Subgroups — C₃×#2244 #72959

Order 384.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#493	C₂	1	1	yes	maximal, characteristic
3	C₃×#357	C₂	1	4	yes	maximal, complemented
4	C₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	#2244	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×D₈	—	2	1	no	—
7	C₂×C₃×D₈	C₂²	1	2	yes	—
8	C₃×#127	—	2	1	no	—
9	C₃×#125	—	2	1	no	—
10	C₂×C₃×C₁₆	C₂²	1	2	yes	—
11	C₃×#107	C₂²	1	2	yes	—
12	C₃×#106	—	2	1	no	—
13	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
14	#499	C₂×C₃	1	1	yes	characteristic, complemented
15	#493	C₂×C₃	1	1	yes	characteristic
16	#357	C₂×C₃	1	4	yes	complemented
17	#346	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₄	—	2	2	no	—
19	C₂×C₃×D₄	—	4	2	no	—
20	C₃×D₈	—	2	4	no	—
21	C₃×D₈	—	4	2	no	—
22	C₂×C₃×C₈	D₄	1	1	yes	characteristic
23	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
24	C₃×C₄⋊C₄	—	2	2	no	—
25	C₃×C₄⋊C₄	—	4	2	no	—
26	C₃×C₄²	D₄	1	1	yes	characteristic
27	C₃×C₁₆	—	2	2	no	—
28	C₂×D₈	—	2	1	no	—
29	C₂×D₈	C₂²×C₃	1	2	yes	—
30	#127	—	2	1	no	—
31	#125	—	2	1	no	—
32	C₂×C₁₆	C₂²×C₃	1	2	yes	—
33	#107	C₂²×C₃	1	2	yes	—
34	#106	—	2	1	no	—
35	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
36	C₂³×C₃	—	4	2	no	—
37	C₃×D₄	—	4	2	no	—
38	C₃×D₄	—	4	2	no	—
39	C₃×D₄	—	8	4	no	—
40	C₂×C₃×C₄	—	4	2	no	—
41	C₂×C₃×C₄	D₈	1	2	yes	—
42	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
43	C₃×C₈	SD₁₆	1	2	yes	—
44	C₃×C₈	#41	1	2	yes	—
45	C₂×D₄	—	2	2	no	—
46	C₂×D₄	—	4	2	no	—
47	D₈	—	2	4	no	—
48	D₈	—	4	2	no	—
49	C₂×C₈	C₃×D₄	1	1	yes	characteristic
50	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
51	C₄⋊C₄	—	2	2	no	—
52	C₄⋊C₄	—	4	2	no	—
53	C₄²	C₃×D₄	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂²×C₃	—	8	2	no	—
56	C₂²×C₃	—	8	4	no	—
57	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
58	C₃×C₄	—	2	2	no	—
59	C₃×C₄	—	8	2	no	—
60	C₃×C₄	#124	1	1	yes	characteristic
61	C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
62	C₂³	—	4	2	no	—
63	D₄	—	4	2	no	—
64	D₄	—	4	2	no	—
65	D₄	—	8	4	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	C₃×D₈	1	2	yes	—
68	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
69	C₈	C₃×SD₁₆	1	2	yes	—
70	C₈	C₃×#41	1	2	yes	—
71	C₂×C₃	—	16	2	no	—
72	C₂×C₃	#486	1	1	yes	characteristic
73	C₂×C₃	#509	1	2	yes	—
74	C₂²	—	8	4	no	—
75	C₂²	—	8	2	no	—
76	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	8	2	no	—
79	C₄	C₃×#124	1	1	yes	characteristic
80	C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
81	C₃	#2244	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	—	16	2	no	—
83	C₂	C₃×#486	1	1	yes	characteristic
84	C₂	C₃×#509	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃
prime radical	C₃×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#499	C₂	semidirect
3. C₃×#357	C₂	semidirect
4. C₃×#346	C₂	semidirect
5. #2244	C₃	direct (N × H)
14. #499	C₂×C₃	semidirect
16. #357	C₂×C₃	semidirect
17. #346	C₂×C₃	semidirect
81. C₃	#2244	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×#499	2
C₃×#493	2
C₃×#357	2
C₃×#346	2
#2244	3

Subgroups — C3×#2244 #72959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2244 #72959