Subgroups — #16835915

Order 3712.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272095	C₂	1	3	yes	maximal, complemented
2	C₂×#11745144	C₂	1	3	yes	maximal, complemented
3	#14271580	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#131	C₄	1	1	yes	characteristic
5	#11745160	C₄	1	3	yes	—
6	C₂×#90768	C₂²	1	3	yes	—
7	#11745144	C₂²	1	1	yes	characteristic
8	#11745144	C₂²	1	3	yes	—
9	#41×C₂₉	C₈	1	1	yes	characteristic
10	M₁₆×C₂₉	C₈	1	3	yes	—
11	C₂×C₈×C₂₉	C₂×C₄	1	3	yes	—
12	#90768	C₂×C₄	1	3	yes	—
13	#90768	C₂³	1	1	yes	characteristic
14	Q₈×C₂₉	C₁₆	1	1	yes	characteristic
15	D₄×C₂₉	C₁₆	1	3	yes	—
16	C₂×C₄×C₂₉	C₂×C₈	1	3	yes	—
17	C₈×C₂₉	C₂×C₈	1	3	yes	—
18	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
19	#2258	—	29	1	no	maximal, Sylow
20	C₂²×C₂₉	C₂×C₁₆	1	3	yes	—
21	C₄×C₂₉	C₂×C₁₆	1	3	yes	—
22	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
23	#504	—	29	1	no	—
24	M₆₄	—	29	3	no	—
25	C₂×C₃₂	—	29	3	no	—
26	C₂×C₂₉	—	2	3	no	—
27	C₂×C₂₉	C₂²×C₁₆	1	1	yes	characteristic
28	#131	#1181	1	1	yes	characteristic
29	M₃₂	—	29	3	no	—
30	C₂×C₁₆	—	29	3	no	—
31	C₃₂	—	29	1	no	—
32	C₃₂	—	29	3	no	—
33	C₂₉	#2258	1	1	yes	characteristic, complemented, Sylow
34	#41	#6599	1	1	yes	characteristic
35	M₁₆	#6599	1	3	yes	—
36	C₂×C₈	C₂×#1181	1	3	yes	—
37	C₁₆	—	29	1	no	—
38	C₁₆	—	29	3	no	—
39	Q₈	#90770	1	1	yes	characteristic
40	D₄	#90770	1	3	yes	—
41	C₂×C₄	C₂×#6599	1	3	yes	—
42	C₈	C₂×#6599	1	3	yes	—
43	C₈	C₂²×#1181	1	1	yes	characteristic
44	C₂²	C₂×#90770	1	3	yes	—
45	C₄	C₂×#90770	1	3	yes	—
46	C₄	C₂²×#6599	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#90770	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#1181
commutator, socle	C₂×C₂₉	C₂²×C₁₆
Fitting	C₂₉×#131	C₄
prime radical	#41×C₂₉	C₈
cosocle	#90768	C₂³
hypercenter	#131	#1181
hypocenter	C₂₉	#2258
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #14272095	C₂	semidirect
2. C₂×#11745144	C₂	semidirect
33. C₂₉	#2258	semidirect

Maximal subgroups

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

subgroup	index
#14272095	2
C₂×#11745144	2
#14271580	2
#2258	29