Subgroups — C₇₃×#62624 #32972028

Order 18688.

2038 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3573	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3407	C₂	1	15	yes	maximal, complemented
3	C₂×#504×C₇₃	C₂	1	15	yes	maximal, complemented
4	#585×C₇₃	C₄	1	1	yes	characteristic
5	#568×C₇₃	C₄	1	15	yes	—
6	C₂×#131×C₇₃	C₂²	1	15	yes	—
7	#504×C₇₃	C₂²	1	20	yes	complemented
8	#504×C₇₃	C₂²	1	60	yes	complemented
9	C₂×M₃₂×C₇₃	C₂²	1	45	yes	complemented
10	C₂²×C₁₆×C₇₃	C₂²	1	15	yes	complemented
11	2₋¹⁺⁴×C₇₃	C₈	1	6	yes	—
12	H(5,𝔽₂)×C₇₃	C₈	1	10	yes	—
13	C₂×#41×C₇₃	C₂×C₄	1	15	yes	—
14	#131×C₇₃	C₂×C₄	1	60	yes	—
15	#131×C₇₃	C₂³	1	20	yes	—
16	C₂×M₁₆×C₇₃	C₂×C₄	1	45	yes	—
17	C₂²×C₈×C₇₃	C₂³	1	15	yes	—
18	M₃₂×C₇₃	C₂³	1	60	yes	—
19	C₂×C₁₆×C₇₃	C₂³	1	45	yes	—
20	C₂×C₁₆×C₇₃	C₂³	1	15	yes	—
21	#41×C₇₃	C₂×C₈	1	60	yes	—
22	#41×C₇₃	C₂²×C₄	1	20	yes	—
23	C₂×Q₈×C₇₃	C₂×C₈	1	15	yes	—
24	C₂×D₄×C₇₃	C₂×C₈	1	45	yes	—
25	C₂²×C₄×C₇₃	C₂²×C₄	1	15	yes	—
26	M₁₆×C₇₃	C₂²×C₄	1	60	yes	—
27	C₂×C₈×C₇₃	C₂²×C₄	1	45	yes	—
28	C₂×C₈×C₇₃	C₂⁴	1	15	yes	—
29	C₁₆×C₇₃	C₂⁴	1	15	yes	—
30	C₁₆×C₇₃	C₂⁴	1	1	yes	characteristic
31	C₂³×C₇₃	C₂²×C₈	1	15	yes	—
32	Q₈×C₇₃	C₂²×C₈	1	20	yes	—
33	D₄×C₇₃	C₂²×C₈	1	60	yes	—
34	C₂×C₄×C₇₃	C₂²×C₈	1	45	yes	—
35	C₂×C₄×C₇₃	C₂³×C₄	1	15	yes	—
36	C₈×C₇₃	C₂³×C₄	1	15	yes	—
37	C₈×C₇₃	C₂⁵	1	1	yes	characteristic
38	C₂²×C₇₃	—	4	15	no	—
39	C₂²×C₇₃	C₂³×C₈	1	15	yes	—
40	C₄×C₇₃	C₂³×C₈	1	15	yes	—
41	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
42	#62624	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₇₃	—	2	15	no	—
44	C₂×C₇₃	C₂⁴×C₈	1	1	yes	characteristic
45	#3573	C₂×C₇₃	1	1	yes	characteristic
46	#3407	C₂×C₇₃	1	15	yes	complemented
47	C₂×#504	C₂×C₇₃	1	15	yes	complemented
48	C₇₃	#62624	1	1	yes	characteristic, direct product factor, Sylow
49	#585	C₄×C₇₃	1	1	yes	characteristic
50	#568	C₄×C₇₃	1	15	yes	—
51	C₂×#131	C₂²×C₇₃	1	15	yes	—
52	#504	C₂²×C₇₃	1	20	yes	complemented
