Subgroups — C₃×#1408 #67968

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₃×#353	C₂	1	2	yes	maximal, complemented
3	#1408	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×D₈	—	2	2	no	—
5	C₃×#127	C₄	1	1	yes	characteristic, complemented
6	C₃×#127	C₂²	1	1	yes	characteristic
7	C₃×#99	—	2	2	no	—
8	C₃×C₄×C₈	C₄	1	1	yes	characteristic, complemented
9	#493	C₂×C₃	1	1	yes	characteristic
10	#353	C₂×C₃	1	2	yes	complemented
11	C₂×C₃×D₄	—	2	1	no	—
12	C₂×C₃×D₄	—	4	1	no	—
13	C₂×C₃×D₄	—	4	1	no	—
14	C₂×C₃×D₄	D₄	1	2	yes	—
15	C₃×D₈	—	4	4	no	—
16	C₂×C₃×C₈	—	2	1	no	—
17	C₃×C₂²⋊C₄	—	4	2	no	—
18	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
19	C₂×D₈	—	2	2	no	—
20	#127	C₃×C₄	1	1	yes	characteristic, complemented
21	#127	C₂²×C₃	1	1	yes	characteristic
22	#99	—	2	2	no	—
23	C₄×C₈	C₃×C₄	1	1	yes	characteristic, complemented
24	C₂³×C₃	—	2	2	no	—
25	C₂³×C₃	—	4	1	no	—
26	C₃×D₄	—	4	2	no	—
27	C₃×D₄	—	4	2	no	—
28	C₃×D₄	—	8	2	no	—
29	C₃×D₄	—	8	2	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	8	2	no	—
32	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
33	C₃×C₈	—	2	2	no	—
34	C₂×D₄	—	2	1	no	—
35	C₂×D₄	—	4	1	no	—
36	C₂×D₄	—	4	1	no	—
37	C₂×D₄	C₃×D₄	1	2	yes	—
38	D₈	—	4	4	no	—
39	C₂×C₈	—	2	1	no	—
40	C₂²⋊C₄	—	4	2	no	—
41	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
42	C₂²×C₃	—	4	2	no	—
43	C₂²×C₃	—	8	2	no	—
44	C₂²×C₃	—	8	2	no	—
45	C₂²×C₃	—	8	1	no	—
46	C₂²×C₃	#99	1	1	yes	characteristic
47	C₃×C₄	—	2	2	no	—
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	—	16	2	no	—
50	C₂³	—	2	2	no	—
51	C₂³	—	4	1	no	—
52	D₄	—	4	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	8	2	no	—
55	D₄	—	8	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	8	2	no	—
58	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	8	2	no	—
62	C₂×C₃	—	16	1	no	—
63	C₂×C₃	#353	1	1	yes	characteristic
64	C₂²	—	4	2	no	—
65	C₂²	—	8	2	no	—
66	C₂²	—	8	2	no	—
67	C₂²	—	8	1	no	—
68	C₂²	C₃×#99	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	2	1	no	—
71	C₄	—	16	2	no	—
72	C₃	#1408	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	2	1	no	—
74	C₂	—	8	2	no	—
75	C₂	—	16	1	no	—
76	C₂	C₃×#353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#353
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	#127	C₂²×C₃
prime radical	C₃×#493	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#127 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#353	C₂	semidirect
3. #1408	C₃	direct (N × H)
5. C₃×#127	C₄	semidirect
8. C₃×C₄×C₈	C₄	semidirect
10. #353	C₂×C₃	semidirect
20. #127	C₃×C₄	semidirect
23. C₄×C₈	C₃×C₄	semidirect
72. C₃	#1408	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×#493	2
C₃×#353	2
#1408	3

Subgroups — C3×#1408 #67968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1408 #67968