Subgroups — #16782428

Order 3328.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130772	C₂	1	6	yes	maximal
2	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#88102	—	2	12	no	—
4	#11719059	C₂²	1	4	yes	—
5	C₄×C₈×D₁₃	C₂²	1	3	yes	—
6	C₈²×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₈×#1055	C₄	1	3	yes	complemented
8	C₂×C₄⋊#261	—	2	12	no	—
9	C₂×C₈×D₁₃	D₄	1	6	yes	—
10	C₄²×D₁₃	C₂³	1	1	yes	characteristic
11	#88102	—	4	24	no	—
12	C₄×C₈×C₁₃	C₂×C₄	1	3	yes	—
13	C₈×Dic₁₃	Q₈	1	6	yes	—
14	C₄×#1055	C₂×C₄	1	3	yes	—
15	#8818	—	13	1	no	maximal, Sylow
16	C₂²×#261	—	4	4	no	—
17	C₂×C₄×D₁₃	C₂×D₄	1	3	yes	—
18	C₄⋊#261	—	4	24	no	—
19	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
20	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₄×Dic₁₃	C₂×Q₈	1	3	yes	—
22	C₂×#1055	C₄⋊C₄	1	6	yes	—
23	C₈×D₁₃	D₈	1	12	yes	—
24	C₈×D₁₃	Q₁₆	1	12	yes	—
25	#1845	—	13	6	no	—
26	C₂×C₈²	—	13	1	no	—
27	C₂²×D₁₃	#127	1	1	yes	characteristic
28	C₂×#261	—	8	12	no	—
29	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
30	C₂×Dic₁₃	C₄⋊Q₈	1	3	yes	—
31	C₄×D₁₃	C₂×D₈	1	6	yes	—
32	C₄×D₁₃	C₂×Q₁₆	1	6	yes	—
33	C₈×C₁₃	#107	1	12	yes	complemented
34	#1055	#107	1	12	yes	complemented
35	C₂×#107	—	26	12	no	—
36	C₂×C₄×C₈	—	13	3	no	—
37	#384	—	13	4	no	—
38	C₈²	—	13	3	no	—
39	C₈²	#261	1	1	yes	characteristic, complemented
40	C₂²×C₁₃	#384	1	1	yes	characteristic
41	C₂×D₁₃	#493	1	3	yes	—
42	C₂×D₁₃	#494	1	3	yes	—
43	#261	—	16	4	no	—
44	C₄×C₁₃	C₂×#107	1	6	yes	—
45	Dic₁₃	#500	1	6	yes	—
46	C₂²×C₈	—	13	6	no	—
47	C₂×C₄⋊C₄	—	26	12	no	—
48	C₂×C₄²	—	13	1	no	—
49	#107	—	52	24	no	—
50	C₄×C₈	—	13	6	no	—
51	C₄×C₈	—	13	3	no	—
52	C₄×C₈	C₂×#261	1	3	yes	—
53	C₂×C₁₃	#1845	1	3	yes	—
54	D₁₃	#1712	1	1	yes	characteristic
55	D₁₃	#1713	1	3	yes	—
56	C₂²×C₄	—	13	3	no	—
57	C₂²×C₄	—	52	4	no	—
58	C₂×C₈	—	13	6	no	—
59	C₂×C₈	—	13	12	no	—
60	C₂×C₈	—	13	12	no	—
61	C₂×C₈	C₄⋊#261	1	6	yes	—
62	C₄⋊C₄	—	52	24	no	—
63	C₄²	—	13	3	no	—
64	C₄²	C₂²×#261	1	1	yes	characteristic
65	C₁₃	#8818	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	13	1	no	—
67	C₂×C₄	—	13	3	no	—
68	C₂×C₄	—	13	6	no	—
69	C₂×C₄	—	13	6	no	—
70	C₂×C₄	—	104	12	no	—
71	C₂×C₄	C₂×C₄⋊#261	1	3	yes	—
72	C₈	—	13	12	no	—
73	C₈	#88102	1	12	yes	complemented
74	C₂²	—	13	3	no	—
75	C₂²	—	13	3	no	—
76	C₂²	#11719059	1	1	yes	characteristic
77	C₄	—	13	6	no	—
78	C₄	—	208	4	no	—
79	C₄	C₂×#88102	1	6	yes	—
80	C₂	—	13	1	no	—
81	C₂	—	13	3	no	—
82	C₂	#13130772	1	3	yes	—

	subgroup	G/H
center	C₂²	#11719059
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	#384
prime radical	C₂²×D₁₃	#127
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#8818
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
6. C₈²×C₁₃	C₄	semidirect
7. C₈×#1055	C₄	semidirect
33. C₈×C₁₃	#107	semidirect
34. #1055	#107	semidirect
39. C₈²	#261	semidirect
65. C₁₃	#8818	semidirect
73. C₈	#88102	semidirect

Maximal subgroups

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

subgroup	index
#13130772	2
C₈²×D₁₃	2
#8818	13