Subgroups — C₃×#88142 #11928779

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₂₆	C₂	1	2	yes	maximal
2	C₃×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₃×#6101	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	#88142	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
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	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₃×Dic₂₆	—	2	4	no	—
13	C₂×Dic₂₆	C₂×C₃	1	2	yes	—
14	C₁₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
15	C₄⋊Dic₁₃	C₂×C₃	1	1	yes	characteristic
16	#6101	C₂×C₃	1	2	yes	—
17	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	Q₈	1	2	yes	complemented
21	C₃×Dic₁₃	—	2	2	no	—
22	C₃×Dic₁₃	D₄	1	2	yes	—
23	C₃×Dic₁₃	Q₈	1	2	yes	complemented
24	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
25	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
27	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
28	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
29	Dic₂₆	—	2	4	no	—
30	C₃×C₄⋊Q₈	—	13	1	no	maximal, Hall
31	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	C₃×Q₈	1	2	yes	complemented
37	Dic₁₃	—	2	2	no	—
38	Dic₁₃	C₃×D₄	1	2	yes	—
39	Dic₁₃	C₃×Q₈	1	2	yes	complemented
40	C₂×C₃×Q₈	—	13	2	no	—
41	C₃×C₄⋊C₄	—	13	2	no	—
42	C₃×C₄⋊C₄	—	13	1	no	—
43	C₃×C₄⋊C₄	D₁₃	1	1	yes	characteristic
44	C₃×C₄²	—	13	1	no	—
45	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
46	C₄⋊Q₈	—	13	1	no	Sylow
47	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
48	C₂×C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic
49	C₂×C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic
50	C₃×Q₈	—	26	4	no	—
51	C₂×C₃×C₄	—	13	1	no	—
52	C₂×C₃×C₄	—	13	1	no	—
53	C₂×C₃×C₄	—	13	2	no	—
54	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
55	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
56	C₂×Q₈	—	13	2	no	—
57	C₄⋊C₄	—	13	2	no	—
58	C₄⋊C₄	—	13	1	no	—
59	C₄⋊C₄	C₃×D₁₃	1	1	yes	characteristic
60	C₄²	—	13	1	no	—
61	C₁₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
63	C₃×C₄	—	2	2	no	—
64	C₃×C₄	—	13	2	no	—
65	C₃×C₄	—	13	2	no	—
66	C₃×C₄	—	26	2	no	—
67	C₃×C₄	Dic₂₆	1	2	yes	complemented
68	Q₈	—	26	4	no	—
69	C₂×C₄	—	13	1	no	—
70	C₂×C₄	—	13	1	no	—
71	C₂×C₄	—	13	2	no	—
72	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
73	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
74	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
75	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
76	C₂×C₃	Q₈×D₁₃	1	1	yes	characteristic
77	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	13	2	no	—
80	C₄	—	13	2	no	—
81	C₄	—	26	2	no	—
82	C₄	C₃×Dic₂₆	1	2	yes	complemented
83	C₃	#88142	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	C₂×C₃×Dic₂₆	1	1	yes	characteristic
85	C₂	C₃×D₄×D₁₃	1	1	yes	characteristic
86	C₂	C₃×Q₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₃×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #88142	C₃	direct (N × H)
20. C₃×C₄×C₁₃	Q₈	semidirect
23. C₃×Dic₁₃	Q₈	semidirect
36. C₄×C₁₃	C₃×Q₈	semidirect
39. Dic₁₃	C₃×Q₈	semidirect
45. C₃×C₁₃	C₄⋊Q₈	semidirect
61. C₁₃	C₃×C₄⋊Q₈	semidirect
67. C₃×C₄	Dic₂₆	semidirect
82. C₄	C₃×Dic₂₆	semidirect
83. C₃	#88142	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×Dic₂₆	2
C₃×C₁₃×C₄⋊C₄	2
C₃×C₄⋊Dic₁₃	2
C₃×#6101	2
C₃×C₄×Dic₁₃	2
#88142	3
C₃×C₄⋊Q₈	13

Subgroups — C3×#88142 #11928779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88142 #11928779