Subgroups — #28405609

Order 14464.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299520	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813696	—	2	2	no	—
4	C₂×#14268622	C₄	1	1	yes	characteristic
5	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
7	#14268650	—	4	2	no	—
8	C₂×#11744751	D₄	1	1	yes	characteristic
9	C₄×Dic₁₁₃	Q₈	1	1	yes	characteristic
10	#14268622	—	2	1	no	—
11	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₁₃	C₈	1	2	yes	—
13	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₁₁₃	—	2	1	no	—
15	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
17	#11744751	D₈	1	1	yes	characteristic
18	#11744751	Q₁₆	1	1	yes	characteristic
19	C₂²×C₁₁₃	#108	1	1	yes	characteristic
20	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₁₃	#107	1	1	yes	characteristic
22	Dic₁₁₃	—	2	2	no	—
23	C₂×C₁₁₃	—	2	1	no	—
24	C₂×C₁₁₃	#335	1	1	yes	characteristic
25	#1373	—	113	1	no	maximal, Sylow
26	C₁₁₃	#1373	1	1	yes	characteristic, complemented, Sylow
27	#364	—	113	2	no	—
28	C₄×C₁₆	—	113	1	no	—
29	M₃₂	—	226	2	no	—
30	C₂×C₁₆	—	113	1	no	—
31	C₂×C₁₆	#90673	1	1	yes	characteristic
32	C₄×C₈	—	113	1	no	—
33	C₂×C₈	—	113	1	no	—
34	C₂×C₈	C₂×#90673	1	1	yes	characteristic
35	C₄²	—	113	1	no	—
36	C₁₆	—	452	2	no	—
37	C₁₆	—	226	1	no	—
38	C₁₆	#11744753	1	2	yes	—
39	C₂×C₄	—	226	1	no	—
40	C₂×C₄	C₄⋊#90673	1	1	yes	characteristic
41	C₈	—	113	1	no	—
42	C₈	—	113	1	no	—
43	C₈	C₂×#11744753	1	1	yes	characteristic
44	C₈	#14268657	1	1	yes	characteristic
45	C₂²	#16813693	1	1	yes	characteristic
46	C₄	—	226	2	no	—
47	C₄	C₄⋊#11744753	1	1	yes	characteristic
48	C₄	#16813691	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#20299461	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16813691
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	#335
prime radical	C₂²×C₁₁₃	#108
cosocle	C₈×Dic₁₁₃	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1373
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
26. C₁₁₃	#1373	semidirect

Maximal subgroups

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

subgroup	index
#20299520	2
C₁₆×Dic₁₁₃	2
#1373	113