Subgroups — C₃×#88194 #11928823

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₂²⋊D₁₃	C₂	1	4	yes	maximal, complemented
3	C₂×C₃×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#88194	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₃×D₁₃	C₂²	1	2	yes	—
8	C₃×D₄×C₁₃	—	2	2	no	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₃×C₂²⋊D₁₃	—	2	8	no	—
11	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
12	C₃×D₅₂	—	2	2	no	—
13	C₂×D₄×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₂²⋊D₁₃	C₂×C₃	1	4	yes	complemented
15	C₂×D₅₂	C₂×C₃	1	1	yes	characteristic, complemented
16	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₁₃	—	2	4	no	—
18	C₂²×C₃×C₁₃	—	2	2	no	—
19	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₃×D₁₃	—	2	2	no	—
21	C₂×C₃×D₁₃	—	2	4	no	—
22	C₃×C₄×C₁₃	D₄	1	2	yes	complemented
23	C₃×Dic₁₃	D₄	1	4	yes	complemented
24	C₂³×C₁₃	C₂²×C₃	1	2	yes	—
25	C₂²×D₁₃	C₂²×C₃	1	2	yes	—
26	D₄×C₁₃	—	2	2	no	—
27	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
28	C₂²⋊D₁₃	—	2	8	no	—
29	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
30	D₅₂	—	2	2	no	—
31	C₃×#127	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	—	4	2	no	—
33	C₂×C₃×C₁₃	C₂×D₄	1	2	yes	—
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₃×D₁₃	—	4	2	no	—
36	C₂²×C₁₃	—	2	4	no	—
37	C₂²×C₁₃	—	2	2	no	—
38	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
39	C₂×D₁₃	—	2	2	no	—
40	C₂×D₁₃	—	2	4	no	—
41	C₄×C₁₃	C₃×D₄	1	2	yes	complemented
42	Dic₁₃	C₃×D₄	1	4	yes	complemented
43	C₂×C₃×D₄	—	13	4	no	—
44	C₂×C₃×D₄	—	13	1	no	—
45	C₂×C₃×D₄	D₁₃	1	1	yes	characteristic, complemented
46	C₃×C₄²	—	13	1	no	—
47	C₃×C₁₃	#127	1	1	yes	characteristic, complemented, Hall
48	#127	—	13	1	no	Sylow
49	C₂×C₁₃	—	4	2	no	—
50	C₂×C₁₃	C₂×C₃×D₄	1	2	yes	—
51	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
52	D₁₃	—	4	2	no	—
53	C₂³×C₃	—	13	2	no	—
54	C₂³×C₃	C₂×D₁₃	1	2	yes	—
55	C₃×D₄	—	2	2	no	—
56	C₃×D₄	—	26	8	no	—
57	C₃×D₄	—	26	2	no	—
58	C₂×C₃×C₄	—	13	2	no	—
59	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
60	C₂×D₄	—	13	4	no	—
61	C₂×D₄	—	13	1	no	—
62	C₂×D₄	C₃×D₁₃	1	1	yes	characteristic, complemented
63	C₄²	—	13	1	no	—
64	C₁₃	C₃×#127	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	—	2	4	no	—
66	C₂²×C₃	—	2	2	no	—
67	C₂²×C₃	—	26	4	no	—
68	C₂²×C₃	—	26	2	no	—
69	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
70	C₃×C₄	—	13	4	no	—
71	C₃×C₄	C₂²⋊D₁₃	1	2	yes	complemented
72	C₂³	—	13	2	no	—
73	C₂³	C₂×C₃×D₁₃	1	2	yes	—
74	D₄	—	2	2	no	—
75	D₄	—	26	8	no	—
76	D₄	—	26	2	no	—
77	C₂×C₄	—	13	2	no	—
78	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
79	C₂×C₃	—	4	2	no	—
80	C₂×C₃	—	52	2	no	—
81	C₂×C₃	D₄×D₁₃	1	2	yes	—
82	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
83	C₂²	—	2	4	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	26	4	no	—
86	C₂²	—	26	2	no	—
87	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
88	C₄	—	13	4	no	—
89	C₄	C₃×C₂²⋊D₁₃	1	2	yes	complemented
90	C₃	#88194	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	4	2	no	—
92	C₂	—	52	2	no	—
93	C₂	C₃×D₄×D₁₃	1	2	yes	—
94	C₂	C₂×C₃×C₂²⋊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	C₂×C₃×D₄×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×C₃×D₄	D₁₃
hypocenter	C₁₃	C₃×#127
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×C₁₃	C₂	semidirect
2. C₂×C₃×C₂²⋊D₁₃	C₂	semidirect
3. C₂×C₃×D₅₂	C₂	semidirect
4. C₃×C₄×Dic₁₃	C₂	semidirect
5. #88194	C₃	direct (N × H)
13. C₂×D₄×C₁₃	C₂×C₃	semidirect
14. C₂×C₂²⋊D₁₃	C₂×C₃	semidirect
15. C₂×D₅₂	C₂×C₃	semidirect
16. C₄×Dic₁₃	C₂×C₃	semidirect
22. C₃×C₄×C₁₃	D₄	semidirect
23. C₃×Dic₁₃	D₄	semidirect
41. C₄×C₁₃	C₃×D₄	semidirect
42. Dic₁₃	C₃×D₄	semidirect
45. C₂×C₃×D₄	D₁₃	semidirect
47. C₃×C₁₃	#127	semidirect
62. C₂×D₄	C₃×D₁₃	semidirect
64. C₁₃	C₃×#127	semidirect
71. C₃×C₄	C₂²⋊D₁₃	semidirect
89. C₄	C₃×C₂²⋊D₁₃	semidirect
90. C₃	#88194	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×D₄×C₁₃	2
C₂×C₃×C₂²⋊D₁₃	2
C₂×C₃×D₅₂	2
C₃×C₄×Dic₁₃	2
#88194	3
C₃×#127	13

Subgroups — C3×#88194 #11928823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88194 #11928823