Subgroups — #16834524

Order 3712.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272026	C₂	1	2	yes	maximal
2	C₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#6599	—	2	2	no	—
4	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
5	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90768	C₄	1	1	yes	characteristic
7	C₂×#6599	—	4	2	no	—
8	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₄×Dic₂₉	D₄	1	1	yes	characteristic
10	C₂×#6597	Q₈	1	1	yes	characteristic
11	C₁₆×C₂₉	—	2	1	no	—
12	#90768	C₈	1	2	yes	complemented
13	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₂₉	D₈	1	1	yes	characteristic
15	C₂×Dic₂₉	Q₁₆	1	1	yes	characteristic
16	#6599	—	8	2	no	—
17	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
18	C₈×C₂₉	M₁₆	1	1	yes	characteristic
19	#6597	—	2	1	no	—
20	#1371	—	29	1	no	maximal, Sylow
21	C₂²×C₂₉	#107	1	1	yes	characteristic
22	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₂₉	#108	1	1	yes	characteristic
24	Dic₂₉	—	2	1	no	—
25	Dic₂₉	D₁₆	1	1	yes	characteristic
26	Dic₂₉	Q₃₂	1	1	yes	characteristic
27	C₄×C₁₆	—	29	1	no	—
28	#335	—	29	2	no	—
29	C₂×C₂₉	#335	1	1	yes	characteristic
30	C₂×C₂₉	#366	1	1	yes	characteristic
31	C₂×C₂₉	#368	1	1	yes	characteristic
32	C₂×C₁₆	—	29	1	no	—
33	C₂×C₁₆	#1181	1	1	yes	characteristic
34	C₄⋊C₈	—	58	2	no	—
35	C₄×C₈	—	29	1	no	—
36	C₂₉	#1371	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₈	—	29	1	no	—
38	C₂×C₈	—	116	2	no	—
39	C₂×C₈	C₂×#1181	1	1	yes	characteristic
40	C₄²	—	29	1	no	—
41	C₁₆	—	2	1	no	—
42	C₁₆	—	29	2	no	—
43	C₂×C₄	—	29	1	no	—
44	C₂×C₄	—	29	1	no	—
45	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
46	C₈	—	58	1	no	—
47	C₈	—	232	2	no	—
48	C₈	D₂₉⋊C₈	1	1	yes	characteristic
49	C₈	#90800	1	1	yes	characteristic
50	C₂²	#11745210	1	1	yes	characteristic
51	C₄	—	29	1	no	—
52	C₄	—	29	1	no	—
53	C₄	—	58	1	no	—
54	C₄	#11745211	1	1	yes	characteristic
55	C₄	#11745220	1	1	yes	characteristic
56	C₂	#14272027	1	1	yes	characteristic
57	C₂	#14272089	1	1	yes	characteristic
58	C₂	#14272092	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745210
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×C₁₆×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	#107
cosocle	C₈×Dic₂₉	C₂²
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	#1371
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. #90768	C₈	semidirect
36. C₂₉	#1371	semidirect

Maximal subgroups

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

subgroup	index
#14272026	2
C₁₆×Dic₂₉	2
#1371	29