Subgroups — #16817695

Order 3712.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745142	C₂	1	1	yes	maximal, characteristic
2	#14270993	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₂₉×#108	—	2	1	no	—
6	#11745167	—	2	1	no	—
7	#11745142	C₄	1	2	yes	—
8	M₁₆×C₂₉	—	4	1	no	—
9	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
10	#90777	—	4	1	no	—
11	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
14	C₈×C₂₉	—	8	1	no	—
15	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
17	#6597	—	8	1	no	—
18	#1425	—	29	1	no	maximal, Sylow
19	C₂²×C₂₉	Q₃₂	1	1	yes	characteristic
20	C₄×C₂₉	#107	1	1	yes	characteristic
21	C₄×C₂₉	D₁₆	1	1	yes	characteristic
22	C₂×C₃₂	—	29	1	no	—
23	#368	—	29	1	no	—
24	#368	D₂₉	1	1	yes	characteristic
25	C₂×C₂₉	—	2	1	no	—
26	C₂×C₂₉	#366	1	1	yes	characteristic
27	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
28	#108	—	2	1	no	—
29	#108	—	58	1	no	—
30	C₃₂	—	29	2	no	—
31	C₂₉	#1425	1	1	yes	characteristic, complemented, Sylow
32	M₁₆	—	4	1	no	—
33	M₁₆	—	116	1	no	—
34	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
35	C₁₆	Dic₅₈	1	1	yes	characteristic
36	C₁₆	C₄×D₂₉	1	1	yes	characteristic
37	C₂×C₄	#90782	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	232	1	no	—
40	C₈	#90779	1	1	yes	characteristic
41	C₈	#90785	1	1	yes	characteristic
42	C₂²	#11745177	1	1	yes	characteristic
43	C₄	#11745155	1	1	yes	characteristic
44	C₄	#11745174	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#14270988	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745174
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#368	C₂
socle	C₂×C₂₉	#366
prime radical	C₂²×C₂₉	Q₃₂
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#368	D₂₉
hypocenter	C₂₉	#1425
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
31. C₂₉	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745142	2
#14270993	2
C₂₉×#368	2
#1425	29