Subgroups — #16817410

Order 3712.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#90768	C₂	1	2	yes	maximal
2	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
4	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90768	C₄	1	4	yes	—
7	C₂×C₈×C₂₉	C₈	1	2	yes	—
8	C₂×C₈×C₂₉	C₈	1	2	yes	—
9	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
10	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
11	#90768	—	2	4	no	—
12	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
15	C₈×C₂₉	—	2	2	no	—
16	C₈×C₂₉	C₁₆	1	4	yes	complemented
17	C₈×C₂₉	M₁₆	1	4	yes	—
18	#1312	—	29	1	no	maximal, Sylow
19	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
20	C₄×C₂₉	#97	1	2	yes	—
21	C₄×C₂₉	C₂×C₁₆	1	2	yes	—
22	C₄×C₂₉	M₃₂	1	2	yes	—
23	C₄×C₁₆	—	29	2	no	—
24	C₈²	D₂₉	1	1	yes	characteristic
25	C₂×C₂₉	#322	1	1	yes	characteristic
26	C₂×C₂₉	C₄×C₁₆	1	1	yes	characteristic
27	C₂×C₂₉	#346	1	1	yes	characteristic
28	C₂×C₁₆	—	29	4	no	—
29	C₄×C₈	Dic₂₉	1	1	yes	characteristic
30	C₄×C₈	Dic₂₉	1	1	yes	characteristic
31	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
32	C₂₉	#1312	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	#6597	1	2	yes	—
34	C₂×C₈	#6597	1	2	yes	—
35	C₂×C₈	C₄×D₂₉	1	2	yes	—
36	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
37	C₁₆	—	58	4	no	—
38	C₂×C₄	C₂×#6597	1	1	yes	characteristic
39	C₂×C₄	C₂×#6597	1	1	yes	characteristic
40	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	#90768	1	4	yes	complemented
43	C₈	#90772	1	4	yes	—
44	C₂²	C₄×#6597	1	1	yes	characteristic
45	C₄	C₂×#90768	1	2	yes	—
46	C₄	#11745160	1	2	yes	—
47	C₄	#11745163	1	2	yes	—
48	C₂	#14270884	1	1	yes	characteristic
49	C₂	C₄×#90768	1	1	yes	characteristic
50	C₂	#14270939	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₉
commutator	C₂×C₂₉	C₄×C₁₆
Fitting	C₈²×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₄×C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₈²	D₂₉
hypocenter	C₂₉	#1312
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
16. C₈×C₂₉	C₁₆	semidirect
32. C₂₉	#1312	semidirect
42. C₈	#90768	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
C₈²×C₂₉	2
#1312	29