Subgroups — #16817692

Order 3712.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270989	C₂	1	2	yes	maximal
2	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
4	#11745166	—	2	2	no	—
5	C₂₉×C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
7	C₄⋊Dic₂₉	—	4	2	no	—
8	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
11	C₂×Dic₂₉	—	8	2	no	—
12	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
14	#1423	—	29	1	no	maximal, Sylow
15	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
16	C₄×C₂₉	#107	1	1	yes	characteristic
17	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
18	Dic₂₉	—	16	2	no	—
19	C₂×C₃₂	D₂₉	1	1	yes	characteristic
20	#366	—	29	2	no	—
21	C₂×C₂₉	#366	1	1	yes	characteristic
22	C₂×C₂₉	D₃₂	1	1	yes	characteristic
23	C₂×C₂₉	Q₆₄	1	1	yes	characteristic
24	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
25	#107	—	58	2	no	—
26	C₃₂	Dic₂₉	1	2	yes	complemented
27	C₂₉	#1423	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₈	D₁₁₆	1	1	yes	characteristic
29	C₄⋊C₄	—	116	2	no	—
30	C₁₆	Dic₅₈	1	1	yes	characteristic
31	C₁₆	C₂×Dic₂₉	1	1	yes	characteristic
32	C₂×C₄	—	232	2	no	—
33	C₂×C₄	D₂₃₂	1	1	yes	characteristic
34	C₈	Dic₁₁₆	1	1	yes	characteristic
35	C₈	C₄⋊Dic₂₉	1	1	yes	characteristic
36	C₂²	D₄₆₄	1	1	yes	characteristic
37	C₄	—	464	2	no	—
38	C₄	Dic₂₃₂	1	1	yes	characteristic
39	C₄	#11745166	1	1	yes	characteristic
40	C₂	#14270989	1	1	yes	characteristic
41	C₂	D₉₂₈	1	1	yes	characteristic
42	C₂	Dic₄₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₆₄
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂×C₂₉×C₃₂	C₂
socle, prime radical	C₂²×C₂₉	D₁₆
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	C₂×C₃₂	D₂₉
hypocenter	C₂₉	#1423
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₂₉×C₃₂	C₄	semidirect
26. C₃₂	Dic₂₉	semidirect
27. C₂₉	#1423	semidirect

Maximal subgroups

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

subgroup	index
#14270989	2
C₂×C₂₉×C₃₂	2
#1423	29