Subgroups — #34001283

Order 18688.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625094	C₂	1	2	yes	maximal
2	C₆₄×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#17989515	—	2	2	no	—
4	C₃₂×D₇₃	C₂²	1	1	yes	characteristic
5	#17988306	C₄	1	1	yes	characteristic
6	C₆₄×C₇₃	C₄	1	1	yes	characteristic
7	#14556662	—	4	2	no	—
8	C₁₆×D₇₃	D₄	1	1	yes	characteristic
9	#14556497	Q₈	1	1	yes	characteristic
10	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
11	#11924038	—	8	2	no	—
12	C₈×D₇₃	D₈	1	1	yes	characteristic
13	#11924003	Q₁₆	1	1	yes	characteristic
14	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×D₇₃	D₁₆	1	1	yes	characteristic
16	#10596833	—	16	2	no	—
17	C₈×C₇₃	#107	1	1	yes	characteristic
18	#10596831	Q₃₂	1	1	yes	characteristic
19	C₂×D₇₃	Q₆₄	1	1	yes	characteristic
20	C₄×C₇₃	#366	1	1	yes	characteristic
21	Dic₇₃	D₃₂	1	1	yes	characteristic
22	#7547	—	73	1	no	maximal, Sylow
23	C₂×C₇₃	#1423	1	1	yes	characteristic
24	D₇₃	—	2	1	no	—
25	C₂×C₆₄	—	73	1	no	—
26	#1425	—	73	2	no	—
27	C₇₃	#7547	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	73	1	no	—
29	#368	—	146	2	no	—
30	C₆₄	—	73	1	no	—
31	C₆₄	#64408	1	1	yes	characteristic
32	C₂×C₁₆	—	73	1	no	—
33	#108	—	292	2	no	—
34	C₃₂	—	73	1	no	—
35	C₃₂	C₂×#64408	1	1	yes	characteristic
36	M₁₆	—	584	2	no	—
37	C₂×C₈	—	73	1	no	—
38	C₁₆	—	73	1	no	—
39	C₁₆	C₄⋊#64408	1	1	yes	characteristic
40	C₂×C₄	—	73	1	no	—
41	C₈	—	73	1	no	—
42	C₈	—	1168	2	no	—
43	C₈	#14556660	1	1	yes	characteristic
44	C₂²	—	73	1	no	—
45	C₄	—	73	1	no	—
46	C₄	#17989513	1	1	yes	characteristic
47	C₂	—	146	1	no	—
48	C₂	#22625092	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22625092
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₃₂	C₂×#64408
Fitting	C₆₄×C₇₃	C₄
socle	C₂×C₇₃	#1423
prime radical	C₂×D₇₃	Q₆₄
cosocle	C₃₂×D₇₃	C₂²
hypercenter	C₆₄	#64408
hypocenter	C₇₃	#7547
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄

Complements

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

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

Maximal subgroups

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

subgroup	index
#22625094	2
C₆₄×D₇₃	2
#7547	73