Subgroups — C₃×#1380 #67940

Order 384.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#107	C₂	1	2	yes	maximal
3	#1380	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
5	C₂×C₃×C₄⋊C₄	—	2	2	no	—
6	C₂×C₃×C₁₆	—	2	2	no	—
7	C₂×C₃×C₁₆	C₄	1	2	yes	complemented
8	C₃×#107	—	2	2	no	—
9	C₃×#107	C₄	1	4	yes	complemented
10	C₂²×C₁₆	C₂×C₃	1	1	yes	characteristic
11	C₂×#107	C₂×C₃	1	2	yes	—
12	C₂²×C₃×C₄	—	4	2	no	—
13	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
14	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₃×C₈	D₄	1	2	yes	—
17	C₂×C₃×C₈	Q₈	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	2	4	no	—
19	C₃×C₄⋊C₄	—	4	2	no	—
20	C₃×C₁₆	—	2	2	no	—
21	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₆	—	2	2	no	—
24	C₂×C₁₆	C₃×C₄	1	2	yes	complemented
25	#107	—	2	2	no	—
26	#107	C₃×C₄	1	4	yes	complemented
27	C₂³×C₃	D₈	1	1	yes	characteristic
28	C₂×C₃×C₄	—	4	4	no	—
29	C₂×C₃×C₄	—	8	2	no	—
30	C₂×C₃×C₄	—	8	2	no	—
31	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
32	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₃×C₄	SD₁₆	1	2	yes	—
34	C₂×C₃×C₄	Q₁₆	1	1	yes	characteristic
35	C₃×C₈	C₄²	1	1	yes	characteristic
36	C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
37	C₃×C₈	C₄⋊C₄	1	2	yes	—
38	C₂²×C₄	—	4	2	no	—
39	C₂²×C₄	C₃×D₄	1	1	yes	characteristic
40	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
42	C₂×C₈	C₃×D₄	1	2	yes	—
43	C₂×C₈	C₃×Q₈	1	1	yes	characteristic
44	C₄⋊C₄	—	2	4	no	—
45	C₄⋊C₄	—	4	2	no	—
46	C₁₆	—	2	2	no	—
47	C₂²×C₃	#102	1	2	yes	—
48	C₂²×C₃	#107	1	1	yes	characteristic
49	C₂²×C₃	D₁₆	1	1	yes	characteristic
50	C₂²×C₃	SD₃₂	1	2	yes	—
51	C₂²×C₃	Q₃₂	1	1	yes	characteristic
52	C₃×C₄	—	8	4	no	—
53	C₃×C₄	#95	1	1	yes	characteristic
54	C₃×C₄	#103	1	2	yes	—
55	C₃×C₄	#106	1	1	yes	characteristic
56	C₂³	C₃×D₈	1	1	yes	characteristic
57	C₂×C₄	—	4	4	no	—
58	C₂×C₄	—	8	2	no	—
59	C₂×C₄	—	8	2	no	—
60	C₂×C₄	C₃×C₂²⋊C₄	1	2	yes	—
61	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄	C₃×SD₁₆	1	2	yes	—
63	C₂×C₄	C₃×Q₁₆	1	1	yes	characteristic
64	C₈	C₃×C₄²	1	1	yes	characteristic
65	C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
66	C₈	C₃×C₄⋊C₄	1	2	yes	—
67	C₂×C₃	#340	1	1	yes	characteristic
68	C₂×C₃	#357	1	2	yes	—
69	C₂×C₃	#358	1	2	yes	—
70	C₂×C₃	#366	1	1	yes	characteristic
71	C₂×C₃	#367	1	1	yes	characteristic
72	C₂²	C₃×#102	1	2	yes	—
73	C₂²	C₃×#107	1	1	yes	characteristic
74	C₂²	C₃×D₁₆	1	1	yes	characteristic
75	C₂²	C₃×SD₃₂	1	2	yes	—
76	C₂²	C₃×Q₃₂	1	1	yes	characteristic
77	C₄	—	8	4	no	—
78	C₄	C₃×#95	1	1	yes	characteristic
79	C₄	C₃×#103	1	2	yes	—
80	C₄	C₃×#106	1	1	yes	characteristic
81	C₃	#1380	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	C₃×#340	1	1	yes	characteristic
83	C₂	C₃×#357	1	2	yes	—
84	C₂	C₃×#358	1	2	yes	—
85	C₂	C₃×#366	1	1	yes	characteristic
86	C₂	C₃×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	D₈
commutator	C₈	C₃×C₄²
Frattini, cosocle	C₂²×C₈	C₂²×C₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1380	C₃	direct (N × H)
7. C₂×C₃×C₁₆	C₄	semidirect
9. C₃×#107	C₄	semidirect
24. C₂×C₁₆	C₃×C₄	semidirect
26. #107	C₃×C₄	semidirect
81. C₃	#1380	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₁₆	2
C₂×C₃×#107	2
#1380	3

Subgroups — C3×#1380 #67940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1380 #67940