Subgroups — #31826248

Order 18112.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22583616	C₂	1	1	yes	maximal, characteristic
2	#22583550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985392	C₄	1	1	yes	characteristic
5	#17985376	C₄	1	1	yes	characteristic
6	#17985375	—	2	1	no	—
7	C₈×D₂₈₃	—	2	1	no	—
8	C₂₈₃⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
10	C₁₆×C₂₈₃	—	2	1	no	—
11	Dic₅₆₆	C₈	1	1	yes	characteristic
12	D₁₁₃₂	C₈	1	1	yes	characteristic
13	C₂²⋊D₂₈₃	—	2	1	no	—
14	C₄×D₂₈₃	—	2	1	no	—
15	C₂₈₃⋊C₈	—	2	1	no	—
16	C₂×C₄×C₂₈₃	C₂×C₄	1	1	yes	characteristic
17	C₈×C₂₈₃	D₄	1	1	yes	characteristic
18	C₈×C₂₈₃	D₄	1	1	yes	characteristic
19	C₂²×C₂₈₃	M₁₆	1	1	yes	characteristic
20	C₂×D₂₈₃	—	2	1	no	—
21	C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₈₃	C₂×C₈	1	1	yes	characteristic
23	Dic₂₈₃	—	2	1	no	—
24	C₂×C₂₈₃	—	2	1	no	—
25	C₂×C₂₈₃	C₂²⋊C₈	1	1	yes	characteristic
26	D₂₈₃	—	4	1	no	—
27	C₂₈₃	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	283	1	no	maximal, Sylow
29	#131	—	283	1	no	—
30	M₃₂	—	283	1	no	—
31	C₂×C₁₆	D₂₈₃	1	1	yes	characteristic, complemented
32	#41	—	283	1	no	—
33	M₁₆	—	283	1	no	—
34	M₁₆	—	566	1	no	—
35	C₂×C₈	—	566	1	no	—
36	C₂×C₈	C₂×D₂₈₃	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	566	1	no	—
39	Q₈	—	283	1	no	—
40	D₄	—	283	1	no	—
41	D₄	—	566	1	no	—
42	C₂×C₄	—	566	1	no	—
43	C₂×C₄	C₄×D₂₈₃	1	1	yes	characteristic
44	C₈	—	566	1	no	—
45	C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
46	C₈	D₁₁₃₂	1	1	yes	characteristic
47	C₂²	—	566	1	no	—
48	C₂²	#17985375	1	1	yes	characteristic
49	C₄	—	566	1	no	—
50	C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
51	C₄	C₈×D₂₈₃	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	1132	1	no	—
54	C₂	(C₂×D₂₈₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₁₃₂
commutator	C₄×C₂₈₃	C₂×C₈
Frattini	C₂×C₈	C₂×D₂₈₃
Fitting	C₂×C₁₆×C₂₈₃	C₂
socle	C₂×C₂₈₃	C₂²⋊C₈
prime radical	#17985392	C₄
cosocle	C₂×C₈×C₂₈₃	C₂²
hypercenter	C₂×C₁₆	D₂₈₃
hypocenter	C₂₈₃	#350
LCS	G ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #22583550	C₂	semidirect
3. C₂×C₁₆×C₂₈₃	C₂	semidirect
27. C₂₈₃	#350	semidirect
31. C₂×C₁₆	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#22583616	2
#22583550	2
C₂×C₁₆×C₂₈₃	2
#350	283