Subgroups — #28405740

Order 14464.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299527	C₂	1	1	yes	maximal, characteristic
2	#20299525	C₂	1	1	yes	maximal, characteristic
3	#20298431	C₂	1	1	yes	maximal, characteristic
4	#16813693	—	2	1	no	—
5	#16813691	—	2	1	no	—
6	C₁₆×D₁₁₃	C₂²	1	1	yes	characteristic
7	#16813528	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₁₁₃	C₄	1	1	yes	characteristic, complemented
9	#14268657	—	4	1	no	—
10	C₄⋊#90673	—	4	1	no	—
11	C₈×D₁₁₃	D₄	1	1	yes	characteristic
12	#14268622	Q₈	1	1	yes	characteristic
13	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#90673	—	8	1	no	—
15	C₄×D₁₁₃	D₈	1	1	yes	characteristic
16	#11744753	—	8	1	no	—
17	C₈×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
18	#11744751	Q₁₆	1	1	yes	characteristic
19	C₂×D₁₁₃	SD₃₂	1	1	yes	characteristic
20	#90673	—	16	1	no	—
21	C₄×C₁₁₃	#107	1	1	yes	characteristic
22	Dic₁₁₃	SD₃₂	1	1	yes	characteristic
23	C₂×C₁₁₃	#367	1	1	yes	characteristic
24	D₁₁₃	—	2	1	no	—
25	#1426	—	113	1	no	maximal, Sylow
26	C₁₁₃	#1426	1	1	yes	characteristic, complemented, Sylow
27	M₆₄	—	113	1	no	—
28	#368	—	113	1	no	—
29	#367	—	113	1	no	—
30	C₂×C₁₆	—	113	1	no	—
31	#108	—	226	1	no	—
32	#107	—	226	1	no	—
33	C₃₂	—	113	1	no	—
34	C₃₂	#90673	1	1	yes	characteristic, complemented
35	M₁₆	—	452	1	no	—
36	C₂×C₈	—	113	1	no	—
37	C₄⋊C₄	—	452	1	no	—
38	C₁₆	—	113	1	no	—
39	C₁₆	C₂×#90673	1	1	yes	characteristic
40	C₂×C₄	—	113	1	no	—
41	C₂×C₄	—	904	1	no	—
42	C₈	—	113	1	no	—
43	C₈	—	904	1	no	—
44	C₈	C₄⋊#90673	1	1	yes	characteristic
45	C₂²	—	113	1	no	—
46	C₄	—	1808	1	no	—
47	C₄	—	113	1	no	—
48	C₄	#16813691	1	1	yes	characteristic
49	C₂	—	226	1	no	—
50	C₂	#20299525	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299525
commutator	C₁₆×C₁₁₃	C₂×C₄
Frattini	C₁₆	C₂×#90673
Fitting	C₃₂×C₁₁₃	C₄
socle	C₂×C₁₁₃	#367
prime radical	C₂×D₁₁₃	SD₃₂
cosocle	C₁₆×D₁₁₃	C₂²
hypercenter	C₃₂	#90673
hypocenter	C₁₁₃	#1426
LCS	G ▷ C₁₆×C₁₁₃ ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #16813528	C₄	semidirect
8. C₃₂×C₁₁₃	C₄	semidirect
26. C₁₁₃	#1426	semidirect
34. C₃₂	#90673	semidirect

Maximal subgroups

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

subgroup	index
#20299527	2
#20299525	2
#20298431	2
#1426	113