Subgroups — C₃×#1414 #67974

Order 384.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#488	C₂	1	1	yes	maximal, characteristic
2	C₃×#355	C₂	1	1	yes	maximal, characteristic
3	C₃×#354	C₂	1	1	yes	maximal, characteristic
4	#1414	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#125	C₄	1	1	yes	characteristic, complemented
6	C₃×#124	C₂²	1	1	yes	characteristic
7	C₃×#103	—	2	1	no	—
8	C₃×#102	—	2	1	no	—
9	C₃×#101	—	2	1	no	—
10	C₃×#99	—	2	1	no	—
11	C₃×C₄×C₈	C₄	1	1	yes	characteristic, complemented
12	#488	C₂×C₃	1	1	yes	characteristic
13	#355	C₂×C₃	1	1	yes	characteristic
14	#354	C₂×C₃	1	1	yes	characteristic
15	C₂×C₃×Q₈	D₄	1	1	yes	characteristic
16	C₂×C₃×D₄	D₄	1	1	yes	characteristic
17	C₃×M₁₆	—	4	1	no	—
18	C₂×C₃×C₈	—	2	1	no	—
19	C₃×C₄⋊C₄	—	2	1	no	—
20	C₃×C₄⋊C₄	—	4	1	no	—
21	C₃×C₂²⋊C₄	—	4	1	no	—
22	C₃×C₂²⋊C₄	—	4	1	no	—
23	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
24	#125	C₃×C₄	1	1	yes	characteristic, complemented
25	#124	C₂²×C₃	1	1	yes	characteristic
26	#103	—	2	1	no	—
27	#102	—	2	1	no	—
28	#101	—	2	1	no	—
29	#99	—	2	1	no	—
30	C₄×C₈	C₃×C₄	1	1	yes	characteristic, complemented
31	C₂³×C₃	—	2	1	no	—
32	C₃×Q₈	—	4	1	no	—
33	C₃×D₄	—	4	1	no	—
34	C₂×C₃×C₄	—	2	1	no	—
35	C₂×C₃×C₄	—	2	1	no	—
36	C₂×C₃×C₄	—	4	1	no	—
37	C₂×C₃×C₄	—	8	1	no	—
38	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
39	C₃×C₈	—	4	1	no	—
40	C₃×C₈	—	8	1	no	—
41	C₂×Q₈	C₃×D₄	1	1	yes	characteristic
42	C₂×D₄	C₃×D₄	1	1	yes	characteristic
43	M₁₆	—	4	1	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	4	1	no	—
48	C₂²⋊C₄	—	4	1	no	—
49	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
50	C₂²×C₃	—	4	1	no	—
51	C₂²×C₃	—	8	1	no	—
52	C₂²×C₃	#99	1	1	yes	characteristic
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	—	8	1	no	—
57	C₃×C₄	—	16	1	no	—
58	C₂³	—	2	1	no	—
59	Q₈	—	4	1	no	—
60	D₄	—	4	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	—	8	1	no	—
65	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
66	C₈	—	4	1	no	—
67	C₈	—	8	1	no	—
68	C₂×C₃	—	2	1	no	—
69	C₂×C₃	—	8	1	no	—
70	C₂×C₃	#354	1	1	yes	characteristic
71	C₂²	—	4	1	no	—
72	C₂²	—	8	1	no	—
73	C₂²	C₃×#99	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	4	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	8	1	no	—
78	C₄	—	16	1	no	—
79	C₃	#1414	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	C₃×#354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#354
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	#124	C₂²×C₃
prime radical	C₂×C₃×D₄	D₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#124 ◁ G

Complements

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

N	H ≅ G/N	type
4. #1414	C₃	direct (N × H)
5. C₃×#125	C₄	semidirect
11. C₃×C₄×C₈	C₄	semidirect
24. #125	C₃×C₄	semidirect
30. C₄×C₈	C₃×C₄	semidirect
79. C₃	#1414	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×#488	2
C₃×#355	2
C₃×#354	2
#1414	3

Subgroups — C3×#1414 #67974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1414 #67974