Subgroups — #16834641

Order 3712.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272089	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	D₈×D₂₉	—	2	1	no	—
5	#11745210	—	2	1	no	—
6	C₂₉×D₁₆	C₄	1	1	yes	characteristic, complemented
7	#11745174	—	2	1	no	—
8	D₄₆₄	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
10	#11745144	—	2	1	no	—
11	D₄×D₂₉	—	4	1	no	—
12	C₄⋊#1181	—	4	1	no	—
13	D₈×C₂₉	—	2	1	no	—
14	#90782	—	4	1	no	—
15	D₂₃₂	—	2	1	no	—
16	C₈×D₂₉	D₄	1	1	yes	characteristic
17	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90768	D₄	1	1	yes	characteristic
19	C₂²×D₂₉	—	8	1	no	—
20	C₂×#1181	—	8	1	no	—
21	D₄×C₂₉	—	4	1	no	—
22	C₂²⋊D₂₉	—	8	1	no	—
23	D₁₁₆	—	4	1	no	—
24	C₄×D₂₉	D₈	1	1	yes	characteristic
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	#6597	SD₁₆	1	1	yes	characteristic
27	#1415	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	—	8	1	no	—
29	C₂×D₂₉	—	8	1	no	—
30	C₂×D₂₉	—	16	1	no	—
31	C₂×D₂₉	—	16	1	no	—
32	C₂×D₂₉	D₁₆	1	1	yes	characteristic
33	#1181	—	16	1	no	—
34	C₄×C₂₉	#102	1	1	yes	characteristic
35	Dic₂₉	SD₃₂	1	1	yes	characteristic
36	C₂×D₁₆	—	29	1	no	—
37	C₂×C₃₂	—	29	1	no	—
38	#366	—	29	1	no	—
39	C₂×C₂₉	—	16	1	no	—
40	C₂×C₂₉	#357	1	1	yes	characteristic
41	D₂₉	—	16	1	no	—
42	D₂₉	D₃₂	1	1	yes	characteristic
43	D₂₉	SD₆₄	1	1	yes	characteristic
44	C₂×D₈	—	58	1	no	—
45	D₁₆	—	29	1	no	—
46	D₁₆	—	58	1	no	—
47	D₁₆	#1181	1	1	yes	characteristic, complemented
48	C₂×C₁₆	—	29	1	no	—
49	#107	—	58	1	no	—
50	C₃₂	—	58	1	no	—
51	C₂₉	#1415	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₄	—	116	1	no	—
53	D₈	—	2	1	no	—
54	D₈	—	58	1	no	—
55	D₈	—	116	1	no	—
56	C₂×C₈	—	29	1	no	—
57	C₄⋊C₄	—	116	1	no	—
58	C₁₆	—	29	1	no	—
59	C₁₆	C₂×#1181	1	1	yes	characteristic
60	C₂³	—	232	1	no	—
61	D₄	—	4	1	no	—
62	D₄	—	116	1	no	—
63	D₄	—	232	1	no	—
64	C₂×C₄	—	29	1	no	—
65	C₂×C₄	—	232	1	no	—
66	C₈	—	29	1	no	—
67	C₈	C₂²⋊#1181	1	1	yes	characteristic
68	C₂²	—	8	1	no	—
69	C₂²	—	29	1	no	—
70	C₂²	—	464	1	no	—
71	C₂²	—	464	1	no	—
72	C₂²	—	232	1	no	—
73	C₄	—	29	1	no	—
74	C₄	—	464	1	no	—
75	C₄	#11745223	1	1	yes	characteristic
76	C₂	—	16	1	no	—
77	C₂	—	29	1	no	—
78	C₂	—	29	1	no	—
79	C₂	—	464	1	no	—
80	C₂	#14272075	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272075
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₁₆	C₂×#1181
Fitting	C₂₉×D₁₆	C₄
socle	C₂×C₂₉	#357
prime radical	D₁₆×D₂₉	C₂
cosocle	C₁₆×D₂₉	C₂²
hypercenter	D₁₆	#1181
hypocenter	C₂₉	#1415
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₂₉⋊C₃₂	C₂	semidirect
2. #14272089	C₂	semidirect
6. C₂₉×D₁₆	C₄	semidirect
8. D₄₆₄	C₄	semidirect
47. D₁₆	#1181	semidirect
51. C₂₉	#1415	semidirect

Maximal subgroups

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

subgroup	index
D₂₉⋊C₃₂	2
#14272089	2
D₁₆×D₂₉	2
#1415	29