Subgroups — #32973895

Order 18688.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22607750	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₇₃	C₄	1	1	yes	characteristic
4	C₆₄×C₇₃	C₄	1	1	yes	characteristic
5	C₆₄×C₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
7	C₃₂×C₇₃	C₈	1	1	yes	characteristic
8	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₇₃	C₁₆	1	1	yes	characteristic
10	C₁₆×C₇₃	C₁₆	1	1	yes	characteristic
11	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₄×C₇₃	C₃₂	1	1	yes	characteristic
13	C₈×C₇₃	C₃₂	1	1	yes	characteristic
14	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
15	C₂²×C₇₃	C₆₄	1	1	yes	characteristic
16	C₄×C₇₃	C₆₄	1	1	yes	characteristic
17	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
18	M₂₅₆	—	73	1	no	maximal, Sylow
19	C₂×C₇₃	—	2	1	no	—
20	C₂×C₇₃	C₂×C₆₄	1	1	yes	characteristic
21	C₂×C₆₄	D₇₃	1	1	yes	characteristic
22	C₁₂₈	—	73	2	no	—
23	C₇₃	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	Dic₇₃	1	1	yes	characteristic
25	C₆₄	Dic₇₃	1	1	yes	characteristic
26	C₆₄	C₂×D₇₃	1	1	yes	characteristic
27	C₂×C₁₆	#10596831	1	1	yes	characteristic
28	C₃₂	#10596831	1	1	yes	characteristic
29	C₃₂	C₂×Dic₇₃	1	1	yes	characteristic
30	C₂×C₈	#11924003	1	1	yes	characteristic
31	C₁₆	#11924003	1	1	yes	characteristic
32	C₁₆	C₂×#10596831	1	1	yes	characteristic
33	C₂×C₄	#14556497	1	1	yes	characteristic
34	C₈	#14556497	1	1	yes	characteristic
35	C₈	C₂×#11924003	1	1	yes	characteristic
36	C₂²	#17988306	1	1	yes	characteristic
37	C₄	#17988306	1	1	yes	characteristic
38	C₄	C₂×#14556497	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	C₂×#17988306	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₆₄	C₂×D₇₃
commutator, socle	C₂×C₇₃	C₂×C₆₄
Fitting	C₂×C₆₄×C₇₃	C₂
prime radical	C₂²×C₇₃	C₆₄
cosocle	C₆₄×C₇₃	C₂²
hypercenter	C₂×C₆₄	D₇₃
hypocenter	C₇₃	M₂₅₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₆₄ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. #22607750	C₂	semidirect
23. C₇₃	M₂₅₆	semidirect

Maximal subgroups

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

subgroup	index
#22607750	2
C₂×C₆₄×C₇₃	2
M₂₅₆	73