Subgroups — #16791500

Order 3328.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130005	C₂	1	3	yes	maximal, complemented
2	C₂×#11718037	C₂	1	3	yes	maximal, complemented
3	#13117130	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#504	C₄	1	1	yes	characteristic
5	#11718091	C₄	1	3	yes	—
6	C₂×#88034	C₂²	1	3	yes	—
7	#11718037	C₂²	1	1	yes	characteristic
8	#11718037	C₂²	1	3	yes	—
9	C₁₃×#131	C₈	1	1	yes	characteristic
10	C₁₃×M₃₂	C₈	1	3	yes	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	3	yes	—
12	#88034	C₂×C₄	1	3	yes	—
13	#88034	C₂³	1	1	yes	characteristic
14	#13737	—	13	1	no	maximal, Sylow
15	C₁₃×#41	C₁₆	1	1	yes	characteristic
16	C₁₃×M₁₆	C₁₆	1	3	yes	—
17	C₂×C₈×C₁₃	C₂×C₈	1	3	yes	—
18	C₁₃×C₁₆	C₂×C₈	1	3	yes	—
19	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
20	#2258	—	13	1	no	—
21	M₁₂₈	—	13	3	no	—
22	C₂×C₆₄	—	13	3	no	—
23	Q₈×C₁₃	C₃₂	1	1	yes	characteristic
24	D₄×C₁₃	C₃₂	1	3	yes	—
25	C₂×C₄×C₁₃	C₂×C₁₆	1	3	yes	—
26	C₈×C₁₃	C₂×C₁₆	1	3	yes	—
27	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
28	#504	#261	1	1	yes	characteristic
29	M₆₄	—	13	3	no	—
30	C₂×C₃₂	—	13	3	no	—
31	C₆₄	—	13	1	no	—
32	C₆₄	—	13	3	no	—
33	C₂²×C₁₃	C₂×C₃₂	1	3	yes	—
34	C₄×C₁₃	C₂×C₃₂	1	3	yes	—
35	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
36	#131	#1057	1	1	yes	characteristic
37	M₃₂	#1057	1	3	yes	—
38	C₂×C₁₆	C₂×#261	1	3	yes	—
39	C₃₂	—	13	1	no	—
40	C₃₂	—	13	3	no	—
41	C₂×C₁₃	—	2	3	no	—
42	C₂×C₁₃	C₂²×C₃₂	1	1	yes	characteristic
43	#41	#6092	1	1	yes	characteristic
44	M₁₆	#6092	1	3	yes	—
45	C₂×C₈	C₂×#1057	1	3	yes	—
46	C₁₆	C₂×#1057	1	3	yes	—
47	C₁₆	C₂²×#261	1	1	yes	characteristic
48	C₁₃	#13737	1	1	yes	characteristic, complemented, Sylow
49	Q₈	#88036	1	1	yes	characteristic
50	D₄	#88036	1	3	yes	—
51	C₂×C₄	C₂×#6092	1	3	yes	—
52	C₈	C₂×#6092	1	3	yes	—
53	C₈	C₂²×#1057	1	1	yes	characteristic
54	C₂²	C₂×#88036	1	3	yes	—
55	C₄	C₂×#88036	1	3	yes	—
56	C₄	C₂²×#6092	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×#88036	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×#261
commutator, socle	C₂×C₁₃	C₂²×C₃₂
Fitting	C₁₃×#504	C₄
prime radical	C₁₃×#41	C₁₆
cosocle	#88034	C₂³
hypercenter	#504	#261
hypocenter	C₁₃	#13737
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #13130005	C₂	semidirect
2. C₂×#11718037	C₂	semidirect
48. C₁₃	#13737	semidirect

Maximal subgroups

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

subgroup	index
#13130005	2
C₂×#11718037	2
#13117130	2
#13737	13