Subgroups — C₂₉×#7462 #20302362

Order 7424.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1373	C₂	1	2	yes	maximal
3	C₂×C₂₉×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₂₉×C₃₂	C₄	1	1	yes	characteristic
5	C₂₉×#364	—	2	2	no	—
6	C₄×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×M₃₂	—	4	2	no	—
8	C₂×C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₂₉	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
11	C₂₉×C₃₂	—	2	1	no	—
12	C₂₉×C₃₂	C₈	1	2	yes	—
13	C₂×C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	D₈	1	1	yes	characteristic
15	C₄²×C₂₉	Q₁₆	1	1	yes	characteristic
16	C₁₆×C₂₉	—	2	1	no	—
17	C₁₆×C₂₉	—	8	2	no	—
18	C₁₆×C₂₉	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₂₉	M₁₆	1	1	yes	characteristic
20	#7462	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	#107	1	1	yes	characteristic
23	C₈×C₂₉	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₂₉	#108	1	1	yes	characteristic
25	C₈×C₂₉	D₁₆	1	1	yes	characteristic
26	C₈×C₂₉	Q₃₂	1	1	yes	characteristic
27	C₄×C₃₂	C₂×C₂₉	1	1	yes	characteristic
28	#1373	C₂×C₂₉	1	2	yes	—
29	C₂²×C₂₉	#368	1	1	yes	characteristic
30	C₄×C₂₉	—	2	2	no	—
31	C₄×C₂₉	#335	1	1	yes	characteristic
32	C₄×C₂₉	#366	1	1	yes	characteristic
33	C₂×C₃₂	C₄×C₂₉	1	1	yes	characteristic
34	C₂×C₃₂	C₄×C₂₉	1	1	yes	characteristic
35	#364	—	2	2	no	—
36	C₄×C₁₆	C₂²×C₂₉	1	1	yes	characteristic
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	#1371	1	1	yes	characteristic
39	M₃₂	—	4	2	no	—
40	C₂×C₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
41	C₂×C₁₆	Q₈×C₂₉	1	1	yes	characteristic
42	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
43	C₃₂	—	2	1	no	—
44	C₃₂	C₈×C₂₉	1	2	yes	—
45	C₂₉	#7462	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
47	C₂×C₈	D₈×C₂₉	1	1	yes	characteristic
48	C₄²	Q₁₆×C₂₉	1	1	yes	characteristic
49	C₁₆	—	2	1	no	—
50	C₁₆	—	8	2	no	—
51	C₁₆	C₂×C₈×C₂₉	1	1	yes	characteristic
52	C₁₆	M₁₆×C₂₉	1	1	yes	characteristic
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	C₂₉×#107	1	1	yes	characteristic
55	C₈	C₂₉×C₄⋊C₈	1	1	yes	characteristic
56	C₈	C₂₉×#108	1	1	yes	characteristic
57	C₈	C₂₉×D₁₆	1	1	yes	characteristic
58	C₈	C₂₉×Q₃₂	1	1	yes	characteristic
59	C₂²	C₂₉×#368	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	C₂₉×#335	1	1	yes	characteristic
62	C₄	C₂₉×#366	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	C₂₉×#1371	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₉	D₁₆
commutator	C₁₆	C₂×C₈×C₂₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₂₉
socle	C₂×C₂₉	#1371
prime radical	C₂²×C₂₉	#368
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₄×C₈×C₂₉ ◁ C₄×C₁₆×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
20. #7462	C₂₉	direct (N × H)
45. C₂₉	#7462	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂₉×C₃₂	2
C₂₉×#1373	2
#7462	29

Subgroups — C29×#7462 #20302362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7462 #20302362