Subgroups — C₂₉×#1424 #16815138

Order 3712.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#366	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
4	C₂₉×#107	—	2	2	no	—
5	C₂₉×C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
7	C₄⋊C₄×C₂₉	—	4	2	no	—
8	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₉	—	8	2	no	—
11	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
12	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
14	#1424	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
16	C₄×C₂₉	—	16	2	no	—
17	C₄×C₂₉	#107	1	1	yes	characteristic
18	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
19	C₂×C₃₂	C₂×C₂₉	1	1	yes	characteristic
20	#366	C₂×C₂₉	1	2	yes	—
21	C₂×C₂₉	#366	1	1	yes	characteristic
22	C₂×C₂₉	SD₆₄	1	2	yes	—
23	C₂×C₁₆	C₂²×C₂₉	1	1	yes	characteristic
24	#107	—	2	2	no	—
25	C₃₂	C₄×C₂₉	1	2	yes	complemented
26	C₂₉	#1424	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₈	D₄×C₂₉	1	1	yes	characteristic
28	C₄⋊C₄	—	4	2	no	—
29	C₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
30	C₁₆	Q₈×C₂₉	1	1	yes	characteristic
31	C₂×C₄	—	8	2	no	—
32	C₂×C₄	D₈×C₂₉	1	1	yes	characteristic
33	C₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
34	C₈	Q₁₆×C₂₉	1	1	yes	characteristic
35	C₂²	C₂₉×D₁₆	1	1	yes	characteristic
36	C₄	—	16	2	no	—
37	C₄	C₂₉×#107	1	1	yes	characteristic
38	C₄	C₂₉×Q₃₂	1	1	yes	characteristic
39	C₂	C₂₉×#366	1	1	yes	characteristic
40	C₂	C₂₉×SD₆₄	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₉	D₁₆
commutator	C₁₆	C₂×C₄×C₂₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₉
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂₉×C₃₂	C₄	semidirect
14. #1424	C₂₉	direct (N × H)
25. C₃₂	C₄×C₂₉	semidirect
26. C₂₉	#1424	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×C₃₂	2
C₂₉×#366	2
#1424	29

Subgroups — C29×#1424 #16815138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1424 #16815138