Subgroups — #20299461

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²	C₄⋊#90673
commutator	C₄×C₁₁₃	C₂×C₈
Frattini	C₂×C₄	C₂×#90673
Fitting	C₂×C₈×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₄⋊C₄
hypercenter	C₂×C₈	#90673
hypocenter	C₁₁₃	#335
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
11. C₈×C₁₁₃	C₈	semidirect
22. C₁₁₃	#335	semidirect
35. C₈	#11744753	semidirect