Subgroups — #15777663

Order 3328.

262 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117118	C₂	1	4	yes	maximal
2	#13114454	C₂	1	2	yes	maximal
3	C₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	#11718360	—	2	2	no	—
5	#11718343	—	2	2	no	—
6	#11718343	C₂²	1	4	yes	—
7	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₈²×C₁₃	C₂²	1	1	yes	characteristic
9	#11718097	—	2	8	no	—
10	C₂×Dic₅₂	—	4	4	no	—
11	#88123	—	2	4	no	—
12	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
13	C₄×C₈×C₁₃	D₄	1	2	yes	—
14	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	#88058	—	2	8	no	—
16	#88058	—	4	4	no	—
17	#12523	—	13	1	no	maximal, Sylow
18	C₂×Dic₂₆	—	4	4	no	—
19	C₂×C₈×C₁₃	D₈	1	4	yes	—
20	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
21	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₄⋊Dic₁₃	—	4	4	no	—
23	C₄⋊Dic₁₃	—	4	4	no	—
24	Dic₅₂	—	8	8	no	—
25	C₁₃×C₁₆	Q₁₆	1	8	yes	complemented
26	#2254	—	13	4	no	—
27	#1713	—	13	2	no	—
28	C₈×C₁₆	D₁₃	1	1	yes	characteristic
29	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
31	C₂×Dic₁₃	—	8	4	no	—
32	Dic₂₆	—	8	8	no	—
33	C₈×C₁₃	SD₃₂	1	8	yes	—
34	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
35	#500	—	13	4	no	—
36	#500	—	26	2	no	—
37	#494	—	26	2	no	—
38	#367	—	26	8	no	—
39	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
40	C₈²	C₂×D₁₃	1	1	yes	characteristic
41	C₂²×C₁₃	#493	1	1	yes	characteristic
42	C₄×C₁₃	#494	1	2	yes	—
43	C₄×C₁₃	C₂×SD₃₂	1	4	yes	—
44	Dic₁₃	—	16	4	no	—
45	C₂×Q₁₆	—	52	4	no	—
46	C₄⋊Q₈	—	26	4	no	—
47	C₂×C₁₆	D₅₂	1	4	yes	—
48	#107	—	26	8	no	—
49	#107	—	52	4	no	—
50	C₄×C₈	D₅₂	1	2	yes	—
51	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
52	C₂×C₁₃	#1713	1	1	yes	characteristic
53	C₂×C₁₃	#2248	1	2	yes	—
54	C₂×Q₈	—	52	4	no	—
55	Q₁₆	—	104	8	no	—
56	C₂×C₈	D₁₀₄	1	4	yes	—
57	C₂×C₈	C₂×D₅₂	1	2	yes	—
58	C₄⋊C₄	—	52	4	no	—
59	C₄⋊C₄	—	52	4	no	—
60	C₄²	C₂×D₅₂	1	1	yes	characteristic
61	C₁₆	Dic₅₂	1	8	yes	complemented
62	C₁₃	#12523	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	104	8	no	—
64	C₂×C₄	—	104	4	no	—
65	C₂×C₄	#88128	1	1	yes	characteristic
66	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
67	C₈	#88040	1	8	yes	—
68	C₈	C₂×Dic₅₂	1	4	yes	—
69	C₂²	#11718356	1	1	yes	characteristic
70	C₄	—	208	4	no	—
71	C₄	#11718360	1	2	yes	—
72	C₄	C₂×#88040	1	4	yes	—
73	C₂	#13114454	1	1	yes	characteristic
74	C₂	#13117092	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	#12523
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
25. C₁₃×C₁₆	Q₁₆	semidirect
61. C₁₆	Dic₅₂	semidirect
62. C₁₃	#12523	semidirect

Maximal subgroups

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

subgroup	index
#13117118	2
#13114454	2
C₈×C₁₃×C₁₆	2
#12523	13