Subgroups — M₁₆×Dic₂₉ #14271114

Order 1856.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#90777	C₂	1	1	yes	maximal, characteristic
4	#11745163	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₂₉	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₉	C₄	1	2	yes	—
8	M₁₆×C₂₉	C₄	1	4	yes	complemented
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄×Dic₂₉	C₄	1	2	yes	—
11	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	#90777	C₄	1	4	yes	complemented
14	C₂×#6597	C₂²	1	2	yes	—
15	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₉	—	2	4	no	—
21	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
22	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
23	C₈×C₂₉	C₂×C₄	1	4	yes	complemented
24	#6597	C₂×C₄	1	4	yes	complemented
25	C₂²×C₂₉	—	2	2	no	—
26	C₂²×C₂₉	C₄²	1	2	yes	—
27	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₉	C₄²	1	2	yes	—
29	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	Dic₂₉	—	2	2	no	—
32	Dic₂₉	M₁₆	1	4	yes	direct product factor
33	C₄×M₁₆	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	—	2	2	no	—
35	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₂₉	C₂×M₁₆	1	2	yes	—
37	C₂×M₁₆	—	29	1	no	—
38	C₂×M₁₆	D₂₉	1	1	yes	characteristic
39	C₂×C₄²	—	29	1	no	—
40	#97	—	29	2	no	—
41	C₄×C₈	—	29	2	no	—
42	C₂₉	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	29	2	no	—
44	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
45	M₁₆	—	29	4	no	—
46	M₁₆	Dic₂₉	1	4	yes	direct product factor
47	C₂×C₈	—	29	2	no	—
48	C₂×C₈	C₂×D₂₉	1	2	yes	—
49	C₄²	—	29	2	no	—
50	C₄²	—	29	1	no	—
51	C₄²	—	29	1	no	—
52	C₂³	C₄×D₂₉	1	1	yes	characteristic
53	C₂×C₄	—	29	2	no	—
54	C₂×C₄	—	29	2	no	—
55	C₂×C₄	—	58	4	no	—
56	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
57	C₂×C₄	C₄×D₂₉	1	2	yes	—
58	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
59	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
60	C₈	—	29	4	no	—
61	C₈	C₂×Dic₂₉	1	4	yes	complemented
62	C₂²	—	2	2	no	—
63	C₂²	C₄×Dic₂₉	1	2	yes	—
64	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
65	C₄	—	29	4	no	—
66	C₄	—	58	2	no	—
67	C₄	C₄×Dic₂₉	1	2	yes	—
68	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
69	C₄	C₂²×Dic₂₉	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	M₁₆×D₂₉	1	2	yes	—
72	C₂	C₂×C₄×Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂×C₄²
Fitting	C₂×M₁₆×C₂₉	C₂
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₂×M₁₆	D₂₉
hypocenter	C₂₉	C₄×M₁₆
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11745163	C₂	semidirect
5. C₈×Dic₂₉	C₂	semidirect
8. M₁₆×C₂₉	C₄	semidirect
13. #90777	C₄	semidirect
23. C₈×C₂₉	C₂×C₄	semidirect
24. #6597	C₂×C₄	semidirect
32. Dic₂₉	M₁₆	direct (N × H)
42. C₂₉	C₄×M₁₆	semidirect
46. M₁₆	Dic₂₉	direct (N × H)
61. C₈	C₂×Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₉	2
C₂×C₄×Dic₂₉	2
C₂×#90777	2
#11745163	2
C₈×Dic₂₉	2
C₄×M₁₆	29

Subgroups — M16×Dic29 #14271114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×Dic₂₉ #14271114