₂²⋊C₄	—	4	6	no	—
43	C₂²×C₃	—	2	12	no	—
44	C₂²×C₃	—	2	6	no	—
45	C₂²×C₃	—	4	16	no	—
46	C₂²×C₃	—	4	8	no	—
47	C₂²×C₃	—	4	4	no	—
48	C₂²×C₃	C₂²×Q₈	1	1	yes	characteristic
49	C₂²×C₃	H(5,𝔽₂)	1	6	yes	—
50	C₃×C₄	—	4	12	no	—
51	C₂³	—	2	12	no	—
52	C₂³	—	2	6	no	—
53	C₂³	—	4	12	no	—
54	C₂³	—	4	16	no	—
55	C₂³	C₂×C₃×Q₈	1	4	yes	—
56	C₂³	C₂×C₃×Q₈	1	2	yes	—
57	C₂³	C₂⁴×C₃	1	1	yes	characteristic
58	C₂×C₄	—	2	24	no	—
59	C₂×C₄	—	2	12	no	—
60	C₂×C₃	—	4	4	no	—
61	C₂×C₃	—	4	2	no	—
62	C₂×C₃	#543	1	3	yes	—
63	C₂×C₃	#560	1	4	yes	—
64	C₂²	—	2	12	no	—
65	C₂²	—	2	6	no	—
66	C₂²	—	4	16	no	—
67	C₂²	—	4	8	no	—
68	C₂²	—	4	4	no	—
69	C₂²	C₂²×C₃×Q₈	1	1	yes	characteristic
70	C₂²	C₃×H(5,𝔽₂)	1	6	yes	—
71	C₄	—	4	12	no	—
72	C₃	#2842	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	4	4	no	—
74	C₂	—	4	2	no	—
75	C₂	C₃×#543	1	3	yes	—
76	C₂	C₃×#560	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
prime radical	C₂⁵×C₃	C₂²
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
1. C₃×#399	C₂	semidirect
2. C₃×#396	C₂	semidirect
4. #2842	C₃	direct (N × H)
6. C₂×C₃×C₄⋊C₄	C₂²	semidirect
9. C₃×#95	C₂²	semidirect
10. #399	C₂×C₃	semidirect
11. #396	C₂×C₃	semidirect
22. C₂×C₄⋊C₄	C₂²×C₃	semidirect
25. #95	C₂²×C₃	semidirect
72. C₃	#2842	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×#399	2
C₃×#396	2
C₃×#379	2
#2842	3

Subgroups — C3×#2842 #84706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2842 #84706