Subgroups — #13129851

Order 1664.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718842	C₂	1	1	yes	maximal, characteristic
2	#11718260	C₂	1	1	yes	maximal, characteristic
3	#11718256	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
5	#88198	—	2	1	no	—
6	C₂×#6107	—	2	1	no	—
7	C₂×Dic₅₂	C₄	1	1	yes	characteristic
8	C₄⋊#1057	—	2	1	no	—
9	C₂×#6092	—	2	1	no	—
10	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₃	—	2	1	no	—
12	C₂×Dic₂₆	—	2	1	no	—
13	C₂×#1057	—	4	1	no	—
14	C₁₃×Q₁₆	—	4	1	no	—
15	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	#6107	—	4	1	no	—
17	#6107	—	4	1	no	—
18	#6101	—	4	1	no	—
19	#6101	—	4	1	no	—
20	C₄×Dic₁₃	D₄	1	1	yes	characteristic
21	C₂×#1055	D₄	1	1	yes	characteristic
22	Dic₅₂	—	4	1	no	—
23	#6092	—	4	1	no	—
24	#1362	—	13	1	no	maximal, Sylow
25	Q₈×C₁₃	—	4	1	no	—
26	Q₈×C₁₃	—	4	1	no	—
27	C₂×C₄×C₁₃	—	4	1	no	—
28	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	1	no	—
30	C₂×Dic₁₃	D₈	1	1	yes	characteristic
31	C₂×Dic₁₃	SD₁₆	1	1	yes	characteristic
32	Dic₂₆	—	4	1	no	—
33	Dic₂₆	—	4	1	no	—
34	#1057	—	8	1	no	—
35	C₈×C₁₃	—	2	1	no	—
36	#1055	D₈	1	1	yes	characteristic
37	#1055	SD₁₆	1	1	yes	characteristic
38	#494	—	13	1	no	—
39	C₄⋊C₁₆	—	13	1	no	—
40	#335	—	13	1	no	—
41	C₂²×C₁₃	#102	1	1	yes	characteristic
42	C₄×C₁₃	—	8	1	no	—
43	C₄×C₁₃	#100	1	1	yes	characteristic
44	C₄×C₁₃	#102	1	1	yes	characteristic
45	Dic₁₃	—	2	1	no	—
46	Dic₁₃	—	8	1	no	—
47	Dic₁₃	SD₃₂	1	1	yes	characteristic
48	Dic₁₃	Q₃₂	1	1	yes	characteristic
49	C₂×Q₁₆	—	13	1	no	—
50	C₂×Q₁₆	—	26	1	no	—
51	C₂×Q₁₆	#261	1	1	yes	characteristic
52	C₄⋊Q₈	—	26	1	no	—
53	C₂×C₁₆	—	26	1	no	—
54	C₄⋊C₈	—	26	1	no	—
55	C₄×C₈	—	13	1	no	—
56	C₂×C₁₃	#331	1	1	yes	characteristic
57	C₂×C₁₃	#358	1	1	yes	characteristic
58	C₂×C₁₃	#362	1	1	yes	characteristic
59	C₂×Q₈	—	2	1	no	—
60	C₂×Q₈	—	26	1	no	—
61	Q₁₆	—	4	1	no	—
62	Q₁₆	—	52	1	no	—
63	Q₁₆	—	52	1	no	—
64	Q₁₆	—	52	1	no	—
65	C₂×C₈	—	13	1	no	—
66	C₂×C₈	—	52	1	no	—
67	C₂×C₈	C₂×#261	1	1	yes	characteristic
68	C₄⋊C₄	—	52	1	no	—
69	C₄⋊C₄	—	52	1	no	—
70	C₄²	—	13	1	no	—
71	C₁₆	—	52	1	no	—
72	C₁₃	#1362	1	1	yes	characteristic, complemented, Sylow
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	52	1	no	—
76	Q₈	—	52	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	13	1	no	—
79	C₂×C₄	—	13	1	no	—
80	C₂×C₄	—	52	1	no	—
81	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	13	1	no	—
84	C₈	—	13	1	no	—
85	C₈	—	104	1	no	—
86	C₂²	#88115	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	13	1	no	—
89	C₄	—	13	1	no	—
90	C₄	—	26	1	no	—
91	C₄	—	104	1	no	—
92	C₄	#88115	1	1	yes	characteristic
93	C₄	#88121	1	1	yes	characteristic
94	C₂	#11718280	1	1	yes	characteristic
95	C₂	#11718282	1	1	yes	characteristic
96	C₂	#11718297	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88115
commutator	C₂×C₈×C₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×#261
Fitting	C₂×C₁₃×Q₁₆	C₄
socle, prime radical	C₂²×C₁₃	#102
cosocle	C₈×Dic₁₃	C₂²
hypercenter	C₂×Q₁₆	#261
hypocenter	C₁₃	#1362
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
72. C₁₃	#1362	semidirect

Maximal subgroups

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

subgroup	index
#11718842	2
#11718260	2
#11718256	2
#1362	13