Subgroups — #16782423

Order 3328.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130771	C₂	1	6	yes	maximal
2	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#88101	—	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	#88101	—	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	#8813	—	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	SD₁₆	1	24	yes	—
24	#1844	—	13	6	no	—
25	C₂×C₈²	—	13	1	no	—
26	C₂²×D₁₃	#127	1	1	yes	characteristic
27	C₂×#261	—	8	12	no	—
28	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
29	C₂×Dic₁₃	C₄⋊Q₈	1	3	yes	—
30	C₄×D₁₃	C₂×SD₁₆	1	12	yes	—
31	C₈×C₁₃	#106	1	12	yes	complemented
32	#1055	#106	1	12	yes	complemented
33	C₂×#106	—	26	12	no	—
34	C₂×C₄×C₈	—	13	3	no	—
35	#384	—	13	4	no	—
36	C₈²	—	13	3	no	—
37	C₈²	#261	1	1	yes	characteristic, complemented
38	C₂²×C₁₃	#384	1	1	yes	characteristic
39	C₂×D₁₃	#492	1	6	yes	—
40	#261	—	16	4	no	—
41	C₄×C₁₃	C₂×#106	1	6	yes	—
42	Dic₁₃	#498	1	6	yes	—
43	C₂²×C₈	—	13	6	no	—
44	C₂×C₄⋊C₄	—	26	12	no	—
45	C₂×C₄²	—	13	1	no	—
46	#106	—	52	24	no	—
47	C₄×C₈	—	13	6	no	—
48	C₄×C₈	—	13	3	no	—
49	C₄×C₈	C₂×#261	1	3	yes	—
50	C₂×C₁₃	#1844	1	3	yes	—
51	D₁₃	#1705	1	4	yes	—
52	C₂²×C₄	—	13	3	no	—
53	C₂²×C₄	—	52	4	no	—
54	C₂×C₈	—	13	6	no	—
55	C₂×C₈	—	13	24	no	—
56	C₂×C₈	C₄⋊#261	1	6	yes	—
57	C₄⋊C₄	—	52	24	no	—
58	C₄²	—	13	3	no	—
59	C₄²	C₂²×#261	1	1	yes	characteristic
60	C₁₃	#8813	1	1	yes	characteristic, complemented, Sylow
61	C₂³	—	13	1	no	—
62	C₂×C₄	—	13	3	no	—
63	C₂×C₄	—	13	12	no	—
64	C₂×C₄	—	104	12	no	—
65	C₂×C₄	C₂×C₄⋊#261	1	3	yes	—
66	C₈	—	13	12	no	—
67	C₈	#88101	1	12	yes	complemented
68	C₂²	—	13	6	no	—
69	C₂²	#11719059	1	1	yes	characteristic
70	C₄	—	13	6	no	—
71	C₄	—	208	4	no	—
72	C₄	C₂×#88101	1	6	yes	—
73	C₂	—	13	4	no	—
74	C₂	#13130771	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	#8813
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
31. C₈×C₁₃	#106	semidirect
32. #1055	#106	semidirect
37. C₈²	#261	semidirect
60. C₁₃	#8813	semidirect
67. C₈	#88101	semidirect

Maximal subgroups

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

subgroup	index
#13130771	2
C₈²×D₁₃	2
#8813	13