Subgroups — #15777660

Order 3328.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117118	C₂	1	2	yes	maximal
2	#13117111	C₂	1	2	yes	maximal
3	#13114446	C₂	1	2	yes	maximal
4	C₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	#11718343	C₂²	1	4	yes	—
6	#11718342	—	2	4	no	—
7	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₈²×C₁₃	C₂²	1	1	yes	characteristic
10	#11718097	—	2	4	no	—
11	#11718096	—	2	4	no	—
12	#88123	—	2	4	no	—
13	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
14	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
15	C₄×C₈×C₁₃	D₄	1	2	yes	—
16	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	#88058	—	2	4	no	—
18	#88058	—	2	4	no	—
19	#88056	—	4	8	no	—
20	#12522	—	13	1	no	maximal, Sylow
21	C₂×Dic₂₆	—	4	4	no	—
22	C₂×C₈×C₁₃	D₈	1	4	yes	—
23	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
26	C₄⋊Dic₁₃	—	4	4	no	—
27	C₄⋊Dic₁₃	—	4	4	no	—
28	C₁₃×C₁₆	Q₁₆	1	4	yes	—
29	C₁₃×C₁₆	Q₁₆	1	4	yes	—
30	#2254	—	13	2	no	—
31	#2252	—	13	2	no	—
32	#1710	—	13	2	no	—
33	C₈×C₁₆	D₁₃	1	1	yes	characteristic
34	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
36	C₂×Dic₁₃	—	8	4	no	—
37	Dic₂₆	—	8	8	no	—
38	C₈×C₁₃	—	2	4	no	—
39	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
40	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
41	#500	—	13	4	no	—
42	#487	—	26	4	no	—
43	#367	—	26	4	no	—
44	#366	—	26	4	no	—
45	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
46	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
47	C₈²	C₂×D₁₃	1	1	yes	characteristic
48	C₂²×C₁₃	#493	1	1	yes	characteristic
49	C₄×C₁₃	#494	1	1	yes	characteristic
50	C₄×C₁₃	#494	1	1	yes	characteristic
51	C₄×C₁₃	#508	1	4	yes	—
52	Dic₁₃	—	16	4	no	—
53	C₄⋊Q₈	—	26	4	no	—
54	C₂×C₁₆	D₅₂	1	2	yes	—
55	C₂×C₁₆	D₅₂	1	2	yes	—
56	#107	—	26	4	no	—
57	#107	—	26	4	no	—
58	#103	—	52	8	no	—
59	C₄×C₈	D₅₂	1	2	yes	—
60	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
61	C₂×C₁₃	#1713	1	1	yes	characteristic
62	C₂×C₁₃	#2249	1	2	yes	—
63	C₂×Q₈	—	52	4	no	—
64	C₂×C₈	D₁₀₄	1	4	yes	—
65	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
66	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
67	C₄⋊C₄	—	52	4	no	—
68	C₄⋊C₄	—	52	4	no	—
69	C₄²	C₂×D₅₂	1	1	yes	characteristic
70	C₁₆	Dic₅₂	1	4	yes	—
71	C₁₆	Dic₅₂	1	4	yes	—
72	C₁₃	#12522	1	1	yes	characteristic, complemented, Sylow
73	Q₈	—	104	8	no	—
74	C₂×C₄	—	104	4	no	—
75	C₂×C₄	#88128	1	1	yes	characteristic
76	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
77	C₈	—	2	4	no	—
78	C₈	C₂×Dic₅₂	1	2	yes	—
79	C₈	C₂×Dic₅₂	1	2	yes	—
80	C₂²	#11718356	1	1	yes	characteristic
81	C₄	—	208	4	no	—
82	C₄	#11718360	1	1	yes	characteristic
83	C₄	#11718360	1	1	yes	characteristic
84	C₄	#11718565	1	4	yes	—
85	C₂	#13114454	1	1	yes	characteristic
86	C₂	#13117097	1	2	yes	—

	subgroup	G/H
center	C₂²	#11718356
commutator, cosocle	C₄×C₈×C₁₃	C₂³
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₈×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	#493
hypercenter	C₈×C₁₆	D₁₃
hypocenter	C₁₃	#12522
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
72. C₁₃	#12522	semidirect

Maximal subgroups

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

subgroup	index
#13117118	2
#13117111	2
#13114446	2
C₈×C₁₃×C₁₆	2
#12522	13