Subgroups — #16817531

Order 3712.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270984	C₂	1	2	yes	maximal
2	C₂₉×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₂₉	—	2	2	no	—
4	C₂₉×C₄⋊Q₈	C₄	1	2	yes	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	#11745160	—	2	2	no	—
7	C₂×Q₈×C₂₉	—	2	2	no	—
8	Q₁₆×C₂₉	—	4	2	no	—
9	Q₁₆×C₂₉	—	4	2	no	—
10	C₂×C₈×C₂₉	D₄	1	2	yes	—
11	C₄⋊C₄×C₂₉	—	4	2	no	—
12	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#90768	—	4	2	no	—
14	Q₈×C₂₉	—	4	4	no	—
15	C₂×C₄×C₂₉	—	2	1	no	—
16	C₂×C₄×C₂₉	—	4	2	no	—
17	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₂₉	D₈	1	2	yes	—
19	C₈×C₂₉	SD₁₆	1	2	yes	—
20	#1358	—	29	1	no	maximal, Sylow
21	C₂²×C₂₉	#100	1	1	yes	characteristic
22	C₄×C₂₉	—	2	2	no	—
23	C₄×C₂₉	—	8	2	no	—
24	C₄×C₂₉	#102	1	2	yes	—
25	#494	D₂₉	1	1	yes	characteristic
26	#364	—	29	2	no	—
27	C₂×C₂₉	—	2	1	no	—
28	C₂×C₂₉	#331	1	1	yes	characteristic
29	C₂×Q₁₆	—	2	2	no	—
30	C₄⋊Q₈	Dic₂₉	1	2	yes	—
31	M₃₂	—	58	2	no	—
32	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
33	C₂₉	#1358	1	1	yes	characteristic, complemented, Sylow
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
40	C₁₆	—	116	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
45	C₈	#90782	1	2	yes	—
46	C₈	#90783	1	2	yes	—
47	C₂²	#11745181	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#11745180	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#14270907	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270907
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#494	C₂
socle	C₂×C₂₉	#331
prime radical	C₂²×C₂₉	#100
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#494	D₂₉
hypocenter	C₂₉	#1358
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
33. C₂₉	#1358	semidirect

Maximal subgroups

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

subgroup	index
#14270984	2
C₂₉×#494	2
#1358	29