Subgroups — C₃×#88049 #11928039

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#88049	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₁₃	—	2	1	no	—
6	C₂×C₃×C₄×C₁₃	—	2	1	no	—
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×D₅₂	—	2	1	no	—
9	C₃×D₅₂	C₄	1	2	yes	complemented
10	C₃×#1055	—	2	1	no	—
11	C₂×D₅₂	C₂×C₃	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×#1055	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₃×D₁₃	—	2	2	no	—
16	C₂×C₃×D₁₃	—	4	1	no	—
17	C₂×C₃×D₁₃	—	4	1	no	—
18	C₃×C₄×C₁₃	—	4	1	no	—
19	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×D₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	2	1	no	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
24	D₅₂	—	2	1	no	—
25	D₅₂	C₃×C₄	1	2	yes	complemented
26	#1055	—	2	1	no	—
27	C₃×#102	—	13	1	no	maximal, Hall
28	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
30	C₂×C₃×C₁₃	SD₁₆	1	1	yes	characteristic
31	C₃×D₁₃	—	4	2	no	—
32	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
33	C₂×D₁₃	—	2	2	no	—
34	C₂×D₁₃	—	4	1	no	—
35	C₂×D₁₃	—	4	1	no	—
36	C₄×C₁₃	—	4	1	no	—
37	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
38	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
39	C₂×C₃×D₄	—	13	1	no	—
40	C₂×C₃×C₈	—	13	1	no	—
41	C₃×C₄⋊C₄	D₁₃	1	1	yes	characteristic, complemented
42	C₃×C₁₃	#102	1	1	yes	characteristic, complemented, Hall
43	#102	—	13	1	no	Sylow
44	C₂×C₁₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₁₃	C₃×D₈	1	1	yes	characteristic
46	C₂×C₁₃	C₃×SD₁₆	1	1	yes	characteristic
47	D₁₃	—	4	2	no	—
48	C₂³×C₃	—	26	1	no	—
49	C₃×D₄	—	13	2	no	—
50	C₃×D₄	—	26	1	no	—
51	C₂×C₃×C₄	—	2	1	no	—
52	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₃×C₈	—	26	1	no	—
54	C₂×D₄	—	13	1	no	—
55	C₂×C₈	—	13	1	no	—
56	C₄⋊C₄	C₃×D₁₃	1	1	yes	characteristic, complemented
57	C₁₃	C₃×#102	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	26	2	no	—
59	C₂²×C₃	—	52	1	no	—
60	C₂²×C₃	—	52	1	no	—
61	C₂²×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
62	C₃×C₄	—	4	1	no	—
63	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
64	C₃×C₄	D₅₂	1	1	yes	characteristic
65	C₂³	—	26	1	no	—
66	D₄	—	13	2	no	—
67	D₄	—	26	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
70	C₈	—	26	1	no	—
71	C₂×C₃	—	52	2	no	—
72	C₂×C₃	#6103	1	1	yes	characteristic
73	C₂×C₃	#6104	1	1	yes	characteristic
74	C₂×C₃	#6106	1	1	yes	characteristic
75	C₂²	—	26	2	no	—
76	C₂²	—	52	1	no	—
77	C₂²	—	52	1	no	—
78	C₂²	C₃×C₂²⋊D₁₃	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	C₃×C₄×D₁₃	1	1	yes	characteristic
81	C₄	C₃×D₅₂	1	1	yes	characteristic
82	C₃	#88049	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	52	2	no	—
84	C₂	C₃×#6103	1	1	yes	characteristic
85	C₂	C₃×#6104	1	1	yes	characteristic
86	C₂	C₃×#6106	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	C₃×C₁₃×C₄⋊C₄	C₂
socle	C₂²×C₃×C₁₃	D₄
prime radical	C₂×C₃×D₅₂	C₂
cosocle	C₂×C₄×C₁₃	C₂²×C₃
hypercenter	C₃×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₃×#102
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₄⋊C₄	C₂	semidirect
3. C₂×C₃×#1055	C₂	semidirect
4. #88049	C₃	direct (N × H)
9. C₃×D₅₂	C₄	semidirect
12. C₁₃×C₄⋊C₄	C₂×C₃	semidirect
13. C₂×#1055	C₂×C₃	semidirect
25. D₅₂	C₃×C₄	semidirect
41. C₃×C₄⋊C₄	D₁₃	semidirect
42. C₃×C₁₃	#102	semidirect
56. C₄⋊C₄	C₃×D₁₃	semidirect
57. C₁₃	C₃×#102	semidirect
82. C₃	#88049	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×D₅₂	2
C₃×C₁₃×C₄⋊C₄	2
C₂×C₃×#1055	2
#88049	3
C₃×#102	13

Subgroups — C3×#88049 #11928039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88049 #11928039