Subgroups — C₃×#88158 #11928794

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6127	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6095	C₂	1	2	yes	maximal, complemented
6	#88158	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊D₁₃	—	2	2	no	—
9	C₃×D₅₂	C₂²	1	2	yes	—
10	C₃×C₄×D₁₃	—	2	2	no	—
11	C₃×Dic₂₆	C₂²	1	2	yes	—
12	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	#6127	C₂×C₃	1	2	yes	complemented
15	C₂×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
16	Dic₅₂	C₂×C₃	1	1	yes	characteristic, complemented
17	D₁₀₄	C₂×C₃	1	1	yes	characteristic, complemented
18	#6095	C₂×C₃	1	2	yes	complemented
19	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
20	C₂×C₃×D₁₃	—	2	2	no	—
21	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₃×Dic₁₃	—	2	2	no	—
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂²⋊D₁₃	—	2	2	no	—
26	D₅₂	C₂²×C₃	1	2	yes	—
27	C₄×D₁₃	—	2	2	no	—
28	Dic₂₆	C₂²×C₃	1	2	yes	—
29	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
30	C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
31	C₃×#135	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	—	2	1	no	—
33	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₃×D₁₃	—	4	2	no	—
35	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
36	C₂×D₁₃	—	2	2	no	—
37	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
38	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
39	Dic₁₃	—	2	2	no	—
40	C₃×#41	—	13	2	no	—
41	C₃×Q₁₆	—	13	1	no	—
42	C₃×SD₁₆	—	13	2	no	—
43	C₃×D₈	—	13	1	no	—
44	C₂×C₃×C₈	D₁₃	1	1	yes	characteristic, complemented
45	C₃×C₁₃	#135	1	1	yes	characteristic, complemented, Hall
46	#135	—	13	1	no	Sylow
47	C₂×C₁₃	—	2	1	no	—
48	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
49	D₁₃	—	4	2	no	—
50	C₃×Q₈	—	13	2	no	—
51	C₃×D₄	—	13	2	no	—
52	C₃×D₄	—	26	2	no	—
53	C₂×C₃×C₄	—	26	2	no	—
54	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
55	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
56	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
57	#41	—	13	2	no	—
58	Q₁₆	—	13	1	no	—
59	SD₁₆	—	13	2	no	—
60	D₈	—	13	1	no	—
61	C₂×C₈	C₃×D₁₃	1	1	yes	characteristic, complemented
62	C₁₃	C₃×#135	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₃	—	26	2	no	—
64	C₂²×C₃	D₅₂	1	1	yes	characteristic
65	C₃×C₄	—	26	2	no	—
66	C₃×C₄	D₅₂	1	1	yes	characteristic
67	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
68	Q₈	—	13	2	no	—
69	D₄	—	13	2	no	—
70	D₄	—	26	2	no	—
71	C₂×C₄	—	26	2	no	—
72	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
73	C₈	C₂×C₃×D₁₃	1	1	yes	characteristic
74	C₈	C₂×C₃×D₁₃	1	1	yes	characteristic
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	—	52	2	no	—
77	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
78	C₂²	—	26	2	no	—
79	C₂²	C₃×D₅₂	1	1	yes	characteristic
80	C₄	—	26	2	no	—
81	C₄	C₃×D₅₂	1	1	yes	characteristic
82	C₄	C₂²×C₃×D₁₃	1	1	yes	characteristic
83	C₃	#88158	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	2	1	no	—
85	C₂	—	52	2	no	—
86	C₂	C₂×C₃×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₅₂
commutator, cosocle	C₄×C₁₃	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
hypercenter	C₂×C₃×C₈	D₁₃
hypocenter	C₁₃	C₃×#135
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₃×#6127	C₂	semidirect
2. C₂×C₃×C₈×C₁₃	C₂	semidirect
3. C₃×Dic₅₂	C₂	semidirect
4. C₃×D₁₀₄	C₂	semidirect
5. C₃×#6095	C₂	semidirect
6. #88158	C₃	direct (N × H)
14. #6127	C₂×C₃	semidirect
15. C₂×C₈×C₁₃	C₂×C₃	semidirect
16. Dic₅₂	C₂×C₃	semidirect
17. D₁₀₄	C₂×C₃	semidirect
18. #6095	C₂×C₃	semidirect
44. C₂×C₃×C₈	D₁₃	semidirect
45. C₃×C₁₃	#135	semidirect
61. C₂×C₈	C₃×D₁₃	semidirect
62. C₁₃	C₃×#135	semidirect
83. C₃	#88158	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
C₂×C₃×C₈×C₁₃	2
C₃×Dic₅₂	2
C₃×D₁₀₄	2
C₃×#6095	2
#88158	3
C₃×#135	13

Subgroups — C3×#88158 #11928794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88158 #11928794