Subgroups — #16817627

Order 3712.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270997	C₂	1	1	yes	maximal, characteristic
2	#14270938	C₂	1	1	yes	maximal, characteristic
3	C₂₉×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₈×Dic₂₉	C₄	1	1	yes	characteristic
6	C₂×#90768	C₄	1	1	yes	characteristic
7	C₂₉×C₃₂	C₄	1	2	yes	complemented
8	#11745142	C₄	1	2	yes	complemented
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₂₉	C₈	1	1	yes	characteristic
11	C₂×#6597	C₈	1	1	yes	characteristic
12	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
14	#90768	C₈	1	2	yes	—
15	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₂₉	—	2	1	no	—
17	C₈×C₂₉	C₄²	1	1	yes	characteristic
18	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
19	#6597	—	2	1	no	—
20	#1398	—	29	1	no	maximal, Sylow
21	C₂²×C₂₉	M₃₂	1	1	yes	characteristic
22	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
23	C₄×C₂₉	M₃₂	1	1	yes	characteristic
24	Dic₂₉	—	4	1	no	—
25	M₆₄	—	29	1	no	—
26	M₆₄	D₂₉	1	1	yes	characteristic
27	#346	—	29	1	no	—
28	C₂×C₂₉	—	2	1	no	—
29	C₂×C₂₉	#346	1	1	yes	characteristic
30	C₂×C₁₆	—	29	1	no	—
31	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
32	C₄×C₈	—	29	1	no	—
33	C₃₂	—	29	2	no	—
34	C₃₂	Dic₂₉	1	2	yes	complemented
35	C₂₉	#1398	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₈	—	29	1	no	—
37	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
38	C₄²	—	29	1	no	—
39	C₁₆	—	29	2	no	—
40	C₁₆	C₄×D₂₉	1	1	yes	characteristic
41	C₁₆	C₂×Dic₂₉	1	1	yes	characteristic
42	C₂×C₄	—	58	1	no	—
43	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
44	C₈	—	58	1	no	—
45	C₈	C₈×D₂₉	1	1	yes	characteristic
46	C₈	C₄×Dic₂₉	1	1	yes	characteristic
47	C₂²	#11745146	1	1	yes	characteristic
48	C₄	—	116	1	no	—
49	C₄	#11745146	1	1	yes	characteristic
50	C₄	C₈×Dic₂₉	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#14270938	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₂₉
commutator	C₄×C₂₉	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×M₆₄	C₂
socle	C₂×C₂₉	#346
prime radical	C₂²×C₂₉	M₃₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	M₆₄	D₂₉
hypocenter	C₂₉	#1398
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₂₉×C₃₂	C₄	semidirect
8. #11745142	C₄	semidirect
34. C₃₂	Dic₂₉	semidirect
35. C₂₉	#1398	semidirect

Maximal subgroups

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

subgroup	index
#14270997	2
#14270938	2
C₂₉×M₆₄	2
#1398	29