Subgroups — C₃×#88072 #11928063

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#88072	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₁₃	—	2	1	no	—
6	C₃×D₄×C₁₃	—	2	1	no	—
7	C₃×D₄×C₁₃	C₄	1	2	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×Dic₁₃	—	2	1	no	—
10	C₃×#1055	—	2	1	no	—
11	C₂×D₄×C₁₃	C₂×C₃	1	1	yes	characteristic
12	C₄⋊Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×#1055	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₁₃	—	2	2	no	—
15	C₂²×C₃×C₁₃	—	4	1	no	—
16	C₂²×C₃×C₁₃	—	4	1	no	—
17	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
18	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
20	C₃×Dic₁₃	—	4	1	no	—
21	C₂³×C₁₃	—	2	1	no	—
22	D₄×C₁₃	—	2	1	no	—
23	D₄×C₁₃	C₃×C₄	1	2	yes	complemented
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×Dic₁₃	—	2	1	no	—
26	#1055	—	2	1	no	—
27	C₃×#102	—	13	1	no	maximal, Hall
28	C₂×C₃×C₁₃	—	4	2	no	—
29	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
31	C₂×C₃×C₁₃	SD₁₆	1	1	yes	characteristic
32	C₂²×C₁₃	—	2	2	no	—
33	C₂²×C₁₃	—	4	1	no	—
34	C₂²×C₁₃	—	4	1	no	—
35	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
36	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
37	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
38	Dic₁₃	—	4	1	no	—
39	C₂×C₃×D₄	D₁₃	1	1	yes	characteristic
40	C₂×C₃×C₈	—	13	1	no	—
41	C₃×C₄⋊C₄	—	13	1	no	—
42	C₃×C₁₃	#102	1	1	yes	characteristic, complemented, Hall
43	#102	—	13	1	no	Sylow
44	C₂×C₁₃	—	4	2	no	—
45	C₂×C₁₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₁₃	C₃×D₈	1	1	yes	characteristic
47	C₂×C₁₃	C₃×SD₁₆	1	1	yes	characteristic
48	C₂³×C₃	—	2	1	no	—
49	C₃×D₄	—	2	1	no	—
50	C₃×D₄	Dic₁₃	1	2	yes	complemented
51	C₂×C₃×C₄	—	26	1	no	—
52	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₃×C₈	—	26	1	no	—
54	C₂×D₄	C₃×D₁₃	1	1	yes	characteristic
55	C₂×C₈	—	13	1	no	—
56	C₄⋊C₄	—	13	1	no	—
57	C₁₃	C₃×#102	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	2	2	no	—
59	C₂²×C₃	—	4	1	no	—
60	C₂²×C₃	—	4	1	no	—
61	C₂²×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
62	C₃×C₄	—	52	1	no	—
63	C₃×C₄	C₂×Dic₁₃	1	1	yes	characteristic
64	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
65	C₂³	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	C₃×Dic₁₃	1	2	yes	complemented
68	C₂×C₄	—	26	1	no	—
69	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
70	C₈	—	26	1	no	—
71	C₂×C₃	—	4	2	no	—
72	C₂×C₃	#6104	1	1	yes	characteristic
73	C₂×C₃	#6105	1	1	yes	characteristic
74	C₂×C₃	C₂²⋊Dic₁₃	1	1	yes	characteristic
75	C₂²	—	2	2	no	—
76	C₂²	—	4	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	C₃×C₂²⋊D₁₃	1	1	yes	characteristic
79	C₄	—	52	1	no	—
80	C₄	C₂×C₃×Dic₁₃	1	1	yes	characteristic
81	C₄	C₃×C₂²⋊D₁₃	1	1	yes	characteristic
82	C₃	#88072	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	4	2	no	—
84	C₂	C₃×#6104	1	1	yes	characteristic
85	C₂	C₃×#6105	1	1	yes	characteristic
86	C₂	C₃×C₂²⋊Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₁₃
Fitting, prime radical	C₂×C₃×D₄×C₁₃	C₂
socle	C₂²×C₃×C₁₃	D₄
cosocle	C₂×C₄×C₁₃	C₂²×C₃
hypercenter	C₂×C₃×D₄	D₁₃
hypocenter	C₁₃	C₃×#102
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄⋊Dic₁₃	C₂	semidirect
3. C₂×C₃×#1055	C₂	semidirect
4. #88072	C₃	direct (N × H)
7. C₃×D₄×C₁₃	C₄	semidirect
12. C₄⋊Dic₁₃	C₂×C₃	semidirect
13. C₂×#1055	C₂×C₃	semidirect
23. D₄×C₁₃	C₃×C₄	semidirect
42. C₃×C₁₃	#102	semidirect
50. C₃×D₄	Dic₁₃	semidirect
57. C₁₃	C₃×#102	semidirect
67. D₄	C₃×Dic₁₃	semidirect
82. C₃	#88072	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₃	2
C₃×C₄⋊Dic₁₃	2
C₂×C₃×#1055	2
#88072	3
C₃×#102	13

Subgroups — C3×#88072 #11928063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88072 #11928063