Subgroups — #16817687

Order 3712.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745142	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₈×Dic₂₉	C₄	1	1	yes	characteristic
6	C₂×#90768	C₄	1	1	yes	characteristic
7	C₂₉×C₃₂	—	2	1	no	—
8	#11745142	—	2	1	no	—
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₂₉	C₈	1	1	yes	characteristic
11	C₂×#6597	C₈	1	1	yes	characteristic
12	C₁₆×C₂₉	D₄	1	1	yes	characteristic
13	C₁₆×C₂₉	Q₈	1	1	yes	characteristic
14	#90768	—	2	1	no	—
15	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
17	C₂×Dic₂₉	C₁₆	1	1	yes	characteristic
18	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₂₉	M₁₆	1	1	yes	characteristic
20	#6597	—	2	1	no	—
21	C₄⋊C₃₂	—	29	1	no	maximal, Sylow
22	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
23	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₂₉	M₃₂	1	1	yes	characteristic
25	Dic₂₉	—	2	1	no	—
26	Dic₂₉	C₃₂	1	2	yes	complemented
27	C₂×C₃₂	—	29	1	no	—
28	C₂×C₃₂	D₂₉	1	1	yes	characteristic
29	C₄×C₁₆	—	29	1	no	—
30	C₂×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂×C₂₉	C₂×C₃₂	1	1	yes	characteristic
32	C₂×C₂₉	M₆₄	1	1	yes	characteristic
33	C₂×C₁₆	—	29	1	no	—
34	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
35	C₄×C₈	—	29	1	no	—
36	C₃₂	—	2	1	no	—
37	C₃₂	—	58	1	no	—
38	C₂₉	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₈	—	29	1	no	—
40	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
41	C₄²	—	29	1	no	—
42	C₁₆	—	58	1	no	—
43	C₁₆	Dic₅₈	1	1	yes	characteristic
44	C₁₆	C₂²⋊D₂₉	1	1	yes	characteristic
45	C₂×C₄	—	29	1	no	—
46	C₂×C₄	—	29	1	no	—
47	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
48	C₈	—	58	1	no	—
49	C₈	#90772	1	1	yes	characteristic
50	C₈	#90779	1	1	yes	characteristic
51	C₂²	C₁₆×D₂₉	1	1	yes	characteristic
52	C₄	—	29	2	no	—
53	C₄	—	58	1	no	—
54	C₄	#11745146	1	1	yes	characteristic
55	C₄	#11745162	1	1	yes	characteristic
56	C₂	#14270981	1	1	yes	characteristic
57	C₂	C₃₂×D₂₉	1	1	yes	characteristic
58	C₂	#14270996	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₃₂
Fitting	C₂×C₂₉×C₃₂	C₂
socle, prime radical	C₂²×C₂₉	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	C₂×C₃₂	D₂₉
hypocenter	C₂₉	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
26. Dic₂₉	C₃₂	semidirect
38. 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×#11745142	2
C₁₆×Dic₂₉	2
C₂×C₂₉×C₃₂	2
C₄⋊C₃₂	29