Subgroups — #16817567

Order 3712.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270984	C₂	1	1	yes	maximal, characteristic
2	C₄×#90768	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#364	C₂	1	1	yes	maximal, characteristic
4	C₂₉×M₃₂	—	2	1	no	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	#11745160	—	2	1	no	—
7	C₂×#90768	C₄	1	1	yes	characteristic
8	C₂×#90768	C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
11	C₄²×C₂₉	Q₈	1	1	yes	characteristic
12	C₁₆×C₂₉	—	4	1	no	—
13	#90768	—	2	1	no	—
14	#90768	—	4	1	no	—
15	#90768	C₈	1	2	yes	—
16	C₂×C₄×C₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₉	M₁₆	1	1	yes	characteristic
20	C₈×C₂₉	D₈	1	1	yes	characteristic
21	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
22	#1373	—	29	1	no	maximal, Sylow
23	C₂²×C₂₉	#108	1	1	yes	characteristic
24	C₄×C₂₉	—	2	2	no	—
25	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₂₉	#107	1	1	yes	characteristic
27	#364	—	29	1	no	—
28	#364	D₂₉	1	1	yes	characteristic
29	C₄×C₁₆	—	29	1	no	—
30	C₂×C₂₉	—	2	1	no	—
31	C₂×C₂₉	#335	1	1	yes	characteristic
32	M₃₂	—	2	1	no	—
33	M₃₂	—	58	1	no	—
34	C₂×C₁₆	—	29	1	no	—
35	C₂×C₁₆	—	29	1	no	—
36	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
37	C₂₉	#1373	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
40	C₄²	Dic₅₈	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	29	2	no	—
43	C₁₆	—	58	1	no	—
44	C₁₆	—	116	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	#90779	1	1	yes	characteristic
47	C₈	C₈×D₂₉	1	1	yes	characteristic
48	C₈	#90772	1	1	yes	characteristic
49	C₈	#90782	1	1	yes	characteristic
50	C₈	#90785	1	1	yes	characteristic
51	C₂²	#11745170	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	#11745155	1	1	yes	characteristic
54	C₄	#11745162	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#14270915	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#90782
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#364	C₂
socle	C₂×C₂₉	#335
prime radical	C₂²×C₂₉	#108
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#364	D₂₉
hypocenter	C₂₉	#1373
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
37. C₂₉	#1373	semidirect

Maximal subgroups

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

subgroup	index
#14270984	2
C₄×#90768	2
C₂₉×#364	2
#1373	29