Subgroups — #16817408

Order 3712.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#90768	C₂	1	1	yes	maximal, characteristic
2	C₈×#6597	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	C₄	1	2	yes	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90768	C₄	1	2	yes	—
7	C₄×#6597	C₄	1	2	yes	—
8	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×#6597	C₈	1	4	yes	—
12	C₁₆×C₂₉	C₈	1	4	yes	complemented
13	#90768	C₈	1	4	yes	complemented
14	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
16	C₈×C₂₉	C₂×C₈	1	2	yes	—
17	C₈×C₂₉	C₂×C₈	1	2	yes	—
18	#6597	—	2	4	no	—
19	#1311	—	29	1	no	maximal, Sylow
20	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
21	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
22	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
23	C₄×C₂₉	M₃₂	1	4	yes	—
24	C₄×C₁₆	—	29	1	no	—
25	C₄×C₁₆	D₂₉	1	1	yes	characteristic
26	C₈²	—	29	1	no	—
27	C₂×C₂₉	C₈²	1	1	yes	characteristic
28	C₂×C₂₉	#346	1	2	yes	—
29	C₂×C₁₆	—	29	2	no	—
30	C₂×C₁₆	Dic₂₉	1	2	yes	—
31	C₄×C₈	—	29	2	no	—
32	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
33	C₂₉	#1311	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₈	—	29	4	no	—
35	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
37	C₄²	C₄×D₂₉	1	1	yes	characteristic
38	C₁₆	—	29	4	no	—
39	C₁₆	#6597	1	4	yes	complemented
40	C₂×C₄	C₈×D₂₉	1	2	yes	—
41	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
42	C₈	—	58	4	no	—
43	C₈	C₈×D₂₉	1	2	yes	—
44	C₈	C₂×#6597	1	2	yes	—
45	C₂²	C₈×Dic₂₉	1	1	yes	characteristic
46	C₄	#11745146	1	4	yes	—
47	C₄	C₄×#6597	1	1	yes	characteristic
48	C₄	C₈×Dic₂₉	1	1	yes	characteristic
49	C₂	C₈×#6597	1	1	yes	characteristic
50	C₂	#14270938	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₉
commutator	C₂×C₂₉	C₈²
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₄×C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#1311
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₂₉	C₈	semidirect
13. #90768	C₈	semidirect
33. C₂₉	#1311	semidirect
39. C₁₆	#6597	semidirect

Maximal subgroups

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

subgroup	index
C₄×#90768	2
C₈×#6597	2
C₄×C₁₆×C₂₉	2
#1311	29