Subgroups — #13129854

Order 1664.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718535	C₂	1	1	yes	maximal, characteristic
2	#11718260	C₂	1	1	yes	maximal, characteristic
3	#11718256	C₂	1	1	yes	maximal, characteristic
4	#88142	—	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	#88047	—	2	1	no	—
11	C₂×Dic₂₆	—	4	1	no	—
12	C₂×#1057	—	4	1	no	—
13	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₄⋊Dic₁₃	—	2	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	#1364	—	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	Dic₂₆	—	8	1	no	—
27	Dic₂₆	—	8	1	no	—
28	#1057	—	8	1	no	—
29	C₈×C₁₃	—	2	1	no	—
30	#1055	SD₁₆	1	1	yes	characteristic
31	#1055	Q₁₆	1	1	yes	characteristic
32	#500	—	13	1	no	—
33	C₄⋊C₁₆	—	13	1	no	—
34	#335	—	13	1	no	—
35	C₂²×C₁₃	#102	1	1	yes	characteristic
36	C₄×C₁₃	—	8	1	no	—
37	C₄×C₁₃	#101	1	1	yes	characteristic
38	C₄×C₁₃	#103	1	1	yes	characteristic
39	Dic₁₃	—	2	1	no	—
40	Dic₁₃	—	8	1	no	—
41	Dic₁₃	D₁₆	1	1	yes	characteristic
42	Dic₁₃	SD₃₂	1	1	yes	characteristic
43	C₄⋊Q₈	—	26	1	no	—
44	C₂×C₁₆	—	26	1	no	—
45	#107	—	13	1	no	—
46	#107	—	26	1	no	—
47	#107	#261	1	1	yes	characteristic
48	C₄⋊C₈	—	26	1	no	—
49	C₄×C₈	—	13	1	no	—
50	C₂×C₁₃	#332	1	1	yes	characteristic
51	C₂×C₁₃	#357	1	1	yes	characteristic
52	C₂×C₁₃	#362	1	1	yes	characteristic
53	C₂×Q₈	—	52	1	no	—
54	C₂×C₈	—	13	1	no	—
55	C₂×C₈	—	52	1	no	—
56	C₂×C₈	C₂×#261	1	1	yes	characteristic
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	—	26	1	no	—
59	C₄⋊C₄	—	52	1	no	—
60	C₄²	—	13	1	no	—
61	C₁₆	—	52	1	no	—
62	C₁₃	#1364	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	104	1	no	—
64	Q₈	—	104	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	13	1	no	—
67	C₂×C₄	—	13	1	no	—
68	C₂×C₄	—	52	1	no	—
69	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	13	1	no	—
72	C₈	—	13	1	no	—
73	C₈	—	104	1	no	—
74	C₂²	#88115	1	1	yes	characteristic
75	C₄	—	8	1	no	—
76	C₄	—	13	1	no	—
77	C₄	—	13	1	no	—
78	C₄	—	26	1	no	—
79	C₄	—	104	1	no	—
80	C₄	#88113	1	1	yes	characteristic
81	C₄	#88117	1	1	yes	characteristic
82	C₂	#11718245	1	1	yes	characteristic
83	C₂	#11718276	1	1	yes	characteristic
84	C₂	#11718282	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	#1364
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
62. C₁₃	#1364	semidirect

Maximal subgroups

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

subgroup	index
#11718535	2
#11718260	2
#11718256	2
#1364	13