Subgroups — #16819248

Order 3712.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271121	C₂	1	3	yes	maximal
2	#14270920	C₂	1	3	yes	maximal
3	C₂₉×#338	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₉	C₂²	1	3	yes	—
5	#11745288	C₂²	1	3	yes	—
6	C₂²×#6597	C₂²	1	1	yes	characteristic
7	#11745163	C₄	1	6	yes	complemented
8	C₈×Dic₂₉	C₄	1	6	yes	complemented
9	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
10	M₁₆×C₂₉	—	2	6	no	—
11	C₂×C₈×C₂₉	C₂×C₄	1	6	yes	—
12	C₂²⋊Dic₂₉	—	2	3	no	—
13	C₄⋊Dic₂₉	—	2	3	no	—
14	C₄×Dic₂₉	C₂×C₄	1	6	yes	—
15	C₂×#6597	C₂×C₄	1	3	yes	—
16	C₂×#6597	C₂×C₄	1	3	yes	—
17	C₂³×C₂₉	#41	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₂₉	#41	1	3	yes	—
20	C₂×Dic₂₉	—	2	6	no	—
21	C₈×C₂₉	—	2	6	no	—
22	#6597	C₄²	1	1	yes	characteristic
23	#6597	C₄²	1	3	yes	—
24	#1747	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	—	4	1	no	—
26	C₂²×C₂₉	#117	1	3	yes	—
27	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
28	C₄×C₂₉	#117	1	3	yes	—
29	Dic₂₉	—	4	6	no	—
30	#405	—	29	3	no	—
31	#338	D₂₉	1	1	yes	characteristic
32	H(3,ℤ/4)	—	29	3	no	—
33	C₂×C₂₉	—	2	3	no	—
34	C₂×C₂₉	#376	1	1	yes	characteristic
35	C₂×M₁₆	C₂×D₂₉	1	3	yes	—
36	C₂²×C₈	—	29	1	no	—
37	#117	—	29	3	no	—
38	#97	—	29	6	no	—
39	C₄×C₈	—	29	6	no	—
40	C₂₉	#1747	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	29	3	no	—
44	C₂×C₈	—	29	3	no	—
45	C₂×C₈	C₄×D₂₉	1	6	yes	—
46	C₄⋊C₄	—	58	3	no	—
47	C₂²⋊C₄	—	58	3	no	—
48	C₄²	—	29	6	no	—
49	C₂³	#90809	1	1	yes	characteristic
50	C₂×C₄	—	58	6	no	—
51	C₂×C₄	C₂×C₄×D₂₉	1	3	yes	—
52	C₂×C₄	#90807	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	29	1	no	—
55	C₈	—	29	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#11745254	1	3	yes	—
58	C₄	—	116	6	no	—
59	C₄	C₄²×D₂₉	1	1	yes	characteristic
60	C₄	#11745239	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#14271008	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#338	C₂
socle	C₂×C₂₉	#376
prime radical	C₂³×C₂₉	#41
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#338	D₂₉
hypocenter	C₂₉	#1747
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
7. #11745163	C₄	semidirect
8. C₈×Dic₂₉	C₄	semidirect
40. C₂₉	#1747	semidirect

Maximal subgroups

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

subgroup	index
#14271121	2
#14270920	2
C₂₉×#338	2
#1747	29