Subgroups — #16778208

Order 3328.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130006	C₂	1	1	yes	maximal, characteristic, complemented
2	#13129998	C₂	1	1	yes	maximal, characteristic, complemented
3	#13117146	C₂	1	1	yes	maximal, characteristic
4	#11718580	—	2	1	no	—
5	#11718221	—	2	1	no	—
6	C₁₃×Q₆₄	C₄	1	1	yes	characteristic, complemented
7	#11718113	—	2	1	no	—
8	D₄₁₆	C₄	1	1	yes	characteristic, complemented
9	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
10	#11718037	—	2	1	no	—
11	#88173	—	4	1	no	—
12	#88102	—	4	1	no	—
13	C₁₃×Q₃₂	—	2	1	no	—
14	#88068	—	4	1	no	—
15	D₂₀₈	—	2	1	no	—
16	C₁₆×D₁₃	D₄	1	1	yes	characteristic
17	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
18	#88034	D₄	1	1	yes	characteristic
19	#7540	—	13	1	no	maximal, Sylow
20	#6131	—	8	1	no	—
21	C₄⋊#261	—	8	1	no	—
22	C₁₃×Q₁₆	—	4	1	no	—
23	#6106	—	8	1	no	—
24	D₁₀₄	—	4	1	no	—
25	C₈×D₁₃	D₈	1	1	yes	characteristic
26	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	#6090	SD₁₆	1	1	yes	characteristic
28	#2262	—	13	1	no	—
29	M₁₂₈	—	13	1	no	—
30	#1424	—	13	1	no	—
31	C₂×#261	—	16	1	no	—
32	Q₈×C₁₃	—	8	1	no	—
33	D₅₂	—	8	1	no	—
34	D₅₂	—	16	1	no	—
35	C₄×D₁₃	—	16	1	no	—
36	C₄×D₁₃	D₁₆	1	1	yes	characteristic
37	C₈×C₁₃	#102	1	1	yes	characteristic
38	#1055	SD₃₂	1	1	yes	characteristic
39	#508	—	26	1	no	—
40	Q₆₄	#261	1	1	yes	characteristic, complemented
41	SD₆₄	—	26	1	no	—
42	D₃₂	—	13	1	no	—
43	C₂×C₃₂	—	13	1	no	—
44	#366	—	26	1	no	—
45	C₆₄	—	26	1	no	—
46	C₂×D₁₃	—	16	1	no	—
47	C₂×D₁₃	D₃₂	1	1	yes	characteristic
48	#261	—	32	1	no	—
49	C₄×C₁₃	—	16	1	no	—
50	C₄×C₁₃	#357	1	1	yes	characteristic
51	Dic₁₃	SD₆₄	1	1	yes	characteristic
52	#135	—	52	1	no	—
53	Q₃₂	—	2	1	no	—
54	SD₃₂	—	52	1	no	—
55	D₁₆	—	26	1	no	—
56	C₂×C₁₆	—	13	1	no	—
57	#107	—	52	1	no	—
58	C₃₂	—	13	1	no	—
59	C₃₂	C₂×#261	1	1	yes	characteristic
60	C₂×C₁₃	#1415	1	1	yes	characteristic
61	D₁₃	—	2	1	no	—
62	D₁₃	—	32	1	no	—
63	#41	—	104	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	104	1	no	—
66	D₈	—	52	1	no	—
67	C₂×C₈	—	13	1	no	—
68	C₄⋊C₄	—	104	1	no	—
69	C₁₆	—	13	1	no	—
70	C₁₆	C₂²⋊#261	1	1	yes	characteristic
71	C₁₃	#7540	1	1	yes	characteristic, complemented, Sylow
72	Q₈	—	8	1	no	—
73	D₄	—	104	1	no	—
74	D₄	—	208	1	no	—
75	C₂×C₄	—	13	1	no	—
76	C₂×C₄	—	208	1	no	—
77	C₂×C₄	—	208	1	no	—
78	C₈	—	13	1	no	—
79	C₈	#88115	1	1	yes	characteristic
80	C₂²	—	13	1	no	—
81	C₂²	—	208	1	no	—
82	C₄	—	13	1	no	—
83	C₄	—	16	1	no	—
84	C₄	—	416	1	no	—
85	C₄	#11718276	1	1	yes	characteristic
86	C₂	—	26	1	no	—
87	C₂	—	416	1	no	—
88	C₂	#13129985	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129985
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₃₂	C₂×#261
Fitting	C₁₃×Q₆₄	C₄
socle	C₂×C₁₃	#1415
prime radical	#13117146	C₂
cosocle	D₁₃×C₃₂	C₂²
hypercenter	Q₆₄	#261
hypocenter	C₁₃	#7540
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #13130006	C₂	semidirect
2. #13129998	C₂	semidirect
6. C₁₃×Q₆₄	C₄	semidirect
8. D₄₁₆	C₄	semidirect
40. Q₆₄	#261	semidirect
71. C₁₃	#7540	semidirect

Maximal subgroups

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

subgroup	index
#13130006	2
#13129998	2
#13117146	2
#7540	13