Subgroups — C₃×#88126 #11928762

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6103	C₂	1	2	yes	maximal
4	C₃×#6101	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#88126	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₃×C₄×D₁₃	C₄	1	4	yes	complemented
13	C₂×C₄×D₁₃	C₂×C₃	1	1	yes	characteristic
14	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	#6103	C₂×C₃	1	2	yes	—
16	#6101	C₂×C₃	1	2	yes	complemented
17	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₃×D₁₃	—	2	2	no	—
20	C₂×C₃×D₁₃	C₂×C₄	1	2	yes	—
21	C₃×C₄×C₁₃	—	2	2	no	—
22	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
23	C₃×Dic₁₃	—	2	2	no	—
24	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
25	C₂²×D₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
27	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
28	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
29	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
30	C₄×D₁₃	C₃×C₄	1	4	yes	complemented
31	C₃×#117	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₃×C₁₃	#41	1	2	yes	—
34	C₃×D₁₃	—	2	2	no	—
35	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
36	C₂×D₁₃	—	2	2	no	—
37	C₂×D₁₃	C₂×C₃×C₄	1	2	yes	—
38	C₄×C₁₃	—	2	2	no	—
39	C₄×C₁₃	C₂×C₃×C₄	1	2	yes	—
40	Dic₁₃	—	2	2	no	—
41	Dic₁₃	C₂×C₃×C₄	1	2	yes	—
42	C₂²×C₃×C₄	—	13	1	no	—
43	C₃×C₄⋊C₄	—	13	2	no	—
44	C₃×C₂²⋊C₄	—	13	2	no	—
45	C₃×C₄²	—	13	1	no	—
46	C₃×C₄²	D₁₃	1	1	yes	characteristic, complemented
47	C₃×C₁₃	#117	1	1	yes	characteristic, complemented, Hall
48	#117	—	13	1	no	Sylow
49	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
50	C₂×C₁₃	C₃×#41	1	2	yes	—
51	D₁₃	—	2	2	no	—
52	C₂³×C₃	—	13	1	no	—
53	C₂×C₃×C₄	—	13	1	no	—
54	C₂×C₃×C₄	—	13	4	no	—
55	C₂×C₃×C₄	—	13	2	no	—
56	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
57	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
58	C₂²×C₄	—	13	1	no	—
59	C₄⋊C₄	—	13	2	no	—
60	C₂²⋊C₄	—	13	2	no	—
61	C₄²	—	13	1	no	—
62	C₄²	C₃×D₁₃	1	1	yes	characteristic, complemented
63	C₁₃	C₃×#117	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	—	13	2	no	—
65	C₂²×C₃	—	26	2	no	—
66	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	—	13	2	no	—
69	C₃×C₄	—	26	2	no	—
70	C₃×C₄	C₄×D₁₃	1	2	yes	—
71	C₂³	—	13	1	no	—
72	C₂×C₄	—	13	1	no	—
73	C₂×C₄	—	13	4	no	—
74	C₂×C₄	—	13	2	no	—
75	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
76	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
77	C₂×C₃	—	26	2	no	—
78	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
79	C₂×C₃	#6127	1	2	yes	—
80	C₂²	—	13	2	no	—
81	C₂²	—	26	2	no	—
82	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	13	2	no	—
85	C₄	—	26	2	no	—
86	C₄	C₃×C₄×D₁₃	1	2	yes	—
87	C₃	#88126	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	26	2	no	—
89	C₂	C₂×C₃×C₄×D₁₃	1	1	yes	characteristic
90	C₂	C₃×#6127	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×C₃×D₁₃	C₂²
cosocle	C₂²×C₁₃	C₂³×C₃
hypercenter	C₃×C₄²	D₁₃
hypocenter	C₁₃	C₃×#117
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₁₃	C₂	semidirect
4. C₃×#6101	C₂	semidirect
5. C₃×C₄×Dic₁₃	C₂	semidirect
6. #88126	C₃	direct (N × H)
12. C₃×C₄×D₁₃	C₄	semidirect
14. C₄²×C₁₃	C₂×C₃	semidirect
16. #6101	C₂×C₃	semidirect
17. C₄×Dic₁₃	C₂×C₃	semidirect
30. C₄×D₁₃	C₃×C₄	semidirect
46. C₃×C₄²	D₁₃	semidirect
47. C₃×C₁₃	#117	semidirect
62. C₄²	C₃×D₁₃	semidirect
63. C₁₃	C₃×#117	semidirect
87. C₃	#88126	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×C₄×D₁₃	2
C₃×C₄²×C₁₃	2
C₃×#6103	2
C₃×#6101	2
C₃×C₄×Dic₁₃	2
#88126	3
C₃×#117	13

Subgroups — C3×#88126 #11928762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88126 #11928762