Subgroups — C₃×#1842 #72557

Order 384.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊C₈	C₂	1	6	yes	maximal
2	C₃×C₄³	C₂	1	1	yes	maximal, characteristic
3	#1842	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₂²	1	4	yes	—
5	C₂×C₃×C₄²	C₄	1	3	yes	—
6	C₂×C₃×C₄²	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄²	C₂²	1	3	yes	—
8	C₃×C₄⋊C₈	—	2	12	no	—
9	C₂×C₄⋊C₈	C₂×C₃	1	6	yes	—
10	C₄³	C₂×C₃	1	1	yes	characteristic
11	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
12	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
13	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
14	C₂×C₃×C₈	—	2	12	no	—
15	C₃×C₄²	—	2	6	no	—
16	C₃×C₄²	C₈	1	4	yes	complemented
17	C₃×C₄²	D₄	1	6	yes	—
18	C₃×C₄²	Q₈	1	6	yes	—
19	C₂²×C₈	C₂²×C₃	1	4	yes	—
20	C₂×C₄²	C₃×C₄	1	3	yes	—
21	C₂×C₄²	C₃×C₄	1	1	yes	characteristic
22	C₂×C₄²	C₂²×C₃	1	3	yes	—
23	C₄⋊C₈	—	2	12	no	—
24	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	—	2	6	no	—
26	C₂×C₃×C₄	C₄⋊C₄	1	6	yes	—
27	C₂×C₃×C₄	C₄⋊C₄	1	6	yes	—
28	C₂×C₃×C₄	C₂×C₈	1	6	yes	—
29	C₂×C₃×C₄	M₁₆	1	6	yes	—
30	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
31	C₂×C₃×C₄	C₂×Q₈	1	3	yes	—
32	C₃×C₈	—	4	4	no	—
33	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
34	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
35	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
36	C₂×C₈	—	2	12	no	—
37	C₄²	—	2	6	no	—
38	C₄²	C₃×C₈	1	4	yes	complemented
39	C₄²	C₃×D₄	1	6	yes	—
40	C₄²	C₃×Q₈	1	6	yes	—
41	C₂²×C₃	C₂×C₄⋊C₄	1	3	yes	—
42	C₂²×C₃	C₂²×C₈	1	1	yes	characteristic
43	C₂²×C₃	C₂×M₁₆	1	3	yes	—
44	C₃×C₄	—	2	6	no	—
45	C₃×C₄	C₄⋊C₈	1	12	yes	complemented
46	C₃×C₄	#127	1	1	yes	characteristic
47	C₃×C₄	C₄⋊Q₈	1	3	yes	—
48	C₂³	C₂²×C₃×C₄	1	1	yes	characteristic
49	C₂×C₄	—	2	6	no	—
50	C₂×C₄	C₃×C₄⋊C₄	1	6	yes	—
51	C₂×C₄	C₃×C₄⋊C₄	1	6	yes	—
52	C₂×C₄	C₂×C₃×C₈	1	6	yes	—
53	C₂×C₄	C₃×M₁₆	1	6	yes	—
54	C₂×C₄	C₂×C₃×D₄	1	3	yes	—
55	C₂×C₄	C₂×C₃×Q₈	1	3	yes	—
56	C₈	—	4	4	no	—
57	C₂×C₃	#384	1	1	yes	characteristic
58	C₂×C₃	C₂×C₄⋊C₈	1	3	yes	—
59	C₂×C₃	#423	1	3	yes	—
60	C₂²	C₂×C₃×C₄⋊C₄	1	3	yes	—
61	C₂²	C₂²×C₃×C₈	1	1	yes	characteristic
62	C₂²	C₂×C₃×M₁₆	1	3	yes	—
63	C₄	—	2	6	no	—
64	C₄	C₃×C₄⋊C₈	1	12	yes	complemented
65	C₄	C₃×#127	1	1	yes	characteristic
66	C₄	C₃×C₄⋊Q₈	1	3	yes	—
67	C₃	#1842	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	C₃×#384	1	1	yes	characteristic
69	C₂	C₂×C₃×C₄⋊C₈	1	3	yes	—
70	C₂	C₃×#423	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂³
commutator	C₂²	C₂²×C₃×C₈
Frattini, cosocle	C₂²×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1842	C₃	direct (N × H)
16. C₃×C₄²	C₈	semidirect
38. C₄²	C₃×C₈	semidirect
45. C₃×C₄	C₄⋊C₈	semidirect
64. C₄	C₃×C₄⋊C₈	semidirect
67. C₃	#1842	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×C₄⋊C₈	2
C₃×C₄³	2
#1842	3

Subgroups — C3×#1842 #72557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1842 #72557