Subgroups — #16790260

Order 3328.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131177	C₂	1	3	yes	maximal
2	#13131173	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	#11718261	—	2	6	no	—
8	#11718260	—	2	6	no	—
9	C₁₃×#338	C₄	1	1	yes	characteristic
10	#11718149	C₄	1	3	yes	—
11	C₂×C₁₃×M₁₆	C₂×C₄	1	3	yes	—
12	#88180	C₂×C₄	1	3	yes	—
13	C₂²×#1055	C₂³	1	1	yes	characteristic
14	#88106	—	2	6	no	—
15	C₂×#6092	—	2	3	no	—
16	C₂×#6092	—	2	3	no	—
17	#88055	Q₈	1	6	yes	—
18	C₈×Dic₁₃	D₄	1	6	yes	—
19	#12902	—	13	1	no	maximal, Sylow
20	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₁₃×M₁₆	—	2	6	no	—
22	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
23	C₂²⋊Dic₁₃	—	2	3	no	—
24	C₄⋊Dic₁₃	—	2	3	no	—
25	C₄×Dic₁₃	C₄⋊C₄	1	6	yes	—
26	C₂×#1055	C₂×D₄	1	3	yes	—
27	C₂×#1055	C₂×Q₈	1	3	yes	—
28	#6092	—	4	1	no	—
29	#6092	—	4	3	no	—
30	#2153	—	13	3	no	—
31	#2151	—	13	3	no	—
32	#1747	—	13	1	no	—
33	C₂³×C₁₃	#131	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
35	C₂×C₄×C₁₃	#131	1	3	yes	—
36	C₂×Dic₁₃	—	2	6	no	—
37	C₈×C₁₃	—	2	6	no	—
38	#1055	#127	1	1	yes	characteristic
39	#1055	C₄⋊Q₈	1	3	yes	—
40	C₂×M₃₂	—	13	3	no	—
41	C₂²×C₁₆	—	13	1	no	—
42	#405	—	13	3	no	—
43	#364	—	26	6	no	—
44	C₄⋊C₁₆	—	26	6	no	—
45	#338	#261	1	1	yes	characteristic
46	H(3,ℤ/4)	—	13	3	no	—
47	C₂²×C₁₃	—	4	1	no	—
48	C₂²×C₁₃	#424	1	3	yes	—
49	C₄×C₁₃	#384	1	1	yes	characteristic
50	C₄×C₁₃	#424	1	3	yes	—
51	Dic₁₃	—	4	6	no	—
52	C₂×M₁₆	C₂×#261	1	3	yes	—
53	C₂²×C₈	—	13	1	no	—
54	#117	—	13	3	no	—
55	M₃₂	—	26	6	no	—
56	C₂×C₁₆	—	26	3	no	—
57	C₂×C₁₆	—	26	3	no	—
58	#97	—	13	6	no	—
59	C₄×C₈	—	13	6	no	—
60	C₂×C₁₃	—	2	3	no	—
61	C₂×C₁₃	#1843	1	1	yes	characteristic
62	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
63	M₁₆	—	2	6	no	—
64	C₂×C₈	—	13	3	no	—
65	C₂×C₈	—	13	3	no	—
66	C₂×C₈	C₄⋊#261	1	6	yes	—
67	C₄⋊C₄	—	26	3	no	—
68	C₂²⋊C₄	—	26	3	no	—
69	C₄²	—	13	6	no	—
70	C₁₆	—	52	1	no	—
71	C₁₆	—	52	3	no	—
72	C₁₃	#12902	1	1	yes	characteristic, complemented, Sylow
73	C₂³	#88240	1	1	yes	characteristic
74	C₂×C₄	—	26	6	no	—
75	C₂×C₄	C₂×C₄⋊#261	1	3	yes	—
76	C₂×C₄	#88238	1	3	yes	—
77	C₈	—	2	6	no	—
78	C₈	—	13	1	no	—
79	C₈	—	13	3	no	—
80	C₂²	—	4	1	no	—
81	C₂²	#11719079	1	3	yes	—
82	C₄	—	52	6	no	—
83	C₄	#11719059	1	1	yes	characteristic
84	C₄	#11719067	1	3	yes	—
85	C₂	—	2	3	no	—
86	C₂	#13130770	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11719059
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₁₃×#338	C₄
socle	C₂×C₁₃	#1843
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×#1055	C₂³
hypercenter	#338	#261
hypocenter	C₁₃	#12902
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
72. C₁₃	#12902	semidirect

Maximal subgroups

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

subgroup	index
#13131177	2
#13131173	2
#13114592	2
#12902	13