Subgroups — #14270945

Order 1856.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745160	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₂₉	C₄	1	1	yes	characteristic
4	M₁₆×C₂₉	—	2	2	no	—
5	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#90768	—	2	2	no	—
8	C₂³×C₂₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₂₉	—	2	1	no	—
10	C₂×C₄×C₂₉	—	2	1	no	—
11	C₂×C₄×C₂₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₂₉	—	2	1	no	—
14	C₈×C₂₉	D₄	1	2	yes	—
15	C₂²×C₂₉	—	2	1	no	—
16	C₂²×C₂₉	—	4	1	no	—
17	C₂²×C₂₉	C₂×C₈	1	1	yes	characteristic
18	C₄×C₂₉	—	2	1	no	—
19	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₂₉	M₁₆	1	1	yes	characteristic
21	#349	—	29	1	no	maximal, Sylow
22	C₂×C₂₉	—	2	1	no	—
23	C₂×C₂₉	—	4	1	no	—
24	C₂×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
25	C₂×M₁₆	D₂₉	1	1	yes	characteristic
26	M₃₂	—	29	2	no	—
27	C₂₉	#349	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₄	Dic₂₉	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	Dic₂₉	1	1	yes	characteristic
31	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
32	C₁₆	—	58	2	no	—
33	C₂³	#6597	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	#6597	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂²⋊D₂₉	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#6597	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	#90777	1	1	yes	characteristic
45	C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#6597	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₂₉
commutator	C₂²×C₂₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₂₉
Fitting	C₂×M₁₆×C₂₉	C₂
socle	C₂×C₂₉	C₂²⋊C₈
prime radical	C₂³×C₂₉	C₈
cosocle	C₂×C₈×C₂₉	C₂²
hypercenter	C₂×M₁₆	D₂₉
hypocenter	C₂₉	#349
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. #11745160	C₂	semidirect
27. C₂₉	#349	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₉	2
#11745160	2
#349	29