Subgroups — #16821720

Order 3712.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271568	C₂	1	1	yes	maximal, characteristic
2	#14271543	C₂	1	1	yes	maximal, characteristic
3	#14270968	C₂	1	4	yes	maximal
4	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₆	—	2	1	no	—
6	C₂×Dic₁₁₆	C₂²	1	2	yes	—
7	#11745231	—	2	1	no	—
8	#11745231	—	2	1	no	—
9	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745166	—	2	1	no	—
12	#11745166	C₂²	1	2	yes	—
13	C₂×Dic₅₈	—	2	2	no	—
14	C₂×Dic₅₈	—	4	1	no	—
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
17	C₄²×C₂₉	D₄	1	1	yes	characteristic
18	C₄⋊Dic₂₉	—	2	2	no	—
19	C₄⋊Dic₂₉	—	4	1	no	—
20	C₄⋊Dic₂₉	—	4	1	no	—
21	C₄⋊Dic₂₉	—	4	1	no	—
22	Dic₁₁₆	—	2	4	no	—
23	Dic₁₁₆	—	4	2	no	—
24	C₁₆×C₂₉	—	2	2	no	—
25	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	2	no	—
29	C₂×Dic₂₉	—	4	2	no	—
30	Dic₅₈	—	4	2	no	—
31	Dic₅₈	—	4	2	no	—
32	Dic₅₈	—	8	2	no	—
33	C₈×C₂₉	SD₁₆	1	2	yes	—
34	C₈×C₂₉	#41	1	2	yes	—
35	#2241	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₂₉	SD₃₂	1	2	yes	—
38	C₄×C₂₉	Q₃₂	1	2	yes	—
39	C₄×C₂₉	#124	1	1	yes	characteristic
40	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₂₉	—	8	2	no	—
42	Dic₂₉	—	8	2	no	—
43	#500	—	29	1	no	—
44	#494	—	29	1	no	—
45	#358	—	29	4	no	—
46	C₄×C₁₆	D₂₉	1	1	yes	characteristic
47	C₂×C₂₉	#486	1	1	yes	characteristic
48	C₂×C₂₉	C₂×SD₃₂	1	1	yes	characteristic
49	C₂×C₂₉	C₂×Q₃₂	1	1	yes	characteristic
50	C₂×Q₁₆	—	29	2	no	—
51	C₂×Q₁₆	—	58	1	no	—
52	C₄⋊Q₈	—	58	1	no	—
53	C₄⋊Q₈	—	58	1	no	—
54	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
55	#107	—	29	2	no	—
56	#107	—	58	1	no	—
57	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
58	C₂₉	#2241	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	58	2	no	—
60	C₂×Q₈	—	116	1	no	—
61	Q₁₆	—	58	4	no	—
62	Q₁₆	—	116	2	no	—
63	C₂×C₈	D₁₁₆	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
65	C₄⋊C₄	—	58	2	no	—
66	C₄⋊C₄	—	116	1	no	—
67	C₄⋊C₄	—	116	1	no	—
68	C₄⋊C₄	—	116	1	no	—
69	C₄²	D₁₁₆	1	1	yes	characteristic
70	C₁₆	—	2	2	no	—
71	Q₈	—	116	2	no	—
72	Q₈	—	116	2	no	—
73	Q₈	—	232	2	no	—
74	C₂×C₄	—	116	2	no	—
75	C₂×C₄	—	116	2	no	—
76	C₂×C₄	D₂₃₂	1	1	yes	characteristic
77	C₂×C₄	D₂₃₂	1	1	yes	characteristic
78	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
79	C₈	#90773	1	2	yes	—
80	C₈	#90805	1	2	yes	—
81	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
82	C₄	—	232	2	no	—
83	C₄	—	232	2	no	—
84	C₄	#11745148	1	2	yes	—
85	C₄	Dic₂₃₂	1	2	yes	—
86	C₄	#11745237	1	1	yes	characteristic
87	C₄	C₂×#90773	1	1	yes	characteristic
88	C₂	#14271510	1	1	yes	characteristic
89	C₂	C₂×#11745148	1	1	yes	characteristic
90	C₂	C₂×Dic₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₂₃₂
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#2241
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
58. C₂₉	#2241	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
#14271543	2
#14270968	2
C₄×C₁₆×C₂₉	2
#2241	29