Subgroups — #16817564

Order 3712.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270916	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₄⋊#6597	—	2	2	no	—
7	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
9	C₄²×C₂₉	D₄	1	1	yes	characteristic
10	C₂×#6597	—	4	2	no	—
11	C₁₆×C₂₉	—	2	1	no	—
12	C₁₆×C₂₉	C₈	1	2	yes	complemented
13	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
15	C₂×C₄×C₂₉	Q₁₆	1	1	yes	characteristic
16	C₈×C₂₉	—	2	1	no	—
17	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
18	C₈×C₂₉	M₁₆	1	1	yes	characteristic
19	#6597	—	8	2	no	—
20	#1371	—	29	1	no	maximal, Sylow
21	C₂²×C₂₉	#107	1	1	yes	characteristic
22	C₄×C₂₉	—	2	1	no	—
23	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₂₉	#108	1	1	yes	characteristic
25	C₄×C₂₉	D₁₆	1	1	yes	characteristic
26	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
27	C₄×C₁₆	D₂₉	1	1	yes	characteristic
28	#335	—	29	2	no	—
29	C₂×C₂₉	#335	1	1	yes	characteristic
30	C₂×C₂₉	#366	1	1	yes	characteristic
31	C₂×C₂₉	#368	1	1	yes	characteristic
32	C₂×C₁₆	Dic₂₉	1	1	yes	characteristic
33	C₂×C₁₆	Dic₂₉	1	1	yes	characteristic
34	C₄⋊C₈	—	58	2	no	—
35	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
36	C₂₉	#1371	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₈	—	116	2	no	—
38	C₂×C₈	Dic₅₈	1	1	yes	characteristic
39	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
40	C₄²	D₁₁₆	1	1	yes	characteristic
41	C₁₆	—	2	1	no	—
42	C₁₆	#6597	1	2	yes	complemented
43	C₂×C₄	D₂₃₂	1	1	yes	characteristic
44	C₂×C₄	Dic₁₁₆	1	1	yes	characteristic
45	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
46	C₈	—	2	1	no	—
47	C₈	—	232	2	no	—
48	C₈	C₂×#6597	1	1	yes	characteristic
49	C₈	#90777	1	1	yes	characteristic
50	C₂²	#11745166	1	1	yes	characteristic
51	C₄	—	2	1	no	—
52	C₄	D₄₆₄	1	1	yes	characteristic
53	C₄	Dic₂₃₂	1	1	yes	characteristic
54	C₄	C₄⋊#6597	1	1	yes	characteristic
55	C₄	#11745167	1	1	yes	characteristic
56	C₂	#14270916	1	1	yes	characteristic
57	C₂	#14270989	1	1	yes	characteristic
58	C₂	#14270993	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₃₂
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	#107
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#1371
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₂₉	C₈	semidirect
36. C₂₉	#1371	semidirect
42. C₁₆	#6597	semidirect

Maximal subgroups

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

subgroup	index
#14270916	2
C₄×C₁₆×C₂₉	2
#1371	29