Subgroups — #28388773

Order 14464.

56 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	#20298424	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#16813556	—	2	1	no	—
5	#16813528	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
7	#107×C₁₁₃	—	2	1	no	—
8	C₄⋊Dic₁₁₃	—	4	1	no	—
9	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₁₃	—	4	1	no	—
11	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₁₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	—	8	1	no	—
14	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
15	C₂×Dic₁₁₃	—	8	1	no	—
16	C₈×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₁₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₁₃	D₁₆	1	1	yes	characteristic
19	C₄×C₁₁₃	—	16	1	no	—
20	C₄×C₁₁₃	#107	1	1	yes	characteristic
21	C₄×C₁₁₃	Q₃₂	1	1	yes	characteristic
22	Dic₁₁₃	—	16	1	no	—
23	C₂×C₁₁₃	#366	1	1	yes	characteristic
24	C₂×C₁₁₃	D₃₂	1	1	yes	characteristic
25	C₂×C₁₁₃	Q₆₄	1	1	yes	characteristic
26	#1423	—	113	1	no	maximal, Sylow
27	C₁₁₃	#1423	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	113	1	no	—
29	#366	—	113	1	no	—
30	#366	D₁₁₃	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	226	1	no	—
34	C₃₂	—	113	2	no	—
35	C₂×C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	452	1	no	—
38	C₁₆	Dic₂₂₆	1	1	yes	characteristic
39	C₁₆	C₄×D₁₁₃	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	904	1	no	—
42	C₂×C₄	#14268632	1	1	yes	characteristic
43	C₈	#14268626	1	1	yes	characteristic
44	C₈	#14268637	1	1	yes	characteristic
45	C₂²	#16813563	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1808	1	no	—
48	C₄	#16813555	1	1	yes	characteristic
49	C₄	#16813568	1	1	yes	characteristic
50	C₂	#20298423	1	1	yes	characteristic
51	C₂	#20298433	1	1	yes	characteristic
52	C₂	#20298438	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813563
commutator	C₁₆×C₁₁₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁₃
Fitting	#366×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	D₁₆
cosocle	C₂×C₁₆×C₁₁₃	C₂²
hypercenter	#366	D₁₁₃
hypocenter	C₁₁₃	#1423
LCS	G ▷ C₁₆×C₁₁₃ ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #16813528	C₄	semidirect
27. C₁₁₃	#1423	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
#20298424	2
#366×C₁₁₃	2
#1423	113