Subgroups — #16821774

Order 3712.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271568	C₂	1	2	yes	maximal
2	#14270991	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	#11745231	—	2	2	no	—
5	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#11745166	—	2	2	no	—
8	#11745166	C₂²	1	4	yes	—
9	C₂×Dic₅₈	—	4	2	no	—
10	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
12	C₄²×C₂₉	D₄	1	1	yes	characteristic
13	C₄⋊Dic₂₉	—	2	4	no	—
14	C₄⋊Dic₂₉	—	4	2	no	—
15	C₁₆×C₂₉	Q₈	1	4	yes	complemented
16	C₂×C₄×C₂₉	D₈	1	2	yes	—
17	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
18	C₂×Dic₂₉	—	4	4	no	—
19	Dic₅₈	—	8	4	no	—
20	C₈×C₂₉	Q₁₆	1	2	yes	—
21	C₈×C₂₉	C₂×Q₈	1	2	yes	—
22	#2254	—	29	1	no	maximal, Sylow
23	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
24	C₄×C₂₉	SD₃₂	1	4	yes	—
25	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
26	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
27	Dic₂₉	—	8	4	no	—
28	#500	—	29	2	no	—
29	#367	—	29	4	no	—
30	C₄×C₁₆	D₂₉	1	1	yes	characteristic
31	C₂×C₂₉	#500	1	1	yes	characteristic
32	C₂×C₂₉	C₂×SD₃₂	1	2	yes	—
33	C₄⋊Q₈	—	58	2	no	—
34	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
35	#107	—	29	4	no	—
36	#107	—	58	2	no	—
37	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
38	C₂₉	#2254	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	116	2	no	—
40	C₂×C₈	D₁₁₆	1	1	yes	characteristic
41	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
42	C₄⋊C₄	—	58	4	no	—
43	C₄⋊C₄	—	116	2	no	—
44	C₄²	D₁₁₆	1	1	yes	characteristic
45	C₁₆	Dic₅₈	1	4	yes	complemented
46	Q₈	—	232	4	no	—
47	C₂×C₄	—	116	4	no	—
48	C₂×C₄	D₂₃₂	1	2	yes	—
49	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
50	C₈	Dic₁₁₆	1	2	yes	—
51	C₈	C₂×Dic₅₈	1	2	yes	—
52	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
53	C₄	—	232	4	no	—
54	C₄	#11745148	1	4	yes	—
55	C₄	#11745231	1	1	yes	characteristic
56	C₄	C₂×Dic₁₁₆	1	1	yes	characteristic
57	C₂	#14271568	1	1	yes	characteristic
58	C₂	C₂×#11745148	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₃₂
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#2254
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₂₉	Q₈	semidirect
38. C₂₉	#2254	semidirect
45. C₁₆	Dic₅₈	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
#14270991	2
C₄×C₁₆×C₂₉	2
#2254	29