Subgroups — C₃×#88131 #11928767

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₂²⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₃×#6101	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×Dic₁₃	C₂	1	2	yes	maximal, complemented
6	#88131	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂×C₃×Dic₁₃	C₄	1	4	yes	complemented
10	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×Dic₁₃	C₂×C₃	1	1	yes	characteristic
14	C₁₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
15	C₂²⋊Dic₁₃	C₂×C₃	1	1	yes	characteristic
16	#6101	C₂×C₃	1	2	yes	complemented
17	C₄×Dic₁₃	C₂×C₃	1	2	yes	complemented
18	C₂²×C₃×C₁₃	—	2	2	no	—
19	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
20	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
21	C₃×C₄×C₁₃	—	2	2	no	—
22	C₃×Dic₁₃	—	2	2	no	—
23	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
24	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
25	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
27	C₂×Dic₁₃	C₃×C₄	1	4	yes	complemented
28	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
29	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
30	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
31	C₃×#117	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	—	2	2	no	—
33	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃×C₁₃	#41	1	2	yes	—
35	C₂²×C₁₃	—	2	2	no	—
36	C₂²×C₁₃	C₂×C₃×C₄	1	2	yes	—
37	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
38	C₄×C₁₃	—	2	2	no	—
39	Dic₁₃	—	2	2	no	—
40	Dic₁₃	C₂×C₃×C₄	1	2	yes	—
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	1	no	—
45	C₃×C₂²⋊C₄	D₁₃	1	1	yes	characteristic
46	C₃×C₄²	—	13	2	no	—
47	C₃×C₁₃	#117	1	1	yes	characteristic, complemented, Hall
48	#117	—	13	1	no	Sylow
49	C₂×C₁₃	—	2	2	no	—
50	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
51	C₂×C₁₃	C₃×#41	1	2	yes	—
52	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
53	C₂×C₃×C₄	—	13	4	no	—
54	C₂×C₃×C₄	—	13	1	no	—
55	C₂×C₃×C₄	—	13	1	no	—
56	C₂×C₃×C₄	—	13	2	no	—
57	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
58	C₂²×C₄	—	13	1	no	—
59	C₄⋊C₄	—	13	2	no	—
60	C₂²⋊C₄	—	13	1	no	—
61	C₂²⋊C₄	C₃×D₁₃	1	1	yes	characteristic
62	C₄²	—	13	2	no	—
63	C₁₃	C₃×#117	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	—	2	2	no	—
65	C₂²×C₃	C₄×D₁₃	1	2	yes	—
66	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	—	13	2	no	—
69	C₃×C₄	—	13	2	no	—
70	C₃×C₄	—	26	2	no	—
71	C₂³	C₂×C₃×D₁₃	1	1	yes	characteristic
72	C₂×C₄	—	13	4	no	—
73	C₂×C₄	—	13	1	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	—	13	2	no	—
76	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
79	C₂×C₃	#6129	1	2	yes	—
80	C₂²	—	2	2	no	—
81	C₂²	C₃×C₄×D₁₃	1	2	yes	—
82	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	13	2	no	—
85	C₄	—	13	2	no	—
86	C₄	—	26	2	no	—
87	C₃	#88131	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	2	2	no	—
89	C₂	C₂×C₃×C₄×D₁₃	1	1	yes	characteristic
90	C₂	C₃×#6129	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₃×#6101	C₂	semidirect
5. C₃×C₄×Dic₁₃	C₂	semidirect
6. #88131	C₃	direct (N × H)
9. C₂×C₃×Dic₁₃	C₄	semidirect
16. #6101	C₂×C₃	semidirect
17. C₄×Dic₁₃	C₂×C₃	semidirect
27. C₂×Dic₁₃	C₃×C₄	semidirect
47. C₃×C₁₃	#117	semidirect
63. C₁₃	C₃×#117	semidirect
87. C₃	#88131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₁₃	2
C₃×C₁₃×C₂²⋊C₄	2
C₃×C₂²⋊Dic₁₃	2
C₃×#6101	2
C₃×C₄×Dic₁₃	2
#88131	3
C₃×#117	13

Subgroups — C3×#88131 #11928767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88131 #11928767