Subgroups — #16817529

Order 3712.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270984	C₂	1	2	yes	maximal, complemented
2	C₂₉×#493	C₂	1	1	yes	maximal, characteristic
3	C₂×D₈×C₂₉	—	2	2	no	—
4	C₂₉×#127	C₄	1	2	yes	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	#11745160	—	2	2	no	—
7	C₂×D₄×C₂₉	—	2	2	no	—
8	C₂×D₄×C₂₉	—	4	2	no	—
9	D₈×C₂₉	—	4	2	no	—
10	D₈×C₂₉	—	4	2	no	—
11	C₂×C₈×C₂₉	D₄	1	2	yes	—
12	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#90768	—	4	2	no	—
14	C₂³×C₂₉	—	4	2	no	—
15	D₄×C₂₉	—	4	4	no	—
16	D₄×C₂₉	—	8	4	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₈×C₂₉	D₈	1	2	yes	—
20	C₈×C₂₉	SD₁₆	1	2	yes	—
21	#1357	—	29	1	no	maximal, Sylow
22	C₂²×C₂₉	—	8	4	no	—
23	C₂²×C₂₉	—	8	2	no	—
24	C₂²×C₂₉	#100	1	1	yes	characteristic
25	C₄×C₂₉	—	2	2	no	—
26	C₄×C₂₉	#102	1	2	yes	—
27	#493	D₂₉	1	1	yes	characteristic
28	#364	—	29	2	no	—
29	C₂×C₂₉	—	2	1	no	—
30	C₂×C₂₉	—	16	2	no	—
31	C₂×C₂₉	#331	1	1	yes	characteristic
32	C₂×D₈	—	2	2	no	—
33	#127	Dic₂₉	1	2	yes	—
34	M₃₂	—	58	2	no	—
35	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
36	C₂₉	#1357	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₄	—	2	2	no	—
38	C₂×D₄	—	4	2	no	—
39	D₈	—	4	2	no	—
40	D₈	—	4	2	no	—
41	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
42	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
43	C₁₆	—	116	2	no	—
44	C₂³	—	4	2	no	—
45	D₄	—	4	4	no	—
46	D₄	—	8	4	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
49	C₈	#90782	1	2	yes	—
50	C₈	#90783	1	2	yes	—
51	C₂²	—	8	4	no	—
52	C₂²	—	8	2	no	—
53	C₂²	#11745181	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#11745180	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	16	2	no	—
58	C₂	#14270907	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270907
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting, prime radical	C₂₉×#493	C₂
socle	C₂×C₂₉	#331
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#493	D₂₉
hypocenter	C₂₉	#1357
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. #14270984	C₂	semidirect
36. C₂₉	#1357	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×#493	2
#1357	29