Subgroups — #106×D₂₉ #14271192

Order 1856.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₂₉	C₂	1	2	yes	maximal
3	C₂₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745165	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745156	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₂₉	—	2	2	no	—
7	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	C₄⋊Dic₂₉	C₂²	1	2	yes	—
11	#90779	—	2	2	no	—
12	C₂×#6597	C₂²	1	1	yes	characteristic
13	C₈×D₂₉	C₄	1	4	yes	complemented
14	C₂²×D₂₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	—	2	2	no	—
16	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₉	—	2	2	no	—
18	C₂×Dic₂₉	D₄	1	1	yes	characteristic
19	C₄×D₂₉	—	4	4	no	—
20	C₄×D₂₉	C₂×C₄	1	2	yes	—
21	C₄×D₂₉	Q₈	1	2	yes	—
22	C₈×C₂₉	C₂×C₄	1	2	yes	complemented
23	#6597	C₂×C₄	1	2	yes	complemented
24	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
25	C₂×D₂₉	C₄⋊C₄	1	2	yes	—
26	C₂×D₂₉	SD₁₆	1	4	yes	—
27	C₄×C₂₉	—	4	2	no	—
28	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
30	Dic₂₉	—	4	2	no	—
31	Dic₂₉	C₄⋊C₄	1	2	yes	—
32	C₂×#106	—	29	1	no	maximal, Sylow
33	C₂×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₂₉	C₂×SD₁₆	1	2	yes	—
35	D₂₉	#106	1	4	yes	direct product factor
36	C₂²×C₈	—	29	1	no	—
37	C₂×C₄⋊C₄	—	29	2	no	—
38	#106	—	29	1	no	—
39	#106	—	29	2	no	—
40	#106	D₂₉	1	1	yes	characteristic, direct product factor
41	C₂₉	C₂×#106	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄	—	29	1	no	—
43	C₂²×C₄	—	58	2	no	—
44	C₂×C₈	—	29	1	no	—
45	C₂×C₈	—	29	4	no	—
46	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
47	C₄⋊C₄	—	29	2	no	—
48	C₄⋊C₄	—	58	2	no	—
49	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
50	C₂³	—	29	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	29	1	no	—
53	C₂×C₄	—	29	2	no	—
54	C₂×C₄	—	29	2	no	—
55	C₂×C₄	—	58	2	no	—
56	C₂×C₄	—	116	4	no	—
57	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
58	C₈	—	29	2	no	—
59	C₈	C₄×D₂₉	1	2	yes	complemented
60	C₂²	—	29	2	no	—
61	C₂²	—	29	4	no	—
62	C₂²	D₄×D₂₉	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	—	29	2	no	—
65	C₄	—	116	2	no	—
66	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
67	C₄	Q₈×D₂₉	1	1	yes	characteristic
68	C₂	—	29	4	no	—
69	C₂	C₄⋊C₄×D₂₉	1	1	yes	characteristic
70	C₂	SD₁₆×D₂₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#106	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂²×D₂₉	D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#106	D₂₉
hypocenter	C₂₉	C₂×#106
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. C₂₉×#106	C₂	semidirect
4. #11745165	C₂	semidirect
5. #11745156	C₂	semidirect
13. C₈×D₂₉	C₄	semidirect
22. C₈×C₂₉	C₂×C₄	semidirect
23. #6597	C₂×C₄	semidirect
35. D₂₉	#106	direct (N × H)
40. #106	D₂₉	direct (N × H)
41. C₂₉	C₂×#106	semidirect
59. C₈	C₄×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₂₉	2
C₄⋊C₄×D₂₉	2
C₂₉×#106	2
#11745165	2
#11745156	2
C₂×#106	29

Subgroups — #106×D29 #14271192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #106×D₂₉ #14271192