Subgroups — #16817626

Order 3712.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745142	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	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
6	#11745142	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₉	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₉	C₈	1	1	yes	characteristic
10	C₁₆×C₂₉	C₈	1	2	yes	—
11	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₉	C₁₆	1	2	yes	—
13	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
14	C₈×C₂₉	C₁₆	1	2	yes	—
15	C₈×C₂₉	C₄²	1	1	yes	characteristic
16	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
17	#1397	—	29	1	no	maximal, Sylow
18	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
19	C₄×C₂₉	—	2	2	no	—
20	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
21	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₃₂	—	29	2	no	—
23	C₄×C₁₆	D₂₉	1	1	yes	characteristic
24	C₂×C₂₉	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₂₉	M₆₄	1	2	yes	—
26	C₂×C₁₆	Dic₂₉	1	1	yes	characteristic
27	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
28	C₄×C₈	Dic₂₉	1	1	yes	characteristic
29	C₃₂	—	29	4	no	—
30	C₂₉	#1397	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	#6597	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
33	C₄²	#6597	1	1	yes	characteristic
34	C₁₆	#6597	1	2	yes	—
35	C₁₆	C₄×D₂₉	1	2	yes	—
36	C₂×C₄	#90768	1	2	yes	—
37	C₂×C₄	C₂×#6597	1	1	yes	characteristic
38	C₈	#90768	1	2	yes	—
39	C₈	C₂×#6597	1	1	yes	characteristic
40	C₈	C₄×Dic₂₉	1	1	yes	characteristic
41	C₂²	C₂×#90768	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₄×#6597	1	1	yes	characteristic
44	C₄	C₂×#90768	1	1	yes	characteristic
45	C₂	C₄×#90768	1	1	yes	characteristic
46	C₂	#14270997	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₉
commutator	C₂×C₂₉	C₄×C₁₆
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#1397
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
6. #11745142	C₄	semidirect
30. C₂₉	#1397	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745142	2
C₄×C₁₆×C₂₉	2
#1397	29