Subgroups — C₂×C₁₆×Dic₂₉ #16821078

Order 3712.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#90768	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₂₉	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
7	C₂²×#6597	C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₂₉	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
10	C₈×Dic₂₉	C₄	1	2	yes	—
11	C₈×Dic₂₉	C₂²	1	2	yes	—
12	C₂×#90768	C₄	1	4	yes	complemented
13	C₂×#90768	C₂²	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₂₉	C₈	1	2	yes	—
16	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
20	C₄×Dic₂₉	C₈	1	2	yes	—
21	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
22	C₂×#6597	C₈	1	4	yes	—
23	C₂×#6597	C₂×C₄	1	2	yes	—
24	C₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
25	#90768	C₂×C₄	1	4	yes	complemented
26	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₄²	1	2	yes	—
28	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₂₉	C₁₆	1	8	yes	direct product factor
32	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
33	C₈×C₂₉	C₄²	1	2	yes	—
34	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	#6597	C₂×C₈	1	4	yes	—
37	C₂×C₄×C₁₆	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	C₄×C₈	1	2	yes	—
39	C₂²×C₂₉	C₂×C₁₆	1	4	yes	—
40	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₂₉	C₄×C₈	1	2	yes	—
42	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
44	Dic₂₉	C₂×C₁₆	1	8	yes	direct product factor
45	C₂²×C₁₆	—	29	1	no	—
46	C₂²×C₁₆	D₂₉	1	1	yes	characteristic
47	C₂×C₄×C₈	—	29	1	no	—
48	C₄×C₁₆	—	29	4	no	—
49	C₂×C₂₉	C₄×C₁₆	1	4	yes	complemented
50	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₂₉	C₂²×C₁₆	1	2	yes	—
52	C₂²×C₈	—	29	1	no	—
53	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
54	C₂×C₄²	—	29	1	no	—
55	C₂×C₁₆	—	29	4	no	—
56	C₂×C₁₆	—	29	2	no	—
57	C₂×C₁₆	Dic₂₉	1	4	yes	direct product factor
58	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
59	C₄×C₈	—	29	2	no	—
60	C₄×C₈	—	29	2	no	—
61	C₂₉	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	29	2	no	—
63	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
64	C₂×C₈	—	29	4	no	—
65	C₂×C₈	—	29	2	no	—
66	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
67	C₂×C₈	C₄×D₂₉	1	2	yes	—
68	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
69	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
70	C₄²	—	29	2	no	—
71	C₄²	—	29	2	no	—
72	C₁₆	—	29	4	no	—
73	C₁₆	C₂×Dic₂₉	1	4	yes	direct product factor
74	C₂³	C₈×D₂₉	1	1	yes	characteristic
75	C₂×C₄	—	29	8	no	—
76	C₂×C₄	—	29	4	no	—
77	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
78	C₂×C₄	C₈×D₂₉	1	2	yes	—
79	C₂×C₄	C₄×Dic₂₉	1	2	yes	—
80	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
81	C₈	—	29	4	no	—
82	C₈	C₄×Dic₂₉	1	2	yes	—
83	C₈	C₂×C₄×D₂₉	1	1	yes	characteristic
84	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
85	C₂²	C₁₆×D₂₉	1	4	yes	—
86	C₂²	C₈×Dic₂₉	1	2	yes	—
87	C₂²	C₂×C₈×D₂₉	1	1	yes	characteristic
88	C₄	—	29	8	no	—
89	C₄	C₈×Dic₂₉	1	2	yes	—
90	C₄	C₂×C₈×D₂₉	1	1	yes	characteristic
91	C₄	C₂×C₄×Dic₂₉	1	1	yes	characteristic
92	C₂	C₁₆×Dic₂₉	1	4	yes	direct product factor
93	C₂	C₂×C₈×Dic₂₉	1	1	yes	characteristic
94	C₂	C₂×C₁₆×D₂₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₆×Dic₂₉	C₂	direct (N × H)
8. C₂×C₁₆×C₂₉	C₄	semidirect
12. C₂×#90768	C₄	semidirect
24. C₁₆×C₂₉	C₂×C₄	semidirect
25. #90768	C₂×C₄	semidirect
31. C₂×Dic₂₉	C₁₆	direct (N × H)
44. Dic₂₉	C₂×C₁₆	direct (N × H)
49. C₂×C₂₉	C₄×C₁₆	semidirect
57. C₂×C₁₆	Dic₂₉	direct (N × H)
61. C₂₉	C₂×C₄×C₁₆	semidirect
73. C₁₆	C₂×Dic₂₉	direct (N × H)
92. C₂	C₁₆×Dic₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#90768	2
C₂×C₈×Dic₂₉	2
C₁₆×Dic₂₉	2
C₂²×C₁₆×C₂₉	2
C₂×C₄×C₁₆	29

Subgroups — C2×C16×Dic29 #16821078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×Dic₂₉ #16821078