Subgroups — #16834651

Order 3712.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272095	C₂	1	2	yes	maximal
2	C₄×#90768	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
4	C₂×#90768	C₄	1	1	yes	characteristic
5	C₂×#90768	C₂²	1	1	yes	characteristic
6	#11745144	—	2	2	no	—
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	#90768	—	2	1	no	—
11	#90768	D₄	1	1	yes	characteristic
12	#90768	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₉	—	2	1	no	—
14	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
15	C₈×C₂₉	C₁₆	1	2	yes	—
16	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₉	M₁₆	1	1	yes	characteristic
18	#1422	—	29	1	no	maximal, Sylow
19	C₂²×C₂₉	M₃₂	1	1	yes	characteristic
20	C₄×C₂₉	—	2	2	no	—
21	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
23	M₆₄	—	29	2	no	—
24	C₄×C₁₆	—	29	1	no	—
25	C₂×C₂₉	—	2	1	no	—
26	C₂×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₁₆	—	29	1	no	—
28	C₂×C₁₆	—	29	1	no	—
29	C₄×C₈	#1181	1	1	yes	characteristic
30	C₃₂	—	58	2	no	—
31	C₂₉	#1422	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	#6599	1	1	yes	characteristic
33	C₂×C₈	C₂×#1181	1	1	yes	characteristic
34	C₄²	#6599	1	1	yes	characteristic
35	C₁₆	—	29	1	no	—
36	C₁₆	—	29	1	no	—
37	C₁₆	—	58	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×#6599	1	1	yes	characteristic
40	C₈	#90770	1	2	yes	—
41	C₈	#90796	1	1	yes	characteristic
42	C₈	C₄⋊#1181	1	1	yes	characteristic
43	C₂²	#11745214	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₂×#90770	1	1	yes	characteristic
46	C₄	C₄⋊#6599	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊#90770	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄⋊#1181
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₂×C₈	C₂×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂×C₂₉	C₄⋊C₁₆
prime radical	C₂²×C₂₉	M₃₂
cosocle	C₂×#90768	C₂²
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1422
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
31. C₂₉	#1422	semidirect

Maximal subgroups

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

subgroup	index
#14272095	2
C₄×#90768	2
#1422	29