53	#504	C₂²×C₇₃	1	60	yes	complemented
54	C₂×M₃₂	C₂²×C₇₃	1	45	yes	complemented
55	C₂²×C₁₆	C₂²×C₇₃	1	15	yes	complemented
56	2₋¹⁺⁴	C₈×C₇₃	1	6	yes	—
57	H(5,𝔽₂)	C₈×C₇₃	1	10	yes	—
58	C₂×#41	C₂×C₄×C₇₃	1	15	yes	—
59	#131	C₂×C₄×C₇₃	1	60	yes	—
60	#131	C₂³×C₇₃	1	20	yes	—
61	C₂×M₁₆	C₂×C₄×C₇₃	1	45	yes	—
62	C₂²×C₈	C₂³×C₇₃	1	15	yes	—
63	M₃₂	C₂³×C₇₃	1	60	yes	—
64	C₂×C₁₆	C₂³×C₇₃	1	15	yes	—
65	C₂×C₁₆	C₂³×C₇₃	1	45	yes	—
66	#41	C₂×C₈×C₇₃	1	60	yes	—
67	#41	C₂²×C₄×C₇₃	1	20	yes	—
68	C₂×Q₈	C₂×C₈×C₇₃	1	15	yes	—
69	C₂×D₄	C₂×C₈×C₇₃	1	45	yes	—
70	C₂²×C₄	C₂²×C₄×C₇₃	1	15	yes	—
71	M₁₆	C₂²×C₄×C₇₃	1	60	yes	—
72	C₂×C₈	C₂²×C₄×C₇₃	1	45	yes	—
73	C₂×C₈	C₂⁴×C₇₃	1	15	yes	—
74	C₁₆	C₂⁴×C₇₃	1	15	yes	—
75	C₁₆	C₂⁴×C₇₃	1	1	yes	characteristic
76	C₂³	C₂²×C₈×C₇₃	1	15	yes	—
77	Q₈	C₂²×C₈×C₇₃	1	20	yes	—
78	D₄	C₂²×C₈×C₇₃	1	60	yes	—
79	C₂×C₄	C₂²×C₈×C₇₃	1	45	yes	—
80	C₂×C₄	C₂³×C₄×C₇₃	1	15	yes	—
81	C₈	C₂³×C₄×C₇₃	1	15	yes	—
82	C₈	C₂⁵×C₇₃	1	1	yes	characteristic
83	C₂²	—	4	15	no	—
84	C₂²	C₂³×C₈×C₇₃	1	15	yes	—
85	C₄	C₂³×C₈×C₇₃	1	15	yes	—
86	C₄	C₂⁴×C₄×C₇₃	1	1	yes	characteristic
87	C₂	—	2	15	no	—
88	C₂	C₂⁴×C₈×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆×C₇₃	C₂⁴
commutator	C₂	C₂⁴×C₈×C₇₃
Frattini, cosocle	C₈	C₂⁵×C₇₃
socle	C₂×C₇₃	C₂⁴×C₈
prime radical	#585×C₇₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#3407	C₂	semidirect
3. C₂×#504×C₇₃	C₂	semidirect
7. #504×C₇₃	C₂²	semidirect
8. #504×C₇₃	C₂²	semidirect
9. C₂×M₃₂×C₇₃	C₂²	semidirect
10. C₂²×C₁₆×C₇₃	C₂²	semidirect
42. #62624	C₇₃	direct (N × H)
46. #3407	C₂×C₇₃	semidirect
47. C₂×#504	C₂×C₇₃	semidirect
48. C₇₃	#62624	direct (N × H)
52. #504	C₂²×C₇₃	semidirect
53. #504	C₂²×C₇₃	semidirect
54. C₂×M₃₂	C₂²×C₇₃	semidirect
55. C₂²×C₁₆	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3573	2
C₇₃×#3407	2
C₂×#504×C₇₃	2
#62624	73

Subgroups — C73×#62624 #32972028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62624 #32972028