Subgroups — #16789036

Order 3328.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131059	C₂	1	3	yes	maximal
2	#13131047	C₂	1	3	yes	maximal
3	#13114592	C₂	1	1	yes	maximal, characteristic
4	C₂×#88106	C₂²	1	3	yes	—
5	C₂²×#6092	C₂²	1	1	yes	characteristic
6	#11718783	C₂²	1	3	yes	—
7	#11718262	C₄	1	12	yes	complemented
8	#11718258	C₄	1	6	yes	complemented
9	#11718257	C₄	1	6	yes	complemented
10	C₁₃×#338	C₄	1	1	yes	characteristic
11	#11718149	C₄	1	3	yes	—
12	C₂×C₁₃×M₁₆	C₂×C₄	1	3	yes	—
13	#88180	C₂×C₄	1	3	yes	—
14	C₂²×#1055	C₂³	1	1	yes	characteristic
15	#88106	C₂×C₄	1	12	yes	—
16	C₂×#6092	C₂×C₄	1	3	yes	—
17	C₂×#6092	C₂×C₄	1	6	yes	—
18	C₂×#6092	C₂×C₄	1	3	yes	—
19	#88055	C₂×C₄	1	6	yes	—
20	C₈×Dic₁₃	C₂×C₄	1	6	yes	—
21	#12542	—	13	1	no	maximal, Sylow
22	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₁₃×M₁₆	—	2	6	no	—
24	C₂×C₈×C₁₃	C₄²	1	6	yes	—
25	C₂²⋊Dic₁₃	—	2	3	no	—
26	C₄⋊Dic₁₃	—	2	3	no	—
27	C₄×Dic₁₃	C₄²	1	6	yes	—
28	C₂×#1055	C₂²×C₄	1	3	yes	—
29	C₂×#1055	C₂²×C₄	1	3	yes	—
30	#6092	C₄²	1	1	yes	characteristic
31	#6092	C₄²	1	3	yes	—
32	#6092	C₄²	1	12	yes	—
33	#2110	—	13	3	no	—
34	#2108	—	13	3	no	—
35	#1747	—	13	1	no	—
36	C₂³×C₁₃	#131	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
38	C₂×C₄×C₁₃	#131	1	3	yes	—
39	C₂×Dic₁₃	—	2	6	no	—
40	C₈×C₁₃	—	2	6	no	—
41	#1055	C₂×C₄²	1	1	yes	characteristic
42	#1055	C₂×C₄²	1	3	yes	—
43	C₂×M₃₂	—	13	3	no	—
44	C₂²×C₁₆	—	13	1	no	—
45	#405	—	13	3	no	—
46	#347	—	13	12	no	—
47	#346	—	13	6	no	—
48	C₄×C₁₆	—	13	6	no	—
49	#338	#261	1	1	yes	characteristic
50	H(3,ℤ/4)	—	13	3	no	—
51	C₂²×C₁₃	—	4	1	no	—
52	C₂²×C₁₃	#405	1	3	yes	—
53	C₄×C₁₃	C₄³	1	1	yes	characteristic
54	C₄×C₁₃	#405	1	3	yes	—
55	Dic₁₃	—	4	6	no	—
56	C₂×M₁₆	C₂×#261	1	3	yes	—
57	C₂²×C₈	—	13	1	no	—
58	#117	—	13	3	no	—
59	M₃₂	—	13	12	no	—
60	C₂×C₁₆	—	13	3	no	—
61	C₂×C₁₆	—	13	6	no	—
62	C₂×C₁₆	—	13	3	no	—
63	#97	—	13	6	no	—
64	C₄×C₈	—	13	6	no	—
65	C₂×C₁₃	—	2	3	no	—
66	C₂×C₁₃	#1726	1	1	yes	characteristic
67	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	13	3	no	—
70	C₂×C₈	—	13	3	no	—
71	C₂×C₈	C₄×#261	1	6	yes	—
72	C₄⋊C₄	—	26	3	no	—
73	C₂²⋊C₄	—	26	3	no	—
74	C₄²	—	13	6	no	—
75	C₁₆	—	13	1	no	—
76	C₁₆	—	13	3	no	—
77	C₁₆	—	13	12	no	—
78	C₁₃	#12542	1	1	yes	characteristic, complemented, Sylow
79	C₂³	#88240	1	1	yes	characteristic
80	C₂×C₄	—	26	6	no	—
81	C₂×C₄	C₂×C₄×#261	1	3	yes	—
82	C₂×C₄	#88238	1	3	yes	—
83	C₈	—	2	6	no	—
84	C₈	—	13	1	no	—
85	C₈	—	13	3	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#11719072	1	3	yes	—
88	C₄	—	52	6	no	—
89	C₄	C₄²×#261	1	1	yes	characteristic
90	C₄	#11719062	1	3	yes	—
91	C₂	—	2	3	no	—
92	C₂	#13130493	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×#261
commutator	C₄×C₁₃	C₄³
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₁₃×#338	C₄
socle	C₂×C₁₃	#1726
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×#1055	C₂³
hypercenter	#338	#261
hypocenter	C₁₃	#12542
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
7. #11718262	C₄	semidirect
8. #11718258	C₄	semidirect
9. #11718257	C₄	semidirect
78. C₁₃	#12542	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13131059	2
#13131047	2
#13114592	2
#12542	13