Subgroups — #16834650

Order 3712.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745144	C₂	1	2	yes	maximal
2	C₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
4	C₈×Dic₂₉	C₄	1	1	yes	characteristic
5	C₂×#90768	C₂²	1	1	yes	characteristic
6	#11745144	—	2	2	no	—
7	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₂₉	C₈	1	1	yes	characteristic
9	C₂×#6597	C₈	1	1	yes	characteristic
10	C₁₆×C₂₉	—	2	1	no	—
11	#90768	D₄	1	1	yes	characteristic
12	#90768	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
15	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
16	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₉	M₁₆	1	1	yes	characteristic
18	#6597	—	2	1	no	—
19	C₄⋊C₃₂	—	29	1	no	maximal, Sylow
20	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₂₉	M₃₂	1	1	yes	characteristic
23	Dic₂₉	—	2	1	no	—
24	Dic₂₉	C₃₂	1	2	yes	complemented
25	C₂×C₃₂	—	29	2	no	—
26	C₄×C₁₆	—	29	1	no	—
27	C₂×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
28	C₂×C₂₉	C₂×C₃₂	1	1	yes	characteristic
29	C₂×C₂₉	M₆₄	1	1	yes	characteristic
30	C₂×C₁₆	—	29	1	no	—
31	C₂×C₁₆	#1181	1	1	yes	characteristic
32	C₄×C₈	—	29	1	no	—
33	C₃₂	—	58	2	no	—
34	C₂₉	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₈	—	29	1	no	—
36	C₂×C₈	C₂×#1181	1	1	yes	characteristic
37	C₄²	—	29	1	no	—
38	C₁₆	—	2	1	no	—
39	C₁₆	—	29	1	no	—
40	C₁₆	—	29	1	no	—
41	C₂×C₄	—	29	1	no	—
42	C₂×C₄	—	29	1	no	—
43	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
44	C₈	—	58	1	no	—
45	C₈	C₄⋊#1181	1	1	yes	characteristic
46	C₈	#90800	1	1	yes	characteristic
47	C₂²	D₂₉⋊C₁₆	1	1	yes	characteristic
48	C₄	—	29	2	no	—
49	C₄	—	58	1	no	—
50	C₄	#11745206	1	1	yes	characteristic
51	C₄	#11745220	1	1	yes	characteristic
52	C₂	#14272084	1	1	yes	characteristic
53	C₂	D₂₉⋊C₃₂	1	1	yes	characteristic
54	C₂	#14272096	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#1181
commutator	C₂×C₂₉	C₂×C₃₂
Fitting	C₂×C₁₆×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	C₂×C₁₆
cosocle	C₂×#90768	C₂²
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
24. Dic₂₉	C₃₂	semidirect
34. C₂₉	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745144	2
C₁₆×Dic₂₉	2
C₄⋊C₃₂	29