Subgroups — #16782396

Order 3328.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129703	C₂	1	3	yes	maximal
2	#13129696	C₂	1	3	yes	maximal
3	#13113138	C₂	1	1	yes	maximal, characteristic
4	#11719061	C₂²	1	1	yes	characteristic
5	#11719055	C₂²	1	3	yes	—
6	C₄×#6094	C₂²	1	3	yes	—
7	C₈²×C₁₃	C₄	1	1	yes	characteristic, complemented
8	#11718047	C₄	1	3	yes	complemented
9	C₂×#6094	—	2	3	no	—
10	C₄²×D₁₃	C₂³	1	1	yes	characteristic
11	(C₂×#261)⋊C₄	—	2	3	no	—
12	#88112	—	2	3	no	—
13	#88111	—	2	3	no	—
14	#88110	—	2	3	no	—
15	C₄×C₈×C₁₃	C₂×C₄	1	3	yes	—
16	#88055	—	2	3	no	—
17	C₄×#1055	C₂×C₄	1	3	yes	—
18	#8803	—	13	1	no	maximal, Sylow
19	C₂²×#261	—	4	1	no	—
20	C₂×C₄×D₁₃	#41	1	3	yes	—
21	C₂×#1057	—	4	3	no	—
22	C₂×C₈×C₁₃	—	2	3	no	—
23	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×Dic₁₃	#41	1	3	yes	—
25	C₂×#1055	—	2	3	no	—
26	#6094	—	4	6	no	—
27	#1455	—	13	1	no	—
28	#1291	—	13	3	no	—
29	#1288	—	13	3	no	—
30	C₂²×D₁₃	#126	1	1	yes	characteristic
31	C₂×#261	—	8	3	no	—
32	C₂×C₄×C₁₃	#117	1	3	yes	—
33	C₂×Dic₁₃	#126	1	3	yes	—
34	C₄×D₁₃	—	4	3	no	—
35	#1057	—	8	3	no	—
36	C₈×C₁₃	—	2	6	no	—
37	#1055	—	4	3	no	—
38	#432	—	13	3	no	—
39	C₄×M₁₆	—	13	3	no	—
40	#383	—	13	1	no	—
41	#322	—	13	3	no	—
42	C₈²	#261	1	1	yes	characteristic, complemented
43	C₂²×C₁₃	#383	1	1	yes	characteristic
44	C₂×D₁₃	—	2	3	no	—
45	#261	—	16	1	no	—
46	C₄×C₁₃	—	2	3	no	—
47	Dic₁₃	—	2	3	no	—
48	C₂×M₁₆	—	26	3	no	—
49	C₂×C₄²	—	13	1	no	—
50	C₄⋊C₈	—	26	3	no	—
51	C₂²⋊C₈	—	26	3	no	—
52	#97	—	26	3	no	—
53	#97	—	26	3	no	—
54	C₄×C₈	—	13	3	no	—
55	C₄×C₈	C₂×#261	1	3	yes	—
56	#95	—	26	3	no	—
57	C₂×C₁₃	#1841	1	3	yes	—
58	D₁₃	—	4	1	no	—
59	C₂²×C₄	—	13	3	no	—
60	C₂²×C₄	—	52	1	no	—
61	M₁₆	—	52	6	no	—
62	C₂×C₈	—	2	3	no	—
63	C₂×C₈	—	26	3	no	—
64	C₂×C₈	—	52	3	no	—
65	C₄²	—	13	3	no	—
66	C₄²	C₂²×#261	1	1	yes	characteristic
67	C₁₃	#8803	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	13	1	no	—
69	C₂×C₄	—	13	3	no	—
70	C₂×C₄	—	52	3	no	—
71	C₂×C₄	—	104	3	no	—
72	C₂×C₄	#88237	1	3	yes	—
73	C₈	—	2	6	no	—
74	C₈	—	52	3	no	—
75	C₈	—	104	3	no	—
76	C₂²	—	26	3	no	—
77	C₂²	#11719061	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	26	3	no	—
80	C₄	—	208	1	no	—
81	C₂	—	52	1	no	—
82	C₂	#13130766	1	3	yes	—

	subgroup	G/H
center	C₂²	#11719061
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	#383
prime radical	C₂²×D₁₃	#126
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#8803
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. C₈²×C₁₃	C₄	semidirect
8. #11718047	C₄	semidirect
42. C₈²	#261	semidirect
67. C₁₃	#8803	semidirect

Maximal subgroups

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

subgroup	index
#13129703	2
#13129696	2
#13113138	2
#8803	13