Subgroups — C₂₉×#14692 #20309592

Order 7424.

2286 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#384	C₂	1	14	yes	maximal
2	C₂×C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊C₄×C₂₉	C₂²	1	28	yes	—
4	C₂²×C₄²×C₂₉	C₂²	1	7	yes	—
5	C₂₉×#384	—	2	56	no	—
6	C₄³×C₂₉	C₄	1	8	yes	complemented
7	C₂³×C₄×C₂₉	C₂³	1	8	yes	—
8	C₂³×C₄×C₂₉	C₂³	1	7	yes	—
9	C₂×C₄⋊C₄×C₂₉	—	2	168	no	—
10	C₂×C₄²×C₂₉	C₂×C₄	1	28	yes	—
11	C₂×C₄²×C₂₉	D₄	1	28	yes	—
12	C₂×C₄²×C₂₉	Q₈	1	28	yes	—
13	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	—	2	56	no	—
15	C₂²×C₄×C₂₉	C₂²×C₄	1	14	yes	—
16	C₂²×C₄×C₂₉	C₂×D₄	1	42	yes	—
17	C₂²×C₄×C₂₉	C₂×Q₈	1	42	yes	—
18	C₄⋊C₄×C₂₉	—	4	112	no	—
19	C₄²×C₂₉	C₄⋊C₄	1	112	yes	complemented
20	#14692	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
22	C₂³×C₂₉	C₂²×D₄	1	7	yes	—
23	C₂³×C₂₉	C₂²×Q₈	1	7	yes	—
24	C₂×C₄×C₂₉	—	4	56	no	—
25	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	84	yes	—
26	C₂×C₄×C₂₉	#127	1	28	yes	—
27	C₂×C₄×C₂₉	C₄⋊Q₈	1	84	yes	—
28	C₂×#384	C₂×C₂₉	1	14	yes	—
29	C₂×C₄³	C₂×C₂₉	1	1	yes	characteristic
30	C₂²×C₂₉	C₂²×C₄⋊C₄	1	7	yes	—
31	C₂²×C₂₉	C₂×#127	1	7	yes	—
32	C₂²×C₂₉	C₂×C₄⋊Q₈	1	21	yes	—
33	C₄×C₂₉	—	8	8	no	—
34	C₄×C₂₉	#384	1	56	yes	complemented
35	C₂²×C₄⋊C₄	C₂²×C₂₉	1	28	yes	—
36	C₂²×C₄²	C₂²×C₂₉	1	7	yes	—
37	#384	—	2	56	no	—
38	C₄³	C₄×C₂₉	1	8	yes	complemented
39	C₂×C₂₉	C₂×#384	1	7	yes	—
40	C₂×C₂₉	#2867	1	1	yes	characteristic
41	C₂×C₂₉	#2868	1	7	yes	—
42	C₂³×C₄	C₂³×C₂₉	1	8	yes	—
43	C₂³×C₄	C₂³×C₂₉	1	7	yes	—
44	C₂×C₄⋊C₄	—	2	168	no	—
45	C₂×C₄²	C₂×C₄×C₂₉	1	28	yes	—
46	C₂×C₄²	D₄×C₂₉	1	28	yes	—
47	C₂×C₄²	Q₈×C₂₉	1	28	yes	—
48	C₂₉	#14692	1	1	yes	characteristic, direct product factor, Sylow
49	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
50	C₂²×C₄	—	2	56	no	—
51	C₂²×C₄	C₂²×C₄×C₂₉	1	14	yes	—
52	C₂²×C₄	C₂×D₄×C₂₉	1	42	yes	—
53	C₂²×C₄	C₂×Q₈×C₂₉	1	42	yes	—
54	C₄⋊C₄	—	4	112	no	—
55	C₄²	C₄⋊C₄×C₂₉	1	112	yes	complemented
56	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
57	C₂³	C₂²×D₄×C₂₉	1	7	yes	—
58	C₂³	C₂²×Q₈×C₂₉	1	7	yes	—
59	C₂×C₄	—	4	56	no	—
60	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	84	yes	—
61	C₂×C₄	C₂₉×#127	1	28	yes	—
62	C₂×C₄	C₂₉×C₄⋊Q₈	1	84	yes	—
63	C₂²	C₂²×C₄⋊C₄×C₂₉	1	7	yes	—
64	C₂²	C₂×C₂₉×#127	1	7	yes	—
65	C₂²	C₂×C₂₉×C₄⋊Q₈	1	21	yes	—
66	C₄	—	8	8	no	—
67	C₄	C₂₉×#384	1	56	yes	complemented
68	C₂	C₂×C₂₉×#384	1	7	yes	—
69	C₂	C₂₉×#2867	1	1	yes	characteristic
70	C₂	C₂₉×#2868	1	7	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₉
Frattini, cosocle	C₂⁴	C₂⁴×C₂₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄³×C₂₉	C₄	semidirect
19. C₄²×C₂₉	C₄⋊C₄	semidirect
20. #14692	C₂₉	direct (N × H)
34. C₄×C₂₉	#384	semidirect
38. C₄³	C₄×C₂₉	semidirect
48. C₂₉	#14692	direct (N × H)
55. C₄²	C₄⋊C₄×C₂₉	semidirect
67. C₄	C₂₉×#384	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#384	2
C₂×C₄³×C₂₉	2
#14692	29

Subgroups — C29×#14692 #20309592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#14692 #20309592