Subgroups — #13129853

Order 1664.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718539	C₂	1	1	yes	maximal, characteristic
2	#11718260	C₂	1	1	yes	maximal, characteristic
3	#11718255	C₂	1	1	yes	maximal, characteristic
4	#88144	—	2	1	no	—
5	C₄⋊#1057	—	2	1	no	—
6	C₂×#6092	—	2	1	no	—
7	C₁₃×#107	C₄	1	1	yes	characteristic
8	#88058	C₄	1	1	yes	characteristic
9	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	#88048	—	2	1	no	—
11	C₂×#1057	—	4	1	no	—
12	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₄⋊Dic₁₃	—	2	1	no	—
15	C₄⋊Dic₁₃	—	4	1	no	—
16	#6101	—	4	1	no	—
17	C₄×Dic₁₃	D₄	1	1	yes	characteristic
18	C₂×#1055	D₄	1	1	yes	characteristic
19	#6092	—	4	1	no	—
20	#1363	—	13	1	no	maximal, Sylow
21	C₂×C₄×C₁₃	—	4	1	no	—
22	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₁₃	—	4	1	no	—
24	C₂×Dic₁₃	D₈	1	1	yes	characteristic
25	C₂×Dic₁₃	SD₁₆	1	1	yes	characteristic
26	#1057	—	8	1	no	—
27	C₈×C₁₃	—	2	1	no	—
28	#1055	SD₁₆	1	1	yes	characteristic
29	#1055	Q₁₆	1	1	yes	characteristic
30	#499	—	13	1	no	—
31	C₄⋊C₁₆	—	13	1	no	—
32	#334	—	13	1	no	—
33	C₂²×C₁₃	#102	1	1	yes	characteristic
34	C₄×C₁₃	—	8	1	no	—
35	C₄×C₁₃	#101	1	1	yes	characteristic
36	C₄×C₁₃	#103	1	1	yes	characteristic
37	Dic₁₃	—	2	1	no	—
38	Dic₁₃	—	2	1	no	—
39	Dic₁₃	—	8	1	no	—
40	#125	—	26	1	no	—
41	C₂×C₁₆	—	26	1	no	—
42	#107	—	13	1	no	—
43	#107	#261	1	1	yes	characteristic
44	#106	—	26	1	no	—
45	C₄⋊C₈	—	26	1	no	—
46	C₄×C₈	—	13	1	no	—
47	C₂×C₁₃	#332	1	1	yes	characteristic
48	C₂×C₁₃	#359	1	1	yes	characteristic
49	C₂×C₁₃	#360	1	1	yes	characteristic
50	C₂×C₈	—	13	1	no	—
51	C₂×C₈	—	52	1	no	—
52	C₂×C₈	C₂×#261	1	1	yes	characteristic
53	C₄⋊C₄	—	2	1	no	—
54	C₄⋊C₄	—	26	1	no	—
55	C₄⋊C₄	—	52	1	no	—
56	C₄⋊C₄	—	52	1	no	—
57	C₄²	—	13	1	no	—
58	C₁₆	—	52	1	no	—
59	C₁₃	#1363	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	13	1	no	—
62	C₂×C₄	—	13	1	no	—
63	C₂×C₄	—	52	1	no	—
64	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	13	1	no	—
67	C₈	—	13	1	no	—
68	C₈	—	104	1	no	—
69	C₂²	#88115	1	1	yes	characteristic
70	C₄	—	8	1	no	—
71	C₄	—	26	1	no	—
72	C₄	—	26	1	no	—
73	C₄	—	104	1	no	—
74	C₄	#88113	1	1	yes	characteristic
75	C₄	#88117	1	1	yes	characteristic
76	C₂	#11718245	1	1	yes	characteristic
77	C₂	#11718275	1	1	yes	characteristic
78	C₂	#11718281	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88115
commutator	C₂×C₈×C₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#107	C₄
socle, prime radical	C₂²×C₁₃	#102
cosocle	C₈×Dic₁₃	C₂²
hypercenter	#107	#261
hypocenter	C₁₃	#1363
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
59. C₁₃	#1363	semidirect

Maximal subgroups

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

subgroup	index
#11718539	2
#11718260	2
#11718255	2
#1363	13