Subgroups — #16834648

Order 3712.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272096	C₂	1	1	yes	maximal, characteristic
2	#14272092	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₂₉	C₂	1	1	yes	maximal, characteristic
4	Q₁₆×D₂₉	—	2	1	no	—
5	#11745212	—	2	1	no	—
6	C₂₉×Q₃₂	C₄	1	1	yes	characteristic
7	#11745177	—	2	1	no	—
8	Dic₂₃₂	C₄	1	1	yes	characteristic
9	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
10	#11745144	—	2	1	no	—
11	Q₈×D₂₉	—	4	1	no	—
12	#90796	—	4	1	no	—
13	Q₁₆×C₂₉	—	2	1	no	—
14	#90785	—	4	1	no	—
15	Dic₁₁₆	—	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	Q₈×C₂₉	—	4	1	no	—
20	C₄×D₂₉	—	8	1	no	—
21	C₄×D₂₉	D₈	1	1	yes	characteristic
22	Dic₅₈	—	4	1	no	—
23	Dic₅₈	—	8	1	no	—
24	#6599	—	8	1	no	—
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	#6597	SD₁₆	1	1	yes	characteristic
27	#1420	—	29	1	no	maximal, Sylow
28	C₂×D₂₉	SD₃₂	1	1	yes	characteristic
29	C₄×C₂₉	—	8	1	no	—
30	C₄×C₂₉	#102	1	1	yes	characteristic
31	Dic₂₉	—	8	1	no	—
32	Dic₂₉	D₁₆	1	1	yes	characteristic
33	C₂×Q₃₂	—	29	1	no	—
34	M₆₄	—	29	1	no	—
35	#368	—	29	1	no	—
36	C₂×C₂₉	#357	1	1	yes	characteristic
37	D₂₉	—	2	1	no	—
38	C₂×Q₁₆	—	58	1	no	—
39	Q₃₂	—	29	1	no	—
40	Q₃₂	—	58	1	no	—
41	Q₃₂	#1181	1	1	yes	characteristic
42	C₂×C₁₆	—	29	1	no	—
43	#108	—	58	1	no	—
44	C₃₂	—	58	1	no	—
45	C₂₉	#1420	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₈	—	116	1	no	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	58	1	no	—
49	Q₁₆	—	116	1	no	—
50	M₁₆	—	116	1	no	—
51	C₂×C₈	—	29	1	no	—
52	C₁₆	—	29	1	no	—
53	C₁₆	C₂×#1181	1	1	yes	characteristic
54	Q₈	—	4	1	no	—
55	Q₈	—	116	1	no	—
56	Q₈	—	232	1	no	—
57	C₂×C₄	—	29	1	no	—
58	C₂×C₄	—	232	1	no	—
59	C₈	—	29	1	no	—
60	C₈	—	232	1	no	—
61	C₈	C₂²⋊#1181	1	1	yes	characteristic
62	C₂²	—	29	1	no	—
63	C₄	—	8	1	no	—
64	C₄	—	29	1	no	—
65	C₄	—	232	1	no	—
66	C₄	#11745223	1	1	yes	characteristic
67	C₂	—	58	1	no	—
68	C₂	#14272075	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272075
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₁₆	C₂×#1181
Fitting	C₂₉×Q₃₂	C₄
socle	C₂×C₂₉	#357
prime radical	C₂×D₂₉	SD₃₂
cosocle	C₁₆×D₂₉	C₂²
hypercenter	Q₃₂	#1181
hypocenter	C₂₉	#1420
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
45. C₂₉	#1420	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
Q₃₂×D₂₉	2
#1420	29