Subgroups — C₂₉×#1711 #16815425

Order 3712.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#487	C₂	1	3	yes	maximal, complemented
2	C₂₉×#486	C₂	1	3	yes	maximal
3	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×C₄⋊Q₈	C₂²	1	3	yes	—
5	C₂₉×#127	C₂²	1	1	yes	characteristic
6	C₂₉×#103	—	2	6	no	—
7	C₂₉×#102	—	2	6	no	—
8	C₄×C₈×C₂₉	C₂²	1	3	yes	—
9	C₂×Q₈×C₂₉	—	2	3	no	—
10	C₂×D₄×C₂₉	—	2	3	no	—
11	C₂×C₈×C₂₉	D₄	1	6	yes	—
12	C₄⋊C₄×C₂₉	—	2	3	no	—
13	C₄⋊C₄×C₂₉	—	2	3	no	—
14	C₄²×C₂₉	C₂³	1	1	yes	characteristic
15	C₂³×C₂₉	—	4	1	no	—
16	Q₈×C₂₉	—	4	6	no	—
17	D₄×C₂₉	—	4	6	no	—
18	C₂×C₄×C₂₉	—	4	3	no	—
19	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
20	C₈×C₂₉	—	2	6	no	—
21	#1711	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₂₉	—	8	3	no	—
23	C₂²×C₂₉	#127	1	1	yes	characteristic
24	C₄×C₂₉	—	8	3	no	—
25	C₄×C₂₉	#135	1	6	yes	—
26	#487	C₂×C₂₉	1	3	yes	complemented
27	#486	C₂×C₂₉	1	3	yes	—
28	C₈²	C₂×C₂₉	1	1	yes	characteristic, complemented
29	C₂×C₂₉	—	16	1	no	—
30	C₂×C₂₉	#495	1	3	yes	—
31	C₄⋊Q₈	C₂²×C₂₉	1	3	yes	—
32	#127	C₂²×C₂₉	1	1	yes	characteristic
33	#103	—	2	6	no	—
34	#102	—	2	6	no	—
35	C₄×C₈	C₂²×C₂₉	1	3	yes	—
36	C₂₉	#1711	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×Q₈	—	2	3	no	—
38	C₂×D₄	—	2	3	no	—
39	C₂×C₈	D₄×C₂₉	1	6	yes	—
40	C₄⋊C₄	—	2	3	no	—
41	C₄⋊C₄	—	2	3	no	—
42	C₄²	C₂³×C₂₉	1	1	yes	characteristic
43	C₂³	—	4	1	no	—
44	Q₈	—	4	6	no	—
45	D₄	—	4	6	no	—
46	C₂×C₄	—	4	3	no	—
47	C₂×C₄	C₂×D₄×C₂₉	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	8	3	no	—
50	C₂²	C₂₉×#127	1	1	yes	characteristic
51	C₄	—	8	3	no	—
52	C₄	C₂₉×#135	1	6	yes	—
53	C₂	—	16	1	no	—
54	C₂	C₂₉×#495	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#487	C₂	semidirect
3. C₈²×C₂₉	C₂	semidirect
21. #1711	C₂₉	direct (N × H)
26. #487	C₂×C₂₉	semidirect
28. C₈²	C₂×C₂₉	semidirect
36. C₂₉	#1711	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#487	2
C₂₉×#486	2
C₈²×C₂₉	2
#1711	29

Subgroups — C29×#1711 #16815425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1711 #16815425