Subgroups — C₂₉×#7100 #20302000

Order 7424.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#1370	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×C₄⋊C₁₆	—	2	2	no	—
4	C₄×C₁₆×C₂₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₂₉	C₄	1	1	yes	characteristic
6	C₈²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₂₉	—	2	1	no	—
8	C₂×C₁₆×C₂₉	—	4	2	no	—
9	C₂×C₁₆×C₂₉	C₈	1	1	yes	characteristic
10	C₂×C₁₆×C₂₉	C₈	1	1	yes	characteristic
11	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
13	C₄×C₈×C₂₉	Q₈	1	1	yes	characteristic
14	C₂×C₈×C₂₉	—	2	1	no	—
15	C₂×C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈×C₂₉	M₁₆	1	1	yes	characteristic
17	C₂×C₈×C₂₉	D₈	1	1	yes	characteristic
18	C₂×C₈×C₂₉	Q₁₆	1	1	yes	characteristic
19	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
20	C₁₆×C₂₉	—	2	2	no	—
21	C₁₆×C₂₉	—	2	1	no	—
22	C₁₆×C₂₉	—	8	2	no	—
23	C₁₆×C₂₉	C₁₆	1	2	yes	complemented
24	#7100	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	#107	1	1	yes	characteristic
27	C₂×C₄×C₂₉	#108	1	1	yes	characteristic
28	C₈×C₂₉	—	2	2	no	—
29	C₈×C₂₉	—	2	1	no	—
30	C₈×C₂₉	—	2	1	no	—
31	C₈×C₂₉	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₂₉	M₃₂	1	1	yes	characteristic
33	C₈×C₂₉	D₁₆	1	1	yes	characteristic
34	C₈×C₂₉	Q₃₂	1	1	yes	characteristic
35	#1370	C₂×C₂₉	1	2	yes	—
36	C₈×C₁₆	C₂×C₂₉	1	1	yes	characteristic
37	C₂²×C₂₉	#335	1	1	yes	characteristic
38	C₄×C₂₉	—	2	1	no	—
39	C₄×C₂₉	C₄⋊C₁₆	1	1	yes	characteristic
40	C₄×C₂₉	#364	1	1	yes	characteristic
41	C₄×C₂₉	#366	1	1	yes	characteristic
42	C₄×C₂₉	#368	1	1	yes	characteristic
43	C₄⋊C₁₆	—	2	2	no	—
44	C₄×C₁₆	C₄×C₂₉	1	1	yes	characteristic
45	C₄×C₁₆	C₄×C₂₉	1	1	yes	characteristic
46	C₈²	C₂²×C₂₉	1	1	yes	characteristic
47	C₂×C₂₉	#1370	1	1	yes	characteristic
48	C₂×C₂₉	#1371	1	1	yes	characteristic
49	C₂×C₂₉	#1373	1	1	yes	characteristic
50	C₂×C₁₆	—	2	1	no	—
51	C₂×C₁₆	—	4	2	no	—
52	C₂×C₁₆	C₈×C₂₉	1	1	yes	characteristic
53	C₂×C₁₆	C₈×C₂₉	1	1	yes	characteristic
54	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
55	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
56	C₄×C₈	Q₈×C₂₉	1	1	yes	characteristic
57	C₂₉	#7100	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	C₂×C₈×C₂₉	1	1	yes	characteristic
60	C₂×C₈	M₁₆×C₂₉	1	1	yes	characteristic
61	C₂×C₈	D₈×C₂₉	1	1	yes	characteristic
62	C₂×C₈	Q₁₆×C₂₉	1	1	yes	characteristic
63	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
64	C₁₆	—	2	2	no	—
65	C₁₆	—	2	1	no	—
66	C₁₆	—	8	2	no	—
67	C₁₆	C₁₆×C₂₉	1	2	yes	complemented
68	C₂×C₄	C₂₉×C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₄	C₂₉×#107	1	1	yes	characteristic
70	C₂×C₄	C₂₉×#108	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₈	—	2	1	no	—
73	C₈	—	2	1	no	—
74	C₈	C₂×C₁₆×C₂₉	1	1	yes	characteristic
75	C₈	C₂₉×M₃₂	1	1	yes	characteristic
76	C₈	C₂₉×D₁₆	1	1	yes	characteristic
77	C₈	C₂₉×Q₃₂	1	1	yes	characteristic
78	C₂²	C₂₉×#335	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	C₂₉×C₄⋊C₁₆	1	1	yes	characteristic
81	C₄	C₂₉×#364	1	1	yes	characteristic
82	C₄	C₂₉×#366	1	1	yes	characteristic
83	C₄	C₂₉×#368	1	1	yes	characteristic
84	C₂	C₂₉×#1370	1	1	yes	characteristic
85	C₂	C₂₉×#1371	1	1	yes	characteristic
86	C₂	C₂₉×#1373	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₉	D₈
commutator	C₈	C₂×C₁₆×C₂₉
Frattini, cosocle	C₈²	C₂²×C₂₉
socle, prime radical	C₂²×C₂₉	#335
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ C₄×C₈×C₂₉ ◁ C₈²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
23. C₁₆×C₂₉	C₁₆	semidirect
24. #7100	C₂₉	direct (N × H)
57. C₂₉	#7100	direct (N × H)
67. C₁₆	C₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#1370	2
C₈×C₁₆×C₂₉	2
#7100	29

Subgroups — C29×#7100 #20302000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7100 #20302000