Subgroups — C₃×#88161 #11928797

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6127	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6094	C₂	1	2	yes	maximal, complemented
5	C₃×C₈×D₁₃	C₂	1	2	yes	maximal, complemented
6	#88161	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊D₁₃	C₄	1	2	yes	—
9	C₃×D₅₂	C₄	1	1	yes	characteristic
10	C₃×C₄×D₁₃	C₂²	1	2	yes	—
11	C₃×Dic₂₆	C₄	1	1	yes	characteristic
12	C₃×C₈×C₁₃	C₂²	1	2	yes	—
13	C₃×#1055	C₂²	1	1	yes	characteristic
14	C₃×#1055	C₂²	1	1	yes	characteristic
15	#6127	C₂×C₃	1	1	yes	characteristic
16	C₁₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×#1055	C₂×C₃	1	1	yes	characteristic, complemented
18	#6094	C₂×C₃	1	2	yes	complemented
19	C₈×D₁₃	C₂×C₃	1	2	yes	complemented
20	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×D₁₃	C₂×C₄	1	2	yes	—
22	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂²⋊D₁₃	C₃×C₄	1	2	yes	—
27	D₅₂	C₃×C₄	1	1	yes	characteristic
28	C₄×D₁₃	C₂²×C₃	1	2	yes	—
29	Dic₂₆	C₃×C₄	1	1	yes	characteristic
30	C₈×C₁₃	C₂²×C₃	1	2	yes	—
31	#1055	C₂²×C₃	1	1	yes	characteristic
32	#1055	C₂²×C₃	1	1	yes	characteristic
33	C₃×#131	—	13	1	no	maximal, Hall
34	C₂×C₃×C₁₃	—	2	1	no	—
35	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×D₁₃	—	2	2	no	—
37	C₂²×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
38	C₂×D₁₃	C₂×C₃×C₄	1	2	yes	—
39	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
40	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
41	Dic₁₃	C₂×C₃×C₄	1	2	yes	—
42	C₃×#41	—	13	1	no	—
43	C₃×M₁₆	—	13	2	no	—
44	C₃×M₁₆	D₁₃	1	1	yes	characteristic, complemented
45	C₂×C₃×C₈	—	13	1	no	—
46	C₂×C₃×C₈	—	13	2	no	—
47	C₃×C₁₃	#131	1	1	yes	characteristic, complemented, Hall
48	#131	—	13	1	no	Sylow
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
51	D₁₃	—	2	2	no	—
52	C₃×Q₈	—	13	1	no	—
53	C₃×D₄	—	13	2	no	—
54	C₃×D₄	—	13	1	no	—
55	C₂×C₃×C₄	—	13	2	no	—
56	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
57	C₃×C₈	—	13	1	no	—
58	C₃×C₈	—	13	1	no	—
59	C₃×C₈	C₂×D₁₃	1	2	yes	—
60	#41	—	13	1	no	—
61	M₁₆	—	13	2	no	—
62	M₁₆	C₃×D₁₃	1	1	yes	characteristic, complemented
63	C₂×C₈	—	13	1	no	—
64	C₂×C₈	—	13	2	no	—
65	C₁₃	C₃×#131	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	13	2	no	—
67	C₂²×C₃	C₄×D₁₃	1	1	yes	characteristic
68	C₃×C₄	—	13	2	no	—
69	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
70	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
71	Q₈	—	13	1	no	—
72	D₄	—	13	2	no	—
73	D₄	—	13	1	no	—
74	C₂×C₄	—	13	2	no	—
75	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
76	C₈	—	13	1	no	—
77	C₈	—	13	1	no	—
78	C₈	C₂×C₃×D₁₃	1	2	yes	—
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	—	26	2	no	—
81	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
82	C₂²	—	13	2	no	—
83	C₂²	C₃×C₄×D₁₃	1	1	yes	characteristic
84	C₄	—	13	2	no	—
85	C₄	C₃×C₄×D₁₃	1	1	yes	characteristic
86	C₄	C₂²×C₃×D₁₃	1	1	yes	characteristic
87	C₃	#88161	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	2	1	no	—
89	C₂	—	26	2	no	—
90	C₂	C₂×C₃×C₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×D₁₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₄	C₂²×C₃×D₁₃
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₂²×C₄
prime radical	C₃×#6127	C₂
cosocle	C₄×C₁₃	C₂³×C₃
hypercenter	C₃×M₁₆	D₁₃
hypocenter	C₁₃	C₃×#131
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃×C₄ ◁ C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×M₁₆	C₂	semidirect
3. C₂×C₃×#1055	C₂	semidirect
4. C₃×#6094	C₂	semidirect
5. C₃×C₈×D₁₃	C₂	semidirect
6. #88161	C₃	direct (N × H)
16. C₁₃×M₁₆	C₂×C₃	semidirect
17. C₂×#1055	C₂×C₃	semidirect
18. #6094	C₂×C₃	semidirect
19. C₈×D₁₃	C₂×C₃	semidirect
44. C₃×M₁₆	D₁₃	semidirect
47. C₃×C₁₃	#131	semidirect
62. M₁₆	C₃×D₁₃	semidirect
65. C₁₃	C₃×#131	semidirect
87. C₃	#88161	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×#6127	2
C₃×C₁₃×M₁₆	2
C₂×C₃×#1055	2
C₃×#6094	2
C₃×C₈×D₁₃	2
#88161	3
C₃×#131	13

Subgroups — C3×#88161 #11928797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88161 #11928797