Subgroups — #1424×C₂₂₃ #43250439

Order 28544.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×C₂₂₃	C₂	1	1	yes	maximal, characteristic
2	#366×C₂₂₃	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₂₂₃	C₂²	1	1	yes	characteristic
4	#107×C₂₂₃	—	2	2	no	—
5	C₃₂×C₂₂₃	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₂₃	D₄	1	1	yes	characteristic
7	C₄⋊C₄×C₂₂₃	—	4	2	no	—
8	C₁₆×C₂₂₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₂₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₂₃	—	8	2	no	—
11	C₂×C₄×C₂₂₃	D₈	1	1	yes	characteristic
12	C₈×C₂₂₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₂₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₂₃	D₁₆	1	1	yes	characteristic
15	C₄×C₂₂₃	—	16	2	no	—
16	C₄×C₂₂₃	#107	1	1	yes	characteristic
17	C₄×C₂₂₃	Q₃₂	1	1	yes	characteristic
18	C₂×C₂₂₃	#366	1	1	yes	characteristic
19	C₂×C₂₂₃	SD₆₄	1	2	yes	—
20	C₂₂₃	#1424	1	1	yes	characteristic, direct product factor, Sylow
21	#1424	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×C₃₂	C₂×C₂₂₃	1	1	yes	characteristic
23	#366	C₂×C₂₂₃	1	2	yes	—
24	C₂×C₁₆	C₂²×C₂₂₃	1	1	yes	characteristic
25	#107	—	2	2	no	—
26	C₃₂	C₄×C₂₂₃	1	2	yes	complemented
27	C₂×C₈	D₄×C₂₂₃	1	1	yes	characteristic
28	C₄⋊C₄	—	4	2	no	—
29	C₁₆	C₂×C₄×C₂₂₃	1	1	yes	characteristic
30	C₁₆	Q₈×C₂₂₃	1	1	yes	characteristic
31	C₂×C₄	—	8	2	no	—
32	C₂×C₄	D₈×C₂₂₃	1	1	yes	characteristic
33	C₈	C₄⋊C₄×C₂₂₃	1	1	yes	characteristic
34	C₈	Q₁₆×C₂₂₃	1	1	yes	characteristic
35	C₂²	D₁₆×C₂₂₃	1	1	yes	characteristic
36	C₄	—	16	2	no	—
37	C₄	#107×C₂₂₃	1	1	yes	characteristic
38	C₄	Q₃₂×C₂₂₃	1	1	yes	characteristic
39	C₂	#366×C₂₂₃	1	1	yes	characteristic
40	C₂	SD₆₄×C₂₂₃	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₂₃	D₁₆
commutator	C₁₆	C₂×C₄×C₂₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₂₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₂₃ ◁ C₂×C₄×C₂₂₃ ◁ C₂×C₈×C₂₂₃ ◁ C₂×C₁₆×C₂₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₂₂₃	C₄	semidirect
20. C₂₂₃	#1424	direct (N × H)
21. #1424	C₂₂₃	direct (N × H)
26. C₃₂	C₄×C₂₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₂×C₂₂₃	2
#366×C₂₂₃	2
#1424	223

Subgroups — #1424×C223 #43250439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1424×C₂₂₃ #43250439