Subgroups — #32973887

Order 18688.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988306	C₂	1	1	yes	maximal, characteristic
2	#22608135	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1425	C₂	1	1	yes	maximal, characteristic
4	#17988417	—	2	1	no	—
5	#17988306	C₄	1	2	yes	—
6	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
7	#368×C₇₃	—	2	1	no	—
8	#14556527	—	4	1	no	—
9	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
10	#108×C₇₃	—	4	1	no	—
11	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₇₃	Q₈	1	1	yes	characteristic
13	#11924012	—	8	1	no	—
14	M₁₆×C₇₃	—	8	1	no	—
15	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
16	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₇₃	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
19	C₈×C₇₃	—	16	1	no	—
20	C₈×C₇₃	#107	1	1	yes	characteristic
21	C₈×C₇₃	Q₃₂	1	1	yes	characteristic
22	#10596831	—	16	1	no	—
23	C₂²×C₇₃	Q₆₄	1	1	yes	characteristic
24	C₄×C₇₃	#366	1	1	yes	characteristic
25	C₄×C₇₃	D₃₂	1	1	yes	characteristic
26	#7547	—	73	1	no	maximal, Sylow
27	C₂×C₇₃	—	2	1	no	—
28	C₂×C₇₃	#1423	1	1	yes	characteristic
29	C₂×C₆₄	—	73	1	no	—
30	#1425	—	73	1	no	—
31	#1425	D₇₃	1	1	yes	characteristic
32	C₇₃	#7547	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
34	#368	—	2	1	no	—
35	#368	—	146	1	no	—
36	C₆₄	—	73	2	no	—
37	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	292	1	no	—
40	C₃₂	Dic₁₄₆	1	1	yes	characteristic
41	C₃₂	C₄×D₇₃	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	584	1	no	—
44	C₂×C₈	#11924013	1	1	yes	characteristic
45	C₁₆	#11924007	1	1	yes	characteristic
46	C₁₆	#11924018	1	1	yes	characteristic
47	C₂×C₄	#14556532	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	1168	1	no	—
50	C₈	#14556524	1	1	yes	characteristic
51	C₈	#14556537	1	1	yes	characteristic
52	C₂²	#17988427	1	1	yes	characteristic
53	C₄	#17988412	1	1	yes	characteristic
54	C₄	#17988422	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#22608130	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17988422
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting	C₇₃×#1425	C₂
socle	C₂×C₇₃	#1423
prime radical	C₂²×C₇₃	Q₆₄
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	#1425	D₇₃
hypocenter	C₇₃	#7547
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
32. C₇₃	#7547	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988306	2
#22608135	2
C₇₃×#1425	2
#7547	73