Subgroups — #16834647

Order 3712.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272096	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272092	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	D₈×D₂₉	—	2	1	no	—
5	#11745212	—	2	1	no	—
6	C₂₉×D₁₆	C₄	1	1	yes	characteristic
7	#11745174	—	2	1	no	—
8	D₄₆₄	C₄	1	1	yes	characteristic
9	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
10	#11745144	—	2	1	no	—
11	D₄×D₂₉	—	4	1	no	—
12	#90796	—	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	D₄×C₂₉	—	4	1	no	—
21	C₂²⋊D₂₉	—	8	1	no	—
22	D₁₁₆	—	4	1	no	—
23	C₄×D₂₉	D₈	1	1	yes	characteristic
24	#6599	—	8	1	no	—
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	#6597	SD₁₆	1	1	yes	characteristic
27	#1419	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	—	8	1	no	—
29	C₂×D₂₉	—	8	1	no	—
30	C₂×D₂₉	—	16	2	no	—
31	C₂×D₂₉	SD₃₂	1	1	yes	characteristic
32	C₄×C₂₉	#102	1	1	yes	characteristic
33	Dic₂₉	D₁₆	1	1	yes	characteristic
34	C₂×D₁₆	—	29	1	no	—
35	M₆₄	—	29	1	no	—
36	#368	—	29	1	no	—
37	C₂×C₂₉	—	16	1	no	—
38	C₂×C₂₉	#357	1	1	yes	characteristic
39	D₂₉	—	2	1	no	—
40	D₂₉	—	16	1	no	—
41	C₂×D₈	—	58	1	no	—
42	D₁₆	—	29	1	no	—
43	D₁₆	—	58	1	no	—
44	D₁₆	#1181	1	1	yes	characteristic
45	C₂×C₁₆	—	29	1	no	—
46	#108	—	58	1	no	—
47	C₃₂	—	58	1	no	—
48	C₂₉	#1419	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	116	1	no	—
50	D₈	—	2	1	no	—
51	D₈	—	58	1	no	—
52	D₈	—	116	1	no	—
53	M₁₆	—	116	1	no	—
54	C₂×C₈	—	29	1	no	—
55	C₁₆	—	29	1	no	—
56	C₁₆	C₂×#1181	1	1	yes	characteristic
57	C₂³	—	232	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	116	1	no	—
60	D₄	—	232	1	no	—
61	C₂×C₄	—	29	1	no	—
62	C₈	—	29	1	no	—
63	C₈	—	232	1	no	—
64	C₈	C₂²⋊#1181	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	29	1	no	—
67	C₂²	—	464	2	no	—
68	C₂²	—	232	1	no	—
69	C₄	—	29	1	no	—
70	C₄	#11745223	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	58	1	no	—
73	C₂	—	464	1	no	—
74	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	#1419
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. #14272096	C₂	semidirect
2. #14272092	C₂	semidirect
48. C₂₉	#1419	semidirect

Maximal subgroups

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

subgroup	index
#14272096	2
#14272092	2
D₁₆×D₂₉	2
#1419	29