Subgroups — C₇₃×#7460 #32916864

Order 18688.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1371	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₇₃	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₇₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
6	#335×C₇₃	—	2	2	no	—
7	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₇₃	Q₈	1	1	yes	characteristic
9	C₄⋊C₈×C₇₃	—	4	2	no	—
10	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
11	C₃₂×C₇₃	—	2	1	no	—
12	C₃₂×C₇₃	C₈	1	2	yes	complemented
13	C₂×C₈×C₇₃	—	8	2	no	—
14	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₇₃	Q₁₆	1	1	yes	characteristic
16	C₄²×C₇₃	D₈	1	1	yes	characteristic
17	C₁₆×C₇₃	—	2	1	no	—
18	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₇₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₇₃	#107	1	1	yes	characteristic
21	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
22	C₂×C₄×C₇₃	Q₃₂	1	1	yes	characteristic
23	C₈×C₇₃	—	2	1	no	—
24	C₈×C₇₃	—	16	2	no	—
25	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₇₃	#108	1	1	yes	characteristic
27	C₂²×C₇₃	#366	1	1	yes	characteristic
28	C₄×C₇₃	—	2	1	no	—
29	C₄×C₇₃	#335	1	1	yes	characteristic
30	C₄×C₇₃	#368	1	1	yes	characteristic
31	C₄×C₇₃	D₃₂	1	1	yes	characteristic
32	C₄×C₇₃	Q₆₄	1	1	yes	characteristic
33	#7460	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂×C₇₃	#1371	1	1	yes	characteristic
35	C₂×C₇₃	#1423	1	1	yes	characteristic
36	C₂×C₇₃	#1425	1	1	yes	characteristic
37	C₄×C₃₂	C₂×C₇₃	1	1	yes	characteristic
38	#1371	C₂×C₇₃	1	2	yes	—
39	C₇₃	#7460	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃₂	C₄×C₇₃	1	1	yes	characteristic
41	C₂×C₃₂	C₄×C₇₃	1	1	yes	characteristic
42	C₄×C₁₆	C₂²×C₇₃	1	1	yes	characteristic
43	#335	—	2	2	no	—
44	C₂×C₁₆	C₂×C₄×C₇₃	1	1	yes	characteristic
45	C₂×C₁₆	Q₈×C₇₃	1	1	yes	characteristic
46	C₄⋊C₈	—	4	2	no	—
47	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
48	C₃₂	—	2	1	no	—
49	C₃₂	C₈×C₇₃	1	2	yes	complemented
50	C₂×C₈	—	8	2	no	—
51	C₂×C₈	C₄⋊C₄×C₇₃	1	1	yes	characteristic
52	C₂×C₈	Q₁₆×C₇₃	1	1	yes	characteristic
53	C₄²	D₈×C₇₃	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	C₂×C₈×C₇₃	1	1	yes	characteristic
56	C₁₆	M₁₆×C₇₃	1	1	yes	characteristic
57	C₂×C₄	#107×C₇₃	1	1	yes	characteristic
58	C₂×C₄	D₁₆×C₇₃	1	1	yes	characteristic
59	C₂×C₄	Q₃₂×C₇₃	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	—	16	2	no	—
62	C₈	C₄⋊C₈×C₇₃	1	1	yes	characteristic
63	C₈	#108×C₇₃	1	1	yes	characteristic
64	C₂²	#366×C₇₃	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	#335×C₇₃	1	1	yes	characteristic
67	C₄	#368×C₇₃	1	1	yes	characteristic
68	C₄	D₃₂×C₇₃	1	1	yes	characteristic
69	C₄	Q₆₄×C₇₃	1	1	yes	characteristic
70	C₂	C₇₃×#1371	1	1	yes	characteristic
71	C₂	C₇₃×#1423	1	1	yes	characteristic
72	C₂	C₇₃×#1425	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₃	D₁₆
commutator	C₁₆	C₂×C₈×C₇₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₇₃
socle, prime radical	C₂²×C₇₃	#366
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ C₄²×C₇₃ ◁ C₄×C₈×C₇₃ ◁ C₄×C₁₆×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₃₂×C₇₃	C₈	semidirect
33. #7460	C₇₃	direct (N × H)
39. C₇₃	#7460	direct (N × H)
49. C₃₂	C₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃₂×C₇₃	2
C₇₃×#1371	2
#7460	73

Subgroups — C73×#7460 #32916864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#7460 #32916864