Subgroups — C₃×#1844 #72559

Order 384.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#106	C₂	1	4	yes	maximal
2	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#384	C₂	1	2	yes	maximal
4	#1844	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₈	C₂²	1	2	yes	—
6	C₂×C₃×C₄⋊C₄	—	2	4	no	—
7	C₂×C₃×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
9	C₃×#106	—	2	8	no	—
10	C₃×C₄×C₈	C₄	1	4	yes	complemented
11	C₂×#106	C₂×C₃	1	4	yes	—
12	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic
13	#384	C₂×C₃	1	2	yes	—
14	C₂²×C₃×C₄	—	2	4	no	—
15	C₂²×C₃×C₄	D₄	1	2	yes	—
16	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
17	C₂×C₃×C₈	C₂×C₄	1	4	yes	—
18	C₂×C₃×C₈	D₄	1	4	yes	—
19	C₂×C₃×C₈	Q₈	1	4	yes	—
20	C₃×C₄⋊C₄	—	2	8	no	—
21	C₃×C₄⋊C₄	—	4	8	no	—
22	C₃×C₄²	C₂×C₄	1	2	yes	—
23	C₃×C₄²	Q₈	1	2	yes	—
24	C₂²×C₈	C₂²×C₃	1	2	yes	—
25	C₂×C₄⋊C₄	—	2	4	no	—
26	C₂×C₄⋊C₄	C₂²×C₃	1	4	yes	—
27	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
28	#106	—	2	8	no	—
29	C₄×C₈	C₃×C₄	1	4	yes	complemented
30	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₃×C₄	—	4	4	no	—
32	C₂×C₃×C₄	—	4	8	no	—
33	C₂×C₃×C₄	C₄⋊C₄	1	4	yes	—
34	C₂×C₃×C₄	SD₁₆	1	8	yes	—
35	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
37	C₂×C₃×C₄	C₂×Q₈	1	2	yes	—
38	C₂×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
39	C₃×C₈	C₄⋊C₄	1	8	yes	complemented
40	C₂²×C₄	—	2	4	no	—
41	C₂²×C₄	C₃×D₄	1	2	yes	—
42	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
43	C₂×C₈	C₂×C₃×C₄	1	4	yes	—
44	C₂×C₈	C₃×D₄	1	4	yes	—
45	C₂×C₈	C₃×Q₈	1	4	yes	—
46	C₄⋊C₄	—	2	8	no	—
47	C₄⋊C₄	—	4	8	no	—
48	C₄²	C₂×C₃×C₄	1	2	yes	—
49	C₄²	C₃×Q₈	1	2	yes	—
50	C₂²×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₃	#127	1	1	yes	characteristic
52	C₂²×C₃	C₄⋊Q₈	1	1	yes	characteristic
53	C₂²×C₃	C₂×SD₁₆	1	4	yes	—
54	C₃×C₄	—	8	4	no	—
55	C₃×C₄	#106	1	8	yes	complemented
56	C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
57	C₃×C₄	C₄⋊Q₈	1	2	yes	—
58	C₂³	C₂×C₃×D₄	1	1	yes	characteristic
59	C₂×C₄	—	4	4	no	—
60	C₂×C₄	—	4	8	no	—
61	C₂×C₄	C₃×C₄⋊C₄	1	4	yes	—
62	C₂×C₄	C₃×SD₁₆	1	8	yes	—
63	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
64	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
65	C₂×C₄	C₂×C₃×Q₈	1	2	yes	—
66	C₂×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
67	C₈	C₃×C₄⋊C₄	1	8	yes	complemented
68	C₂×C₃	#384	1	1	yes	characteristic
69	C₂×C₃	C₂×#106	1	2	yes	—
70	C₂×C₃	#492	1	2	yes	—
71	C₂×C₃	#498	1	2	yes	—
72	C₂²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
73	C₂²	C₃×#127	1	1	yes	characteristic
74	C₂²	C₃×C₄⋊Q₈	1	1	yes	characteristic
75	C₂²	C₂×C₃×SD₁₆	1	4	yes	—
76	C₄	—	8	4	no	—
77	C₄	C₃×#106	1	8	yes	complemented
78	C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
79	C₄	C₃×C₄⋊Q₈	1	2	yes	—
80	C₃	#1844	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	C₃×#384	1	1	yes	characteristic
82	C₂	C₂×C₃×#106	1	2	yes	—
83	C₂	C₃×#492	1	2	yes	—
84	C₂	C₃×#498	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
4. #1844	C₃	direct (N × H)
10. C₃×C₄×C₈	C₄	semidirect
29. C₄×C₈	C₃×C₄	semidirect
39. C₃×C₈	C₄⋊C₄	semidirect
55. C₃×C₄	#106	semidirect
67. C₈	C₃×C₄⋊C₄	semidirect
77. C₄	C₃×#106	semidirect
80. C₃	#1844	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#106	2
C₂×C₃×C₄×C₈	2
C₃×#384	2
#1844	3

Subgroups — C3×#1844 #72559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1844 #72559