Subgroups — #13115008

Order 1664.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88059	C₂	1	4	yes	maximal
3	#11718585	C₂	1	2	yes	maximal
4	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6099	C₂²	1	4	yes	—
7	C₄×C₈×C₁₃	C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₄	1	2	yes	—
9	#88059	—	2	8	no	—
10	C₄⋊#1055	—	2	4	no	—
11	C₂²×C₄×C₁₃	Q₈	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₁₃	D₄	1	4	yes	—
15	C₂×C₈×C₁₃	Q₈	1	4	yes	—
16	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₁₃	D₄	1	2	yes	—
19	#6099	—	2	8	no	—
20	C₂×#1055	—	2	4	no	—
21	#1848	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	—	2	4	no	—
24	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
30	C₈×C₁₃	C₄⋊C₄	1	8	yes	—
31	#1055	—	4	4	no	—
32	C₂×#108	—	13	4	no	—
33	#423	—	13	2	no	—
34	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
35	C₂²×C₁₃	—	2	2	no	—
36	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₁₃	C₄⋊Q₈	1	2	yes	—
38	C₄×C₁₃	—	2	2	no	—
39	C₄×C₁₃	#108	1	4	yes	complemented
40	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
41	C₄×C₁₃	#127	1	1	yes	characteristic
42	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×M₁₆	—	13	4	no	—
44	C₂²×C₈	C₂×D₁₃	1	2	yes	—
45	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
46	#108	—	26	8	no	—
47	C₄⋊C₈	—	26	4	no	—
48	C₄×C₈	Dic₁₃	1	2	yes	—
49	C₄×C₈	Dic₁₃	1	2	yes	—
50	C₂×C₁₃	—	2	2	no	—
51	C₂×C₁₃	#384	1	1	yes	characteristic
52	C₂×C₁₃	C₂×#108	1	2	yes	—
53	C₂²×C₄	Dic₂₆	1	2	yes	—
54	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
55	M₁₆	—	26	8	no	—
56	C₂×C₈	—	26	4	no	—
57	C₂×C₈	Dic₂₆	1	4	yes	—
58	C₂×C₈	D₅₂	1	4	yes	—
59	C₂×C₈	C₂×Dic₁₃	1	4	yes	—
60	C₄²	D₅₂	1	2	yes	—
61	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
62	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
63	C₁₃	#1848	1	1	yes	characteristic, complemented, Sylow
64	C₂³	C₂×Dic₂₆	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
68	C₂×C₄	C₂×Dic₂₆	1	2	yes	—
69	C₂×C₄	C₂×D₅₂	1	2	yes	—
70	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
72	C₈	—	52	4	no	—
73	C₈	C₄⋊Dic₁₃	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	#88123	1	2	yes	—
76	C₂²	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	#88059	1	4	yes	complemented
79	C₄	#88123	1	1	yes	characteristic
80	C₄	#88128	1	1	yes	characteristic
81	C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
82	C₂	—	2	2	no	—
83	C₂	#11718596	1	1	yes	characteristic
84	C₂	C₂×#88059	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	#1848
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
39. C₄×C₁₃	#108	semidirect
63. C₁₃	#1848	semidirect
78. C₄	#88059	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₁₃	2
C₂×#88059	2
#11718585	2
#1848	13