Subgroups — C₃⋊#1309 #67712

Order 384.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#423	C₂	1	1	yes	maximal, characteristic
2	#4924	C₂	1	2	yes	maximal
3	#1309	—	3	1	no	maximal, Sylow
4	C₂×C₃×M₁₆	C₄	1	2	yes	—
5	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
6	C₂×#208	C₄	1	4	yes	—
7	C₃×C₄⋊C₈	—	2	2	no	—
8	C₄⋊(C₃⋊C₈)	—	2	2	no	—
9	C₄⋊(C₃⋊C₈)	—	2	2	no	—
10	#423	—	3	2	no	—
11	#423	D₃	1	1	yes	characteristic
12	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
13	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃×M₁₆	—	4	2	no	—
15	C₂×C₃×C₈	—	2	2	no	—
16	C₃×C₄²	D₄	1	1	yes	characteristic
17	C₃×C₄²	D₄	1	2	yes	—
18	C₃×C₄²	Q₈	1	1	yes	characteristic
19	#208	—	4	4	no	—
20	C₂×C₃⋊C₈	—	2	4	no	—
21	C₂×M₁₆	—	3	4	no	—
22	C₂×M₁₆	Dic₃	1	2	yes	—
23	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
24	C₄⋊C₈	—	2	2	no	—
25	C₄⋊C₈	—	6	2	no	—
26	C₄⋊C₈	—	6	2	no	—
27	C₂³×C₃	C₄²	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	2	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	2	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
33	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
35	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
36	C₃×C₈	—	4	2	no	—
37	C₃⋊C₈	—	4	4	no	—
38	C₂²×C₄	C₄×D₃	1	2	yes	—
39	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
40	M₁₆	—	4	2	no	—
41	M₁₆	—	12	4	no	—
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	—	6	4	no	—
44	C₄²	Dic₆	1	1	yes	characteristic
45	C₄²	D₁₂	1	1	yes	characteristic
46	C₄²	#67	1	2	yes	—
47	C₂²×C₃	—	2	1	no	—
48	C₂²×C₃	—	2	2	no	—
49	C₂²×C₃	#95	1	1	yes	characteristic
50	C₃×C₄	—	2	1	no	—
51	C₃×C₄	—	2	2	no	—
52	C₃×C₄	#100	1	2	yes	—
53	C₃×C₄	#100	1	1	yes	characteristic
54	C₃×C₄	#101	1	2	yes	—
55	C₃×C₄	#101	1	1	yes	characteristic
56	C₂³	C₄×Dic₃	1	1	yes	characteristic
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	Dic₃⋊C₄	1	2	yes	—
62	C₂×C₄	C₄⋊Dic₃	1	1	yes	characteristic
63	C₂×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
64	C₂×C₄	#217	1	1	yes	characteristic
65	C₈	—	4	2	no	—
66	C₈	—	12	4	no	—
67	C₂×C₃	—	4	1	no	—
68	C₂×C₃	#343	1	1	yes	characteristic
69	C₂×C₃	#343	1	2	yes	—
70	C₂²	—	2	1	no	—
71	C₂²	—	2	2	no	—
72	C₂²	C₃⋊#95	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	2	2	no	—
75	C₄	#823	1	2	yes	—
76	C₄	#824	1	2	yes	—
77	C₄	#833	1	1	yes	characteristic
78	C₄	#836	1	1	yes	characteristic
79	C₃	#1309	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	4	1	no	—
81	C₂	#4530	1	1	yes	characteristic
82	C₂	#4554	1	2	yes	—

	subgroup	G/H
center	C₂²	C₃⋊#95
commutator, prime radical	C₂³×C₃	C₄²
Frattini	C₂×C₄²	C₂×D₃
Fitting	C₃×#423	C₂
socle	C₂²×C₃	#95
cosocle	C₂×C₃×C₄²	C₂²
hypercenter	#423	D₃
hypocenter	C₃	#1309
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
79. C₃	#1309	semidirect

Maximal subgroups

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

subgroup	index
C₃×#423	2
#4924	2
#1309	3

Subgroups — C3⋊#1309 #67712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#1309 #67712