Subgroups — C₃×#88129 #11928765

Order 1248.

152 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	C₂×C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6103	C₂	1	4	yes	maximal, complemented
5	#88129	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×D₁₃	C₂²	1	2	yes	—
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
10	C₃×D₅₂	—	2	2	no	—
11	C₃×Dic₂₆	—	2	2	no	—
12	C₂×D₅₂	C₂×C₃	1	1	yes	characteristic
13	C₂×Dic₂₆	C₂×C₃	1	1	yes	characteristic, complemented
14	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	#6103	C₂×C₃	1	4	yes	complemented
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₃×D₁₃	—	2	2	no	—
18	C₂×C₃×D₁₃	—	2	4	no	—
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	D₄	1	2	yes	—
21	C₃×Dic₁₃	—	2	2	no	—
22	C₂²×D₁₃	C₂²×C₃	1	2	yes	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
26	D₅₂	—	2	2	no	—
27	Dic₂₆	—	2	2	no	—
28	C₃×#124	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃×C₁₃	#41	1	2	yes	—
31	C₃×D₁₃	—	4	2	no	—
32	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
33	C₂×D₁₃	—	2	2	no	—
34	C₂×D₁₃	—	2	4	no	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	C₃×D₄	1	2	yes	—
37	Dic₁₃	—	2	2	no	—
38	C₂×C₃×Q₈	—	13	1	no	—
39	C₂×C₃×D₄	—	13	1	no	—
40	C₃×C₂²⋊C₄	—	13	4	no	—
41	C₃×C₄²	D₁₃	1	1	yes	characteristic, complemented
42	C₃×C₁₃	#124	1	1	yes	characteristic, complemented, Hall
43	#124	—	13	1	no	Sylow
44	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
45	C₂×C₁₃	C₃×#41	1	2	yes	—
46	D₁₃	—	4	2	no	—
47	C₂³×C₃	—	13	2	no	—
48	C₃×Q₈	—	26	2	no	—
49	C₃×D₄	—	26	2	no	—
50	C₂×C₃×C₄	—	13	2	no	—
51	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
52	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₂×Q₈	—	13	1	no	—
54	C₂×D₄	—	13	1	no	—
55	C₂²⋊C₄	—	13	4	no	—
56	C₄²	C₃×D₁₃	1	1	yes	characteristic, complemented
57	C₁₃	C₃×#124	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	26	2	no	—
59	C₂²×C₃	—	26	4	no	—
60	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	—	26	2	no	—
63	C₃×C₄	D₅₂	1	2	yes	—
64	C₂³	—	13	2	no	—
65	Q₈	—	26	2	no	—
66	D₄	—	26	2	no	—
67	C₂×C₄	—	13	2	no	—
68	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
69	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
70	C₂×C₃	—	52	2	no	—
71	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
72	C₂×C₃	#6127	1	2	yes	—
73	C₂²	—	26	2	no	—
74	C₂²	—	26	4	no	—
75	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	26	2	no	—
78	C₄	C₃×D₅₂	1	2	yes	—
79	C₃	#88129	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	52	2	no	—
81	C₂	C₂×C₃×D₅₂	1	1	yes	characteristic
82	C₂	C₃×#6127	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂×C₃×D₅₂	C₂
hypercenter	C₃×C₄²	D₁₃
hypocenter	C₁₃	C₃×#124
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Dic₂₆	C₂	semidirect
3. C₃×C₄²×C₁₃	C₂	semidirect
4. C₃×#6103	C₂	semidirect
5. #88129	C₃	direct (N × H)
13. C₂×Dic₂₆	C₂×C₃	semidirect
14. C₄²×C₁₃	C₂×C₃	semidirect
15. #6103	C₂×C₃	semidirect
41. C₃×C₄²	D₁₃	semidirect
42. C₃×C₁₃	#124	semidirect
56. C₄²	C₃×D₁₃	semidirect
57. C₁₃	C₃×#124	semidirect
79. C₃	#88129	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
C₂×C₃×Dic₂₆	2
C₃×C₄²×C₁₃	2
C₃×#6103	2
#88129	3
C₃×#124	13

Subgroups — C3×#88129 #11928765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88129 #11928765