Subgroups — #16834657

Order 3712.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272092	C₂	1	1	yes	maximal, characteristic
2	#14272090	C₂	1	1	yes	maximal, characteristic
3	#14270996	C₂	1	1	yes	maximal, characteristic
4	#11745212	—	2	1	no	—
5	#11745210	—	2	1	no	—
6	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×C₃₂	C₄	1	1	yes	characteristic, complemented
8	#11745142	C₄	1	1	yes	characteristic, complemented
9	C₄⋊#1181	—	4	1	no	—
10	#90796	—	4	1	no	—
11	C₈×D₂₉	D₄	1	1	yes	characteristic
12	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#90768	Q₈	1	1	yes	characteristic
14	C₂×#1181	—	8	1	no	—
15	C₄×D₂₉	D₈	1	1	yes	characteristic
16	#6599	—	8	1	no	—
17	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
18	#6597	Q₁₆	1	1	yes	characteristic
19	#1426	—	29	1	no	maximal, Sylow
20	C₂×D₂₉	SD₃₂	1	1	yes	characteristic
21	#1181	—	16	1	no	—
22	C₄×C₂₉	#107	1	1	yes	characteristic
23	Dic₂₉	SD₃₂	1	1	yes	characteristic
24	M₆₄	—	29	1	no	—
25	#368	—	29	1	no	—
26	#367	—	29	1	no	—
27	C₂×C₂₉	#367	1	1	yes	characteristic
28	D₂₉	—	2	1	no	—
29	C₂×C₁₆	—	29	1	no	—
30	#108	—	58	1	no	—
31	#107	—	58	1	no	—
32	C₃₂	—	29	1	no	—
33	C₃₂	#1181	1	1	yes	characteristic, complemented
34	C₂₉	#1426	1	1	yes	characteristic, complemented, Sylow
35	M₁₆	—	116	1	no	—
36	C₂×C₈	—	29	1	no	—
37	C₄⋊C₄	—	116	1	no	—
38	C₁₆	—	29	1	no	—
39	C₁₆	C₂×#1181	1	1	yes	characteristic
40	C₂×C₄	—	29	1	no	—
41	C₂×C₄	—	232	1	no	—
42	C₈	—	29	1	no	—
43	C₈	—	232	1	no	—
44	C₈	C₄⋊#1181	1	1	yes	characteristic
45	C₂²	—	29	1	no	—
46	C₄	—	29	1	no	—
47	C₄	—	464	1	no	—
48	C₄	#11745210	1	1	yes	characteristic
49	C₂	—	58	1	no	—
50	C₂	#14272090	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272090
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₁₆	C₂×#1181
Fitting	C₂₉×C₃₂	C₄
socle	C₂×C₂₉	#367
prime radical	C₂×D₂₉	SD₃₂
cosocle	C₁₆×D₂₉	C₂²
hypercenter	C₃₂	#1181
hypocenter	C₂₉	#1426
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

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
33. C₃₂	#1181	semidirect
34. C₂₉	#1426	semidirect

Maximal subgroups

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

subgroup	index
#14272092	2
#14272090	2
#14270996	2
#1426	29