Subgroups — #28388777

Order 14464.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813528	C₂	1	1	yes	maximal, characteristic
2	#20298428	C₂	1	1	yes	maximal, characteristic
3	#368×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#16813558	—	2	1	no	—
5	#16813528	C₄	1	2	yes	—
6	C₂×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
7	#108×C₁₁₃	—	2	1	no	—
8	#14268631	—	4	1	no	—
9	M₁₆×C₁₁₃	—	4	1	no	—
10	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
11	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₁₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
14	C₈×C₁₁₃	—	8	1	no	—
15	C₈×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₁₁₃	Q₁₆	1	1	yes	characteristic
17	#11744751	—	8	1	no	—
18	C₂²×C₁₁₃	Q₃₂	1	1	yes	characteristic
19	C₄×C₁₁₃	#107	1	1	yes	characteristic
20	C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
21	C₂×C₁₁₃	—	2	1	no	—
22	C₂×C₁₁₃	#366	1	1	yes	characteristic
23	#1425	—	113	1	no	maximal, Sylow
24	C₁₁₃	#1425	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	113	1	no	—
26	#368	—	113	1	no	—
27	#368	D₁₁₃	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	226	1	no	—
31	C₃₂	—	113	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	452	1	no	—
34	C₂×C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
35	C₁₆	Dic₂₂₆	1	1	yes	characteristic
36	C₁₆	C₄×D₁₁₃	1	1	yes	characteristic
37	C₂×C₄	#14268632	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	904	1	no	—
40	C₈	#14268626	1	1	yes	characteristic
41	C₈	#14268637	1	1	yes	characteristic
42	C₂²	#16813568	1	1	yes	characteristic
43	C₄	#16813555	1	1	yes	characteristic
44	C₄	#16813563	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#20298423	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16813563
commutator	C₁₆×C₁₁₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁₃
Fitting	#368×C₁₁₃	C₂
socle	C₂×C₁₁₃	#366
prime radical	C₂²×C₁₁₃	Q₃₂
cosocle	C₂×C₁₆×C₁₁₃	C₂²
hypercenter	#368	D₁₁₃
hypocenter	C₁₁₃	#1425
LCS	G ▷ C₁₆×C₁₁₃ ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
24. C₁₁₃	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813528	2
#20298428	2
#368×C₁₁₃	2
#1425	113