Subgroups — #16834601

Order 3712.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272096	C₂	1	1	yes	maximal, characteristic
2	#14272050	C₂	1	1	yes	maximal, characteristic
3	#14270996	C₂	1	1	yes	maximal, characteristic
4	C₈×#1181	C₄	1	1	yes	characteristic
5	D₂₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
7	#11745144	C₄	1	2	yes	complemented
8	C₂₉×C₃₂	C₄	1	1	yes	characteristic, complemented
9	#11745142	C₄	1	1	yes	characteristic, complemented
10	C₄×#1181	C₈	1	1	yes	characteristic
11	D₂₉⋊C₈	C₈	1	1	yes	characteristic
12	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
13	#90770	C₈	1	2	yes	—
14	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
15	#90768	C₂×C₄	1	1	yes	characteristic
16	C₂×#1181	—	2	1	no	—
17	C₄×D₂₉	C₂×C₈	1	1	yes	characteristic
18	#6599	—	2	1	no	—
19	C₈×C₂₉	C₄²	1	1	yes	characteristic
20	#6597	C₂×C₈	1	1	yes	characteristic
21	#1398	—	29	1	no	maximal, Sylow
22	C₂×D₂₉	M₃₂	1	1	yes	characteristic
23	#1181	—	4	1	no	—
24	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
25	Dic₂₉	M₃₂	1	1	yes	characteristic
26	M₆₄	—	29	1	no	—
27	M₆₄	—	29	1	no	—
28	#346	—	29	1	no	—
29	C₂×C₂₉	#346	1	1	yes	characteristic
30	D₂₉	—	2	1	no	—
31	C₂×C₁₆	—	29	1	no	—
32	C₂×C₁₆	—	29	1	no	—
33	C₄×C₈	—	29	1	no	—
34	C₃₂	—	29	2	no	—
35	C₃₂	—	29	1	no	—
36	C₃₂	#1181	1	1	yes	characteristic, complemented
37	C₂₉	#1398	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₈	—	29	1	no	—
39	C₂×C₈	—	29	1	no	—
40	C₄²	—	29	1	no	—
41	C₁₆	—	29	2	no	—
42	C₁₆	—	29	1	no	—
43	C₁₆	C₂×#1181	1	1	yes	characteristic
44	C₂×C₄	—	29	1	no	—
45	C₂×C₄	—	58	1	no	—
46	C₈	—	29	1	no	—
47	C₈	—	58	1	no	—
48	C₈	C₄×#1181	1	1	yes	characteristic
49	C₂²	—	29	1	no	—
50	C₄	—	29	1	no	—
51	C₄	—	116	1	no	—
52	C₄	C₈×#1181	1	1	yes	characteristic
53	C₂	—	58	1	no	—
54	C₂	#14272050	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#1181
commutator	C₄×C₂₉	C₄×C₈
Frattini	C₁₆	C₂×#1181
Fitting	C₂₉×C₃₂	C₄
socle	C₂×C₂₉	#346
prime radical	C₂×D₂₉	M₃₂
cosocle	C₁₆×D₂₉	C₂²
hypercenter	C₃₂	#1181
hypocenter	C₂₉	#1398
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #11745144	C₄	semidirect
8. C₂₉×C₃₂	C₄	semidirect
9. #11745142	C₄	semidirect
36. C₃₂	#1181	semidirect
37. C₂₉	#1398	semidirect

Maximal subgroups

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

subgroup	index
#14272096	2
#14272050	2
#14270996	2
#1398	29