Subgroups — #28388776

Order 14464.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298424	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813556	—	2	2	no	—
4	C₂×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₁₃	C₄	1	2	yes	complemented
6	C₄⋊Dic₁₁₃	—	4	2	no	—
7	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
8	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₁₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
11	C₂×Dic₁₁₃	—	8	2	no	—
12	C₈×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₁₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₁₃	D₁₆	1	1	yes	characteristic
15	C₄×C₁₁₃	#107	1	1	yes	characteristic
16	C₄×C₁₁₃	Q₃₂	1	1	yes	characteristic
17	Dic₁₁₃	—	16	2	no	—
18	C₂×C₁₁₃	#366	1	1	yes	characteristic
19	C₂×C₁₁₃	SD₆₄	1	2	yes	—
20	#1424	—	113	1	no	maximal, Sylow
21	C₁₁₃	#1424	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃₂	D₁₁₃	1	1	yes	characteristic
23	#366	—	113	2	no	—
24	C₂×C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
25	#107	—	226	2	no	—
26	C₃₂	Dic₁₁₃	1	2	yes	complemented
27	C₂×C₈	D₄₅₂	1	1	yes	characteristic
28	C₄⋊C₄	—	452	2	no	—
29	C₁₆	Dic₂₂₆	1	1	yes	characteristic
30	C₁₆	C₂×Dic₁₁₃	1	1	yes	characteristic
31	C₂×C₄	—	904	2	no	—
32	C₂×C₄	D₉₀₄	1	1	yes	characteristic
33	C₈	C₄⋊Dic₁₁₃	1	1	yes	characteristic
34	C₈	Dic₄₅₂	1	1	yes	characteristic
35	C₂²	D₁₈₀₈	1	1	yes	characteristic
36	C₄	—	1808	2	no	—
37	C₄	#16813556	1	1	yes	characteristic
38	C₄	Dic₉₀₄	1	1	yes	characteristic
39	C₂	#20298424	1	1	yes	characteristic
40	C₂	#20298437	1	2	yes	—

	subgroup	G/H
center	C₂²	D₁₈₀₈
commutator	C₁₆×C₁₁₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁₃
Fitting	C₂×C₃₂×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	D₁₆
cosocle	C₂×C₁₆×C₁₁₃	C₂²
hypercenter	C₂×C₃₂	D₁₁₃
hypocenter	C₁₁₃	#1424
LCS	G ▷ C₁₆×C₁₁₃ ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₁₁₃	C₄	semidirect
21. C₁₁₃	#1424	semidirect
26. C₃₂	Dic₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20298424	2
C₂×C₃₂×C₁₁₃	2
#1424	